https://wiki.swarma.org/api.php?action=feedcontributions&user=%E8%B6%A3%E6%9C%A8%E6%9C%A8&feedformat=atom集智百科 - 伊辛模型 - 用户贡献 [zh-cn]2021-10-19T15:24:03Z用户贡献MediaWiki 1.35.0https://wiki.swarma.org/index.php?title=%E9%9B%86%E6%99%BA%E7%99%BE%E7%A7%91%E7%BF%BB%E8%AF%91%E5%9B%A2%E9%98%9F%E5%B7%A5%E4%BD%9C%E6%8C%87%E5%8D%97&diff=14878集智百科翻译团队工作指南2020-10-09T11:48:31Z<p>趣木木：/* 提交积分审核 */</p>
<hr />
<div><br />
==新手须知==<br />
===创建账户===<br />
确定自己是否有集智百科页面的用户账号，若没有，点击页面右上角“创建账户”进行创建，并可以补充完善好自己的个人主页。<br />
<br />
===领取任务===<br />
====领取渠道一 直接选择已有的词条任务====<br />
点击石墨文档中的'''[https://shimo.im/sheets/VH8pVcJtDVHqyDCJ/hl9sY 词条生产总表]''',在对应日期阶段的任务表中选择自己感兴趣的词条，在'''“词条领取人”'''一栏中填上自己的用户名，并且根据自身情况估计完成日期，填写在'''“初次完成时间”'''中，关注词条的'''“需求点”'''，在翻译过程中按照要求进行翻译。<br />
<br />
注意：一般词条生产最晚应在一周内完成，根据所设积分可以大体推算完成日期。如积分在20以下，完成时间往后退一至两天，积分为20-50区间内，完成时间往后退三至四天，积分为50以上，原则上在一周内完成。有特殊情况则私聊[[用户:趣木木|趣木木]]。<br />
<br />
'''提交完词条任务后，即时就在[https://shimo.im/sheets/VH8pVcJtDVHqyDCJ/hl9sY 词条生产总表]领取下次的词条。<br />
'''<br />
====领取渠道二 选择自己感兴趣的词条作为自己的词条任务====<br />
点击石墨文档中的[https://shimo.im/sheets/VxGcDcJ6vJtQdkgQ/q1eR9 词条生产表]中的“机器已搬运”子表，选择自己感兴趣的词条并修改“是否翻译”一栏（将否改为是）。此外，为确保没有重复工作，在[https://wiki.swarma.org/index.php?title=%E9%82%93%E5%B7%B4%E6%95%B0#Criticism_.E8.AF.84.E8.AE.BA 集智百科新版],[http://wiki.swarma.net/index.php/%E8%AF%BA%E4%BC%AF%E7%89%B9%C2%B7%E7%BB%B4%E7%BA%B3_Norbert_Wiener#.E7.9B.B8.E5.85.B3.E8.91.97.E4.BD.9C 集智百科旧版]搜索对应词条，查看编辑历史，确保其没有进行过翻译。汇总感兴趣的词条，填入到''[https://shimo.im/sheets/VH8pVcJtDVHqyDCJ/hl9sY 词条生产总表]'''对应日期阶段的任务表中，填写完成时间、领取人。并联系[[用户:趣木木|趣木木]]填写对应积分。<br />
<br />
===明确生产形式===<br />
点击所领取词条下对应的'''“集智百科链接地址”'''，首先查看页面是否存在英文文本缺失的问题，若存在，点击对应的英文wiki地址进行补充。对于公式显示错误或遇到其余页面显示问题，请私聊[[用户:趣木木|趣木木]]进行反映。页面形式为两段重复的英文文本及由彩云小译初步翻译出来的中文文本。译者点击右上角的“登录”，登录上自己的账号，在编辑页面的最上端写上“本词条由[[用户名]]初步翻译”。<br />
<br />
以[[LFR算法]]为例，可看到以下界面，只需查看第二次出现的英文原文，对比中文进行翻译。点击“编辑”，即可编辑页面，其具体操作为：<br />
<br />
[[File:编辑操作.png|1000px]]<br />
<br />
<br />
<br />
<br />
'''根据蓝色框内的英文，修改重译红色框中的中文。借助维基百科的英文原文进行翻译，利用翻译工具有彩云小译、网易有道翻译等翻译软件，译者需要自行翻译，将中文换为符合习惯的表达，多方查询相关释义，及时反馈，以确保专业性。'''<br />
<br />
[[File:翻译对比.png|1000px]]<br />
对于页面的基本操作可查看[https://wiki.swarma.org/index.php?title=%E7%BC%96%E8%BE%91%E8%A7%84%E8%8C%83 编辑入门]<br />
<br />
===知识储备===<br />
<br />
可从集智学园，集智斑图以及公众号搜索相关资料，查看中文维基百科中相对应的词条，对词条内容有一个初步的认识和了解；将查阅到的资料、课程相关链接放到编者推荐、相关链接的内容中；可从[https://campus.swarma.org/ 集智学园]查看相关课程资源、在[https://swarma.org/ 集智俱乐部]中的集智斑图获取学习路径，从'''集智微信公众号： 集智俱乐部'''查看相关科普文章和学习资源。<br />
<br />
===明确生产职责===<br />
译者需将英文wiki的原文通畅且较为准确、完整、专业的人工翻译出来，符合中文的语言表达，借助机器翻译但不完全是机器翻译。<br />
===达到翻译过程中的生产要求===<br />
====规范性====<br />
<br />
*专业名词格式<br />
译者通过英文原文中含有链接的英文、小标题对应的英文确定哪些为专业名词。在确定过程中注意人名、机构、与词条本身的专业领域关系不大的名词不在考虑范围内，通过语法[[File:标橙语法.png|300px]]'''<font color="#ff8000"> 专业名词</font>'''即可对专业名词标橙。且将专业名词的格式设为“中文+英文”（注：不加括号,英文首字母均大写），示例:[[File:专业名词格式.png|200px]]<br />
*文本格式<br />
1、中文文本用中文对应括号（） 英文数学文本用英文对应括号()<br><br />
<br />
2、人名译名缩写大写 如j.a 实际上应为J.A<br><br />
<br />
3、排除多余的句点"。。"→"。"<br><br />
<br />
4、中文文本用“。”而不是“.” <br><br />
<br />
5、变量采用斜体 ''N''<br><br />
<br />
<br />
*图片的图注翻译格式<br />
图注翻译格式为：【图1：英文原文＋翻译内容】<br />
<br />
*文本统一<br />
注意全文一致同一术语释义、同一人名释义（与集智俱乐部公众号一致）<br />
<br />
*利用讨论标注出省略翻译、意译的句子<br />
利用讨论语法[[File:讨论.png|100px]]添加讨论<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）该句省译<br />
<br />
*具体年份不宜省略翻译，如"2012年"不可只写"12年"<br />
<br />
====完整性====<br />
避免存在漏译的情况，特别注意图注、“see also”部分、章节名的翻译完整。<br />
<br />
====专业性====<br />
*词条标题核实<br />
如果对词条标题的意思有异议，可以私聊[[用户:趣木木|趣木木]]进行反映。核实之后，会设置重定向。<br />
*专业名词查询释义<br />
对于筛选出来的专业名词请在[https://campus.swarma.org/translation/ 翻译词库]中进行查询，不论是否查询得到，均需将专业名词标橙。对于查询到的释义，采用该专业名词释义；对于未查询到的释义，点击“新增翻译词”，补充上未查询到的英文，中文填为“待补充”。其具体操作如下，操作完毕即有下图中蓝色框内的形式。<br />
[[File:词库新增.png|1000px]]<br />
此外，还可在[http://dict.cnki.net/dict_result.aspx cnki翻译助手]里面初步检索专业名词，选取引用量最高的释义，待后续专家审校进行反馈纠正释义后，再将纠正的准确释义添加在[https://campus.swarma.org/translation/ 翻译词库]中 <br />
* 疑难句标绿<br />
对于自己翻译不清楚、存疑的疑难句，采用语法[[File:段落标绿.png|250px]]将'''<font color="#32CD32">疑难句</font>'''进行标绿，且在后面附加上疑难句所对应的英文。<br />
<br />
====通顺性====<br />
通读全文一至两遍，保证全文的语句通顺，符合语言表达，且释义统一。<br />
<br />
====进阶需求（不做要求）====<br />
可在页面中加一个模块：专家对于该术语/概念的一些描述（从书籍资源中补充概念）<br />
<br />
<br />
===复查词条===<br />
至少通读一至两遍译文，按照[https://shimo.im/docs/pX8Pgy66gDjG9WCR 自审清单]进行自审，寻找是否有语序、逻辑不通的地方，前后表述并不一致的地方，以及同一单词尽量用同一释义；注意检查相关的术语加粗，变量斜体，公式是否显示正常，图片图注序号是否正确等格式问题；在确保自己已达到上述的生产要求后，递交给负责人[[用户:趣木木|趣木木]]，负责人进行通读，检查，反馈，译者进行修改。<br />
<br />
===复修改词条===<br />
在规定时间内，负责人[[用户:趣木木|趣木木]]提交给审校，审校会添加讨论以及反馈，译者查看进行复核与复修改。'''（注：若被审校打回重译，所得积分减半）'''<br />
===提交积分审核===<br />
完成上述工作后，向负责人[[用户:趣木木|趣木木]]发送以下信息，以[[经济复杂性指数]]为例：<br />
<br />
词条名：[[经济复杂性指数]]<br />
词条领取人：[[用户:趣木木|趣木木]]<br />
词条对应链接：https://wiki.swarma.org/index.php?title=%E7%BB%8F%E6%B5%8E%E5%A4%8D%E6%9D%82%E6%80%A7%E6%8C%87%E6%95%B0_Economic_Complexity_Index<br />
词条对应积分：30<br />
词条初次完成时间:2020.07.09(这里指提交给负责人审核的日期）<br />
是否领取下一个词条：是/否<br />
是否按照自审清单自审并通读完一遍:是/否<br />
<br />
负责人审核，确定词条达到要求后，记录积分。<br />
<br />
==新手提升==<br />
===与审校部门联合进行相关培训===<br />
接受一些定期对译者的培训，收集译者在翻译过程中存在的问题，进行分享解析；分享翻译时的一些技巧，以提高翻译能力。<br />
===入门资源推荐===<br />
<br />
1.张江复杂性思维课程 （集智学园）<br><br />
<br />
2.《复杂》梅拉妮·米歇尔，网上有视频课程（喜马拉雅APP）[https://www.complexityexplorer.org/courses/104-introduction-to-complexity 《复杂》]<br><br />
<br />
3.教材《网络、群体与市场》，网上有[http://www.chinesemooc.org/mooc/4406 视频课程] <br><br />
<br />
4.郝柏林：圣菲研究所与复杂性研究<br><br />
<br />
5.复杂性科学、网络科学、计算社会科学研究机构推介（北美篇）<br><br />
<br />
6.新英格兰复杂系统研究所长文综述：复杂系统科学及其应用<br><br />
<br />
7.新英格兰复杂系统研究所长文综述：复杂系统科学及其应用，集智斑图网站负责人如意整理的[https://pattern.swarma.org/path?id=22 路径1] 、[https://pattern.swarma.org/path?id=30 路径2] 、 [https://pattern.swarma.org/path?id=32" 路径3]<br />
<br />
8.[https://pattern.swarma.org/path?id=68 图神经网络、网络科学、系统科学综合交叉入门学习路径]</div>趣木木https://wiki.swarma.org/index.php?title=%E7%BA%A7%E8%81%94%E5%A4%B1%E6%95%88&diff=14736级联失效2020-10-04T07:40:48Z<p>趣木木：</p>
<hr />
<div>本词条由11初步翻译<br />
<br />
{{short description|System of interconnected parts in which the failure of one or few parts can trigger the failure of others}}<br />
<br />
[[Image:Networkfailure.gif|thumb|right|An animation demonstrating how a single failure may result in other failures throughout a network.]]<br />
<br />
[[Image:Networkfailure.gif|thumb|right|演示单个故障如何导致整个网络中其他故障的动画]]<br />
<br />
An animation demonstrating how a single failure may result in other failures throughout a network.<br />
<br />
演示单个故障如何导致整个网络中其他故障的动画。<br />
<br />
A cascading failure is a process in a system of [[interconnection|interconnected]] parts in which the failure of one or few parts can trigger the failure of other parts and so on. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, transportation systems, organisms, the human body, and ecosystems.<br />
<br />
A cascading failure is a process in a system of interconnected parts in which the failure of one or few parts can trigger the failure of other parts and so on. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, transportation systems, organisms, the human body, and ecosystems.<br />
<br />
'''<font color="#ff8000"> 级联故障 Cascading Failure</font>'''是一个相互连接的部件系统中的一个或几个部件的故障可以引发其他部件的故障等过程。这种故障可能发生在许多类型的系统中，包括电力输送、计算机网络、金融、交通系统、微生物、人体和生态系统。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“'''<font color="#ff8000"> 级联故障 Cascading Failure</font>'''是一个相互连接的部件系统中的一个或几个部件的故障可以引发其他部件的故障等过程”有点不太顺<br />
<br />
Cascading failures may occur when one part of the system fails. When this happens, other parts must then compensate for the failed component. This in turn overloads these nodes, causing them to fail as well, prompting additional nodes to fail one after another.<br />
<br />
Cascading failures may occur when one part of the system fails. When this happens, other parts must then compensate for the failed component. This in turn overloads these nodes, causing them to fail as well, prompting additional nodes to fail one after another.<br />
<br />
当系统的一部分发生故障时，可能会发生级联故障。当这种情况发生时，其他部分必须对发生故障的部分进行补偿，这反过来又使这些节点超载，导致它们也发生故障，促使更多的节点相继发生故障。<br />
<br />
<br />
<br />
== In power transmission ==<br />
在电力输送中<br />
<br />
<br />
<br />
Cascading failure is common in [[power grid]]s when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. Those nearby elements are then pushed beyond their capacity so they become overloaded and shift their load onto other elements. Cascading failure is a common effect seen in [[high voltage]] systems, where a [[single point of failure]] (SPF) on a fully loaded or slightly overloaded system results in a sudden spike across all nodes of the system. This surge current can induce the already overloaded nodes into failure, setting off more overloads and thereby taking down the entire system in a very short time.<br />
<br />
Cascading failure is common in power grids when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. Those nearby elements are then pushed beyond their capacity so they become overloaded and shift their load onto other elements. Cascading failure is a common effect seen in high voltage systems, where a single point of failure (SPF) on a fully loaded or slightly overloaded system results in a sudden spike across all nodes of the system. This surge current can induce the already overloaded nodes into failure, setting off more overloads and thereby taking down the entire system in a very short time.<br />
<br />
级联故障在电网中很常见，当其中一个元件(完全或部分)发生故障并将其负荷转移到系统中附近的元件时，就会推动那些附近的元件超出其容量，从而过载，并将其负荷转移到其他元件上。级联故障在高压系统中也很常见，在一个满载或轻度过载的系统中，一个'''<font color="#ff8000"> 单点故障 Single Point of Failure (SPF)</font>'''会导致系统所有节点突然出现尖峰。这种'''<font color="#ff8000"> 浪涌电流 <br />
Surge Current</font>'''可能会导致已经超载的节点发生故障，引发更多过载，从而在很短的时间内使整个系统瘫痪。<br />
<br />
<br />
<br />
This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. For example, under certain conditions a large power grid can collapse after the failure of a single transformer.<br />
<br />
This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. For example, under certain conditions a large power grid can collapse after the failure of a single transformer.<br />
<br />
这个故障过程就像池塘上的涟漪一样，在系统的各个元件中层层叠加，直到系统中的所有元件都受到损害和/或系统在功能上与负载源断开。例如，在某些情况下，一个大型电网可能因为单个变压器的故障而崩溃。<br />
<br />
<br />
<br />
Monitoring the operation of a system, in [[real-time computing|real-time]], and judicious disconnection of parts can help stop a cascade. Another common technique is to calculate a safety margin for the system by computer simulation of possible failures, to establish safe operating levels below which none of the calculated scenarios is predicted to cause cascading failure, and to identify the parts of the network which are most likely to cause cascading failures.<ref name="chao">{{cite arXiv |last1=Zhai |first1=Chao |title=Modeling and Identification of Worst-Case Cascading Failures in Power Systems |eprint=1703.05232 |class=cs.SY |year=2017}}</ref><br />
<br />
Monitoring the operation of a system, in real-time, and judicious disconnection of parts can help stop a cascade. Another common technique is to calculate a safety margin for the system by computer simulation of possible failures, to establish safe operating levels below which none of the calculated scenarios is predicted to cause cascading failure, and to identify the parts of the network which are most likely to cause cascading failures.<br />
<br />
实时监测系统的运行情况，并明智地断开部件的连接，有助于阻止级联。 另一种常见的技术是通过计算机模拟可能发生的故障来计算系统的安全边际，确定安全运行水平，在此水平之下，预计计算出的任何一种情况都不会引起级联故障，并确定网络中最有可能引起级联故障的部分。<br />
<br />
<br />
<br />
One of the primary problems with preventing electrical grid failures is that the speed of the control signal is no faster than the speed of the propagating power overload, i.e. since both the control signal and the electrical power are moving at the same speed, it is not possible to isolate the outage by sending a warning ahead to isolate the element.<br />
<br />
One of the primary problems with preventing electrical grid failures is that the speed of the control signal is no faster than the speed of the propagating power overload, i.e. since both the control signal and the electrical power are moving at the same speed, it is not possible to isolate the outage by sending a warning ahead to isolate the element.<br />
<br />
防止电网故障的主要问题之一是，控制信号的速度不快于传播功率过载的速度，即由于控制信号和电力都以同样的速度运动，所以无法通过提前发出警告来隔离元件从而隔离停电。<br />
<br />
<br />
<br />
The question if power grid failures are correlated have been studied in Daqing Li et al.<ref>{{Cite journal|last=Daqing|first=Li|last2=Yinan|first2=Jiang|last3=Rui|first3=Kang|last4=Havlin|first4=Shlomo|date=2014-06-20|title=Spatial correlation analysis of cascading failures: Congestions and Blackouts|journal=Scientific Reports|language=En|volume=4|issue=1|pages=5381|doi=10.1038/srep05381|pmid=24946927|pmc=4064325|issn=2045-2322|bibcode=2014NatSR...4E5381D}}</ref> as well as by Paul DH Hines et al.<ref>{{Cite journal|last=Hines|first=Paul D. H.|last2=Dobson|first2=Ian|last3=Rezaei|first3=Pooya|date=2016|title=Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology|arxiv=1508.01775|journal=IEEE Transactions on Power Systems|pages=1|doi=10.1109/TPWRS.2016.2578259|issn=0885-8950}}</ref><br />
<br />
The question if power grid failures are correlated have been studied in Daqing Li et al. as well as by Paul DH Hines et al.<br />
<br />
电网故障是否具有相关性的问题，李大庆等人以及Paul DH Hines等人都有研究。<br />
<br />
<br />
=== Examples ===<br />
案例<br />
<br />
Cascading failure caused the following [[power outage]]s:<br />
<br />
Cascading failure caused the following power outages:<br />
<br />
级联故障曾导致以下停电:<br />
<br />
* [[Northeast blackout of 1965|Blackout in Northeast America in 1965]]<br />
* [[1965年东北大停电|1965年美国东北大停电]]<br />
<br />
* [[1999 Southern Brazil blackout|Blackout in Southern Brazil in 1999]]<br />
* [[1999年巴西南部停电|1999年巴西南部停电]]<br />
<br />
* [[Northeast blackout of 2003|Blackout in Northeast America in 2003]]<br />
* [[2003年东北大停电|2003年美国东北大停电]]<br />
<br />
* [[2003 Italy blackout|Blackout in Italy in 2003]]<br />
* [[2003年意大利停电|2003年意大利停电]]<br />
<br />
* [[2003 London blackout|Blackout in London in 2003]]<br />
* [[2003年伦敦大停电|2003年伦敦大停电]]<br />
<br />
* [[2006 European blackout|European Blackout in 2006]]<br />
* [[2006年欧洲停电|2006年欧洲停电]]<br />
<br />
* [[2012 northern India power grid failure|Blackout in Northern India in 2012]]<br />
* [[2012年印度北部电网故障|2012年印度北部停电]]<br />
<br />
* [[2016 South Australian blackout|Blackout in South Australia in 2016]]<br />
* [[2016年南澳停电|2016年南澳停电]]<br />
<br />
* [[2019 Argentina, Paraguay and Uruguay blackout|Blackout in southeast South America in 2019]]<br />
* [[2019年阿根廷、巴拉圭和乌拉圭停电|2019年南美洲东南部停电]]<br />
<br />
<br />
<br />
== In computer networks ==<br />
在计算机网络中<br />
<br />
<br />
<br />
<br />
Cascading failures can also occur in [[computer network]]s (such as the [[Internet]]) in which [[Network traffic control|network traffic]] is severely impaired or halted to or between larger sections of the network, caused by failing or disconnected hardware or software. In this context, the cascading failure is known by the term '''cascade failure'''. A cascade failure can affect large groups of people and systems.<br />
<br />
Cascading failures can also occur in computer networks (such as the Internet) in which network traffic is severely impaired or halted to or between larger sections of the network, caused by failing or disconnected hardware or software. In this context, the cascading failure is known by the term cascade failure. A cascade failure can affect large groups of people and systems.<br />
<br />
级联故障也可能发生在计算机网络(如因特网)中，由于硬件或软件的故障或断开，导致网络中较大部分的网络通信严重受损或停止。在这种情况下，级联故障被称为术语级联故障。级联故障会影响到大批人员和系统。<br />
<br />
<br />
<br />
The cause of a cascade failure is usually the overloading of a single, crucial [[Router (computing)|router]] or node, which causes the node to go down, even briefly. It can also be caused by taking a node down for maintenance or upgrades. In either case, traffic is [[routing|routed]] to or through another (alternative) path. This alternative path, as a result, becomes overloaded, causing it to go down, and so on. It will also affect systems which depend on the node for regular operation.<br />
<br />
The cause of a cascade failure is usually the overloading of a single, crucial router or node, which causes the node to go down, even briefly. It can also be caused by taking a node down for maintenance or upgrades. In either case, traffic is routed to or through another (alternative) path. This alternative path, as a result, becomes overloaded, causing it to go down, and so on. It will also affect systems which depend on the node for regular operation.<br />
<br />
级联故障的原因通常是一个单个关键的路由器或节点的超载，导致节点宕机或短暂地宕机。它也可能是由于为了维护或升级而关闭一个节点引起的。在这两种情况下，流量都被路由到或通过另一条(替代)路径。结果，这条替代路径变得过载，导致它宕机，等等。它还会影响依赖该节点正常运行的系统。<br />
<br />
<br />
<br />
=== Symptoms ===<br />
症状<br />
<br />
<br />
<br />
The symptoms of a cascade failure include: [[packet loss]] and high network [[lag|latency]], not just to single systems, but to whole sections of a network or the internet. The high latency and packet loss is caused by the nodes that fail to operate due to [[congestion collapse]], which causes them to still be present in the network but without much or any useful communication going through them. As a result, routes can still be considered valid, without them actually providing communication.<br />
<br />
The symptoms of a cascade failure include: packet loss and high network latency, not just to single systems, but to whole sections of a network or the internet. The high latency and packet loss is caused by the nodes that fail to operate due to congestion collapse, which causes them to still be present in the network but without much or any useful communication going through them. As a result, routes can still be considered valid, without them actually providing communication.<br />
<br />
级联故障的症状包括: 数据包丢失和高网络延迟，不仅仅是对单个系统，而是对整个网络或互联网部分。高延迟和数据包丢失是由于网络拥塞崩溃导致节点无法正常运行，这使得它们仍然存在于网络中，但是没有太多或任何有用的通信通过它们。因此，路由仍然可被认为是有效的，而实际上它们并没有提供通信。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“级联故障的症状” 中的症状是不是可以思考换一下词语 印象中症状一般形容人 换成“表现”或其他是否更好<br />
<br />
If enough routes go down because of a cascade failure, a complete section of the network or internet can become unreachable. Although undesired, this can help speed up the recovery from this failure as connections will time out, and other nodes will give up trying to establish connections to the section(s) that have become cut off, decreasing load on the involved nodes.<br />
<br />
If enough routes go down because of a cascade failure, a complete section of the network or internet can become unreachable. Although undesired, this can help speed up the recovery from this failure as connections will time out, and other nodes will give up trying to establish connections to the section(s) that have become cut off, decreasing load on the involved nodes.<br />
<br />
如果有足够多的路由因为级联故障而中断，网络或互联网的一个完整部分就会无法访问。尽管我们不希望出现这种情况，但这有助于加快从故障中恢复的速度，因为连接会超时，其他节点会放弃尝试与被切断的部分建立连接，从而减少相关节点的负载。<br />
<br />
<br />
<br />
A common occurrence during a cascade failure is a '''walking failure''', where sections go down, causing the next section to fail, after which the first section comes back up. This '''ripple''' can make several passes through the same sections or connecting nodes before stability is restored.<br />
<br />
A common occurrence during a cascade failure is a walking failure, where sections go down, causing the next section to fail, after which the first section comes back up. This ripple can make several passes through the same sections or connecting nodes before stability is restored.<br />
<br />
在级联故障中，一个常见的现象是行走故障，即各段下行，导致下一段故障，之后第一段回升。在恢复稳定之前，这种波纹可能会在相同的区段或连接节点上进行多次传递。<br />
<br />
<br />
=== History ===<br />
历史<br />
<br />
<br />
<br />
Cascade failures are a relatively recent development, with the massive increase in traffic and the high interconnectivity between systems and networks. The term was first applied in this context in the late 1990s by a Dutch IT professional and has slowly become a relatively common term for this kind of large-scale failure.{{Citation needed|date=January 2009}}<br />
<br />
Cascade failures are a relatively recent development, with the massive increase in traffic and the high interconnectivity between systems and networks. The term was first applied in this context in the late 1990s by a Dutch IT professional and has slowly become a relatively common term for this kind of large-scale failure.<br />
<br />
级联故障是一个相对较新的发展，随着流量的大量增加和系统与网络之间的高度互连性而出现。这个术语最早是在90年代末由一位荷兰的IT专业人员在此情况下使用的，后来慢慢成为这种大规模故障的一个比较常见的术语。<br />
<br />
<br />
<br />
<br />
=== Example ===<br />
案例<br />
<br />
<br />
<br />
Network failures typically start when a single network node fails. Initially, the traffic that would normally go through the node is stopped. Systems and users get errors about not being able to reach hosts. Usually, the redundant systems of an ISP respond very quickly, choosing another path through a different backbone. The routing path through this alternative route is longer, with more [[Hop (telecommunications)|hops]] and subsequently going through more systems that normally do not process the amount of traffic suddenly offered.<br />
<br />
Network failures typically start when a single network node fails. Initially, the traffic that would normally go through the node is stopped. Systems and users get errors about not being able to reach hosts. Usually, the redundant systems of an ISP respond very quickly, choosing another path through a different backbone. The routing path through this alternative route is longer, with more hops and subsequently going through more systems that normally do not process the amount of traffic suddenly offered.<br />
<br />
网络故障通常在单个网络节点故障时开始。最初，正常情况下会经过该节点的流量被停止。系统和用户会得到无法到达主机的错误。通常，ISP的冗余系统会很快做出反应，选择另一条通过不同骨干网的路径。通过这条替代路径的路由路径更长，跳数更多，随后要经过更多的系统，而这些系统通常不会处理突然提供的流量。<br />
<br />
<br />
<br />
This can cause one or more systems along the alternative route to go down, creating similar problems of their own.<br />
<br />
This can cause one or more systems along the alternative route to go down, creating similar problems of their own.<br />
<br />
这可能会导致替代路线上的一个或多个系统瘫痪，造成自身的类似问题。<br />
<br />
<br />
<br />
Also, related systems are affected in this case. As an example, [[Domain name system|DNS]] resolution might fail and what would normally cause systems to be interconnected, might break connections that are not even directly involved in the actual systems that went down. This, in turn, may cause seemingly unrelated nodes to develop problems, that can cause another cascade failure all on its own.<br />
<br />
Also, related systems are affected in this case. As an example, DNS resolution might fail and what would normally cause systems to be interconnected, might break connections that are not even directly involved in the actual systems that went down. This, in turn, may cause seemingly unrelated nodes to develop problems, that can cause another cascade failure all on its own.<br />
<br />
此外，在这种情况下，相关系统也会受到影响。例如，DNS解析可能会失败，通常会导致系统互连的情况可能会破坏甚至没有直接参与实际系统故障的连接。而这又可能导致看似不相关的节点出现问题，从而导致另一个级联故障的发生。<br />
<br />
<br />
<br />
In December 2012, a partial loss (40%) of [[Gmail]] service occurred globally, for 18 minutes. This loss of service was caused by a routine update of load balancing software which contained faulty logic—in this case, the error was caused by logic using an [https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ inappropriate ''all'' instead of the more appropriate ''some''.] The cascading error was fixed by fully updating a single node in the network instead of partially updating all nodes at one time.<br />
<br />
In December 2012, a partial loss (40%) of Gmail service occurred globally, for 18 minutes. This loss of service was caused by a routine update of load balancing software which contained faulty logic—in this case, the error was caused by logic using an [https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ inappropriate all instead of the more appropriate some.] The cascading error was fixed by fully updating a single node in the network instead of partially updating all nodes at one time.<br />
<br />
2012年12月，Gmail服务在全球范围内出现了部分损失(40%)，持续了18分钟。这次服务损失是由包含错误逻辑的负载平衡软件的例行更新引起的--在这种情况下，该错误是由使用[https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ 不合适的all而不是更合适的some]的逻辑引起的。通过完全更新网络中的一个节点，而不是一次部分更新所有节点，修复了级联错误。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“The cascading error”可以思考一下 级联错误 与级联故障是否一样<br />
<br />
== Cascading structural failure ==<br />
级联结构故障<br />
<br />
Certain load-bearing structures with discrete structural components can be subject to the "zipper effect", where the failure of a single structural member increases the load on adjacent members. In the case of the [[Hyatt Regency walkway collapse]], a suspended walkway (which was already overstressed due to an error in construction) failed when a single vertical suspension rod failed, overloading the neighboring rods which failed sequentially (i.e. like a [[zipper]]). A bridge that can have such a failure is called fracture critical, and numerous bridge collapses have been caused by the failure of a single part. Properly designed structures use an adequate [[factor of safety]] and/or alternate load paths to prevent this type of mechanical cascade failure.<ref name="petroski">{{cite book| title=To Engineer Is Human: The Role of Failure in Structural Design| first=Henry| last=Petroski| year=1992| isbn=978-0-679-73416-1| publisher=Vintage| place=| url-access=registration| url=https://archive.org/details/toengineerishuma00petr}}</ref><br />
<br />
Certain load-bearing structures with discrete structural components can be subject to the "zipper effect", where the failure of a single structural member increases the load on adjacent members. In the case of the Hyatt Regency walkway collapse, a suspended walkway (which was already overstressed due to an error in construction) failed when a single vertical suspension rod failed, overloading the neighboring rods which failed sequentially (i.e. like a zipper). A bridge that can have such a failure is called fracture critical, and numerous bridge collapses have been caused by the failure of a single part. Properly designed structures use an adequate factor of safety and/or alternate load paths to prevent this type of mechanical cascade failure.<br />
<br />
某些具有离散结构构件的承重结构可能会出现 "拉链效应"，即单个结构构件的失效会增加相邻构件的荷载。 在凯悦酒店人行道坍塌事件中，当单根垂直悬杆失效时，悬空的人行道（由于施工中的错误，人行道已经过度受力）失效，使相邻的悬杆超载，相邻的悬杆依次失效（像拉链一样）。一座可能发生这种破坏的桥梁被称为断裂临界桥梁，许多桥梁的坍塌都是由单一部件的故障引起的。正确设计的结构使用足够的安全系数和/或交替的荷载路径来防止这种类型的机械级联失效。<br />
<br />
<br />
<br />
== Other examples ==<br />
其他例子<br />
<br />
<br />
<br />
=== Biology ===<br />
生物<br />
<br />
<br />
[[Biochemical cascade]]s exist in biology, where a small reaction can have system-wide implications. One negative example is [[ischemic cascade]], in which a small [[ischemia|ischemic]] attack releases [[toxin]]s which kill off far more cells than the initial damage, resulting in more toxins being released. Current research is to find a way to block this cascade in [[stroke]] patients to minimize the damage.<br />
<br />
Biochemical cascades exist in biology, where a small reaction can have system-wide implications. One negative example is ischemic cascade, in which a small ischemic attack releases toxins which kill off far more cells than the initial damage, resulting in more toxins being released. Current research is to find a way to block this cascade in stroke patients to minimize the damage.<br />
<br />
生物学中存在着生化级联，一个小的反应就会对整个系统产生影响。一个负面的例子是缺血性级联反应，在这种反应中，一个小的缺血性发作释放出的毒素比最初的损伤杀死更多的细胞，导致更多的毒素被释放。目前的研究正在寻找一种方法来阻断中风患者的这种级联反应，以最大限度地减少损伤。<br />
<br />
<br />
<br />
In the study of extinction, sometimes the extinction of one species will cause many other extinctions to happen. Such a species is known as a [[keystone species]].<br />
<br />
In the study of extinction, sometimes the extinction of one species will cause many other extinctions to happen. Such a species is known as a keystone species.<br />
<br />
在物种灭绝的研究中，有时一个物种的灭绝会导致许多其他物种的灭绝。这样的物种被称为关键物种。<br />
<br />
<br />
<br />
=== Electronics ===<br />
电子学<br />
<br />
<br />
Another example is the [[Cockcroft–Walton generator]], which can also experience cascade failures wherein one failed [[diode]] can result in all the diodes failing in a fraction of a second.<br />
<br />
Another example is the Cockcroft–Walton generator, which can also experience cascade failures wherein one failed diode can result in all the diodes failing in a fraction of a second.<br />
<br />
另一个例子是Cockcroft-Walton发电机，它也会发生级联故障，其中一个故障的二极管会导致所有二极管在几分之一秒内发生故障。<br />
<br />
<br />
<br />
Yet another example of this effect in a scientific experiment was the [[Implosion (mechanical process)|implosion]] in 2001 of several thousand fragile glass photomultiplier tubes used in the [[Super-Kamiokande]] experiment, where the shock wave caused by the failure of a single detector appears to have triggered the implosion of the other detectors in a chain reaction.<br />
<br />
Yet another example of this effect in a scientific experiment was the implosion in 2001 of several thousand fragile glass photomultiplier tubes used in the Super-Kamiokande experiment, where the shock wave caused by the failure of a single detector appears to have triggered the implosion of the other detectors in a chain reaction.<br />
<br />
在科学实验中，这种效应的另一个例子是2001年用于超级神冈探测器实验中使用的几千支易碎的玻璃光电倍增管发生内爆，其中一个探测器的故障造成的冲击波似乎引发了连锁反应中其他探测器的内爆。<br />
<br />
<br />
=== Finance ===<br />
金融<br />
<br />
<br />
{{main|Systemic risk}} {{main|Cascades in financial networks}}<br />
{{主要}系统性风险}} {{主要}金融网络中的级联}}}<br />
<br />
<br />
In [[finance]], the risk of cascading failures of financial institutions is referred to as ''[[systemic risk]]:'' the failure of one financial institution may cause other financial institutions (its [[Counterparty|counterparties]]) to fail, cascading throughout the system.<ref name="HuangVodenska2013">{{cite journal|last1=Huang|first1=Xuqing|last2=Vodenska|first2=Irena|last3=Havlin|first3=Shlomo|last4=Stanley|first4=H. Eugene|title=Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation|journal=Scientific Reports|volume=3|pages=1219|year=2013|issn=2045-2322|doi=10.1038/srep01219|pmid=23386974|pmc=3564037|arxiv=1210.4973|bibcode=2013NatSR...3E1219H}}</ref><br />
<br />
In finance, the risk of cascading failures of financial institutions is referred to as systemic risk: the failure of one financial institution may cause other financial institutions (its counterparties) to fail, cascading throughout the system.<br />
<br />
在金融领域，金融机构连锁倒闭的风险被称为系统性风险：一家金融机构的倒闭可能会引起其他金融机构（其交易对手）的倒闭，在整个系统中连锁倒闭。<br />
<br />
Institutions that are believed to pose systemic risk are deemed either "[[too big to fail]]" (TBTF) or "too interconnected to fail" (TICTF), depending on why they appear to pose a threat.<br />
<br />
Institutions that are believed to pose systemic risk are deemed either "too big to fail" (TBTF) or "too interconnected to fail" (TICTF), depending on why they appear to pose a threat.<br />
<br />
那些被认为构成系统性风险的机构要么被视为“太大而不能倒”(TBTF) ，要么被视为“太相关而不能倒闭”(TICTF) ，这取决于它们为什么会构成威胁。<br />
<br />
<br />
<br />
Note however that systemic risk is not due to individual institutions per se, but due to the interconnections. For detailed models in economics and finance, see Elliott et al. (2014) and Acemoglu et al. (2015).<ref name="Acemoglu Ozdaglar Tahbaz-Salehi 2015 pp. 564–608">{{cite journal | last=Acemoglu | first=Daron | last2=Ozdaglar | first2=Asuman | last3=Tahbaz-Salehi | first3=Alireza | title=Systemic Risk and Stability in Financial Networks | journal=American Economic Review | publisher=American Economic Association | volume=105 | issue=2 | year=2015 | issn=0002-8282 | doi=10.1257/aer.20130456 | pages=564–608| hdl=1721.1/100979 | hdl-access=free }}</ref><ref name="Elliott Golub Jackson 2014 pp. 3115–3153">{{cite journal | last=Elliott | first=Matthew | last2=Golub | first2=Benjamin | last3=Jackson | first3=Matthew O. | title=Financial Networks and Contagion | journal=American Economic Review | publisher=American Economic Association | volume=104 | issue=10 | year=2014 | issn=0002-8282 | doi=10.1257/aer.104.10.3115 | pages=3115–3153}}</ref><br />
<br />
Note however that systemic risk is not due to individual institutions per se, but due to the interconnections. For detailed models in economics and finance, see Elliott et al. (2014) and Acemoglu et al. (2015).<br />
<br />
但请注意，系统性风险不是由于单个机构本身造成的，而是由于它们相互之间的联系。关于经济学和金融学的详细模型，请参阅Elliott等人（2014）和Acemoglu等人（2015）的文章。<br />
<br />
<br />
<br />
A related (though distinct) type of cascading failure in finance occurs in the stock market, exemplified by the [[2010 Flash Crash]].<br />
<br />
A related (though distinct) type of cascading failure in finance occurs in the stock market, exemplified by the 2010 Flash Crash.<br />
<br />
金融领域的一种相关的（但不同的）级联失败发生在股票市场，2010年的闪电崩盘就是一个例子。<br />
<br />
<br />
<br />
For another framework to study and predict the effect of cascading failures in finance see <ref>{{cite journal|last1=Li|first1=W|last2=Kenett|first2=DY|last3=Yamasaki|first3=K|last4=Stanley|first4=HE|last5=Havlin|first5=S|title=Ranking the economic importance of countries and industries|journal=Journal of Network Theory in Finance|volume=3|pages=1–17|year=2017|issn=2055-7795|doi=10.21314/JNTF.2017.031|arxiv=1408.0443}}</ref><ref name="HuangVodenska2013"/><br />
<br />
For another framework to study and predict the effect of cascading failures in finance see <br />
<br />
有关研究和预测金融连锁反应影响的另一个框架，请参见<br />
<br />
<br />
<br />
== Interdependent cascading failures ==<br />
相互依赖的级联故障<br />
<br />
<br />
[[File:Interdependent_relationship_among_different_infrastructures.tif|thumb|right|Fig. 1: Illustration of the interdependent relationship among different infrastructures]]<br />
<br />
Fig. 1: Illustration of the interdependent relationship among different infrastructures<br />
<br />
图1: 不同基础设施之间的相互依存关系的说明<br />
<br />
[[File:Schematic_demonstration_of_first-_and_second-order_percolation_transitions.tif|thumb|right|Fig. 2. Schematic demonstration of first- and second-order percolation transitions. In the second-order case, the giant component is continuously approaching zero at the percolation threshold p = p_c. In the first-order case, the giant component approaches zero discontinuously]]<br />
<br />
Fig. 2. Schematic demonstration of first- and second-order percolation transitions. In the second-order case, the giant component is continuously approaching zero at the percolation threshold p = p_c. In the first-order case, the giant component approaches zero discontinuously<br />
<br />
图2： 一阶和二阶渗流过渡的示意图。在二阶情况下，'''<font color="#32CD32">最大连通分支 giant component</font>'''在渗流阈值p=p_c时不断接近零。在一阶情况下，最大连通分支不连续地接近零。<br />
<br />
<br />
<br />
Diverse [[infrastructure]]s such as [[water supply]], [[transportation]], fuel and [[power station]]s are coupled together and depend on each other for functioning, see Fig. 1. Owing to this coupling, interdependent networks are extremely sensitive to random failures, and in particular to [[Targeted threat|targeted attacks]], such that a failure of a small fraction of nodes in one network can triger an iterative cascade of failures in several interdependent networks.<ref>{{cite web|title=Report of the Commission to Assess the Threat to the United States from Electromagnetic Pulse (EMP) Attack|url=http://empcommission.org/docs/A2473-EMP_Commission-7MB.pdf}}</ref><ref>{{Cite journal|last=Rinaldi|first=S.M.|last2=Peerenboom|first2=J.P.|last3=Kelly|first3=T.K.|date=2001|title=Identifying, understanding, and analyzing critical infrastructure interdependencies|url=|journal= IEEE Control Systems Magazine|volume=21|pages=11–25|via=}}</ref> [[Power outage|Electrical blackouts]] frequently result from a cascade of failures between interdependent networks, and the problem has been dramatically exemplified by the several large-scale blackouts that have occurred in recent years. Blackouts are a fascinating demonstration of the important role played by the dependencies between networks. For example, the [[2003 Italy blackout]] resulted in a widespread failure of the [[Rail transport|railway network]], [[Health system|health care systems]], and [[financial services]] and, in addition, severely influenced the [[telecommunication network]]s. The partial failure of the communication system in turn further impaired the [[electrical grid]] management system, thus producing a positive feedback on the power grid.<ref>{{cite journal|last=V. Rosato |first=Issacharoff, L., Tiriticco, F., Meloni, S., Porcellinis, S.D., & Setola, R. |title=Modelling interdependent infrastructures using interacting dynamical models |journal=International Journal of Critical Infrastructures |year=2008 |volume=4 |pages=63–79 |doi=10.1504/IJCIS.2008.016092 }}</ref> This example emphasizes how inter-dependence can significantly magnify the damage in an interacting network system. A framework to study the cascading failures between coupled networks based on percolation theory was developed recently.<ref>{{cite journal|last=S. V. Buldyrev|first=R. Parshani, G. Paul, H. E. Stanley, S. Havlin|title=Catastrophic cascade of failures in interdependent networks|journal=Nature|year=2010|volume=464|pages=1025–8|doi=10.1038/nature08932|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291<br />
<br />
Diverse infrastructures such as water supply, transportation, fuel and power stations are coupled together and depend on each other for functioning, see Fig. 1. Owing to this coupling, interdependent networks are extremely sensitive to random failures, and in particular to targeted attacks, such that a failure of a small fraction of nodes in one network can triger an iterative cascade of failures in several interdependent networks. Electrical blackouts frequently result from a cascade of failures between interdependent networks, and the problem has been dramatically exemplified by the several large-scale blackouts that have occurred in recent years. Blackouts are a fascinating demonstration of the important role played by the dependencies between networks. For example, the 2003 Italy blackout resulted in a widespread failure of the railway network, health care systems, and financial services and, in addition, severely influenced the telecommunication networks. The partial failure of the communication system in turn further impaired the electrical grid management system, thus producing a positive feedback on the power grid. This example emphasizes how inter-dependence can significantly magnify the damage in an interacting network system. A framework to study the cascading failures between coupled networks based on percolation theory was developed recently.<ref>{{cite journal|last=S. V. Buldyrev|first=R. Parshani, G. Paul, H. E. Stanley, S. Havlin|title=Catastrophic cascade of failures in interdependent networks|journal=Nature|year=2010|volume=464|pages=1025–8|doi=10.1038/nature08932|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291<br />
<br />
诸如供水、运输、燃料和发电站等多种基础设施都是耦合在一起的，并相互依赖着运行，见图1。 由于这种耦合，相互依存的网络对随机故障，特别是对有针对性的攻击极为敏感，因此，一个网络中一小部分节点的故障就会导致几个相互依存的网络中出现一连串的故障。电气停电经常是由相互依赖的网络之间的故障级联造成的，近年来发生的几次大规模停电事件就极大地说明了这个问题。停电是网络之间的依存关系所起的重要作用的一个引人入胜的证明。例如，2003年意大利大停电导致铁路网、医疗系统、金融服务大面积瘫痪，此外，还严重影响了电信网络。通信系统的部分故障又进一步损害了电网管理系统，从而对电网产生了正反馈。这个例子强调了在一个相互影响的网络系统中，相互依赖性是如何显著放大损害的。基于'''<font color="#ff8000"> 渗流理论 Percolation Theory</font>'''，最近发展了一个研究耦合网络之间级联故障的框架。1 = r.在相互依赖的网络中灾难性的级联故障 | 杂志 = 自然 | 年 = 2010 | 卷 = 464 | 页 = 1025-8 | doi = 10.1038/nature08932 | url = http://Havlin.biu.ac.il/publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291<br />
<br />
|arxiv=1012.0206|bibcode=2010Natur.464.1025B}}</ref> The cascading failures can lead to abrupt collapse compare to percolation in a single network where the breakdown of the network is continuous, see Fig. 2.<br />
<br />
|arxiv=1012.0206|bibcode=2010Natur.464.1025B}}</ref> The cascading failures can lead to abrupt collapse compare to percolation in a single network where the breakdown of the network is continuous, see Fig. 2.<br />
<br />
与级联故障可能会导致突然崩溃相比，在单一网络中，网络的崩溃是连续的，见图2。<br />
<br />
Cascading failures in spatially embedded systems have been<br />
<br />
Cascading failures in spatially embedded systems have been<br />
<br />
空间嵌入式系统中的级联故障已经成为当前研究的热点。<br />
<br />
shown to lead to extreme vulnerability.<ref name="BashanBerezin2013">{{cite journal|last1=Bashan|first1=Amir|last2=Berezin|first2=Yehiel|last3=Buldyrev|first3=Sergey V.|last4=Havlin|first4=Shlomo|title=The extreme vulnerability of interdependent spatially embedded networks|journal=Nature Physics|year=2013|issn=1745-2473|doi=10.1038/nphys2727|volume=9|issue=10|pages=667–672|arxiv=1206.2062|bibcode=2013NatPh...9..667B}}</ref> For the dynamic process of cascading failures see ref.<ref>{{Cite journal|last=Zhou|first=D.|last2=Bashan|first2=A.|last3=Cohen|first3=R.|last4=Berezin|first4=Y.|last5=Shnerb|first5=N.|last6=Havlin|first6=S.|date=2014|title=Simultaneous first- and second-order percolation transitions in interdependent networks|url=|journal=Phys. Rev. E|volume=90|issue=1|pages=012803|bibcode=2014PhRvE..90a2803Z|doi=10.1103/PhysRevE.90.012803|pmid=25122338|arxiv=1211.2330}}</ref> A model for repairing failures in order to avoid cascading failures was developed by Di Muro et al.<ref>{{Cite journal|last=Di Muro|first=M. A.|last2=La Rocca|first2=C. E.|last3=Stanley|first3=H. E.|last4=Havlin|first4=S.|last5=Braunstein|first5=L. A.|date=2016-03-09|title=Recovery of Interdependent Networks|journal=Scientific Reports|language=En|volume=6|issue=1|pages=22834|doi=10.1038/srep22834|pmid=26956773|pmc=4783785|issn=2045-2322|arxiv=1512.02555|bibcode=2016NatSR...622834D}}</ref><br />
<br />
shown to lead to extreme vulnerability. For the dynamic process of cascading failures see ref. A model for repairing failures in order to avoid cascading failures was developed by Di Muro et al.<br />
<br />
显示会导致极端的脆弱性。关于级联故障的动态过程见参考文献。Di Muro等人开发了一个修复故障的模型，以避免级联故障。<br />
<br />
<br />
Furthermore, it was shown that such systems when embedded in space are extremely vulnerable to localized attacks or failures. Above a critical radius of damage, the failure may spread to the entire system.<ref>{{Cite journal|last=Berezin|first=Yehiel|last2=Bashan|first2=Amir|last3=Danziger|first3=Michael M.|last4=Li|first4=Daqing|last5=Havlin|first5=Shlomo|date=2015-03-11|title=Localized attacks on spatially embedded networks with dependencies|journal=Scientific Reports|language=en|volume=5|issue=1|pages=8934|doi=10.1038/srep08934|pmid=25757572|pmc=4355725|issn=2045-2322|bibcode=2015NatSR...5E8934B}}</ref><br />
<br />
Furthermore, it was shown that such systems when embedded in space are extremely vulnerable to localized attacks or failures. Above a critical radius of damage, the failure may spread to the entire system.<br />
<br />
此外，研究表明，当这种系统嵌入空间时，极易受到局部攻击或故障的影响。超过临界损伤半径，故障可能扩散到整个系统。<br />
<br />
<br />
<br />
== Model for overload cascading failures ==<br />
过载级联故障模型<br />
<br />
A model for cascading failures due to overload propagation is the Motter–Lai model.<ref>{{Cite journal|last=Motter|first=A. E.|last2=Lai|first2=Y. C.|date=2002|title=Cascade-based attacks on complex networks|url=|journal=Phys. Rev. E|volume=66|issue=6 Pt 2|pages=065102|doi=10.1103/PhysRevE.66.065102|pmid=12513335|bibcode=2002PhRvE..66f5102M|arxiv=cond-mat/0301086}}</ref> The tempo-spatial propagation of such failures have been studied by Jichang Zhao et al.<ref>{{Cite journal|last=Zhao|first=J.|last2=Li|first2=D.|last3=Sanhedrai|first3=H.|last4=Cohen|first4=R.|last5=Havlin|first5=S.|date=2016|title=Spatio-temporal propagation of cascading overload failures in spatially embedded networks|url=|journal=Nature Communications|volume=7|pages=10094|bibcode=2016NatCo...710094Z|doi=10.1038/ncomms10094|pmid=26754065|pmc=4729926}}</ref><br />
<br />
A model for cascading failures due to overload propagation is the Motter–Lai model. The tempo-spatial propagation of such failures have been studied by Jichang Zhao et al.<br />
<br />
过载传播导致的级联故障的模型是Motter-Lai模型。赵继昌等人对这种故障的速度空间传播进行了研究。<br />
<br />
<br />
<br />
== See also ==<br />
请参阅<br />
<br />
{{div col}}<br />
<br />
* [[Power outage|Blackouts]]<br />
*[[停电|停电]]。<br />
<br />
* [[Brittle system]]<br />
* [[脆性系统]]<br />
<br />
* [[Butterfly effect]]<br />
* [[蝴蝶效应]]<br />
<br />
* [[Byzantine failure]]<br />
* [[拜占庭故障]]<br />
<br />
* [[Cascading rollback]]<br />
* [[级联回滚]]<br />
<br />
* [[Chain reaction]]<br />
* [[连锁反应]]<br />
<br />
* [[Chaos theory]]<br />
* [[混沌理论]]<br />
<br />
* [[Cache stampede]]<br />
* [[缓存雪崩]]<br />
<br />
<br />
* [[Congestion collapse]]<br />
* [[拥堵崩溃]]<br />
<br />
* [[Domino effect]]<br />
* [[多米诺效应]]<br />
<br />
* [[For Want of a Nail (proverb)]]<br />
* [[只因少了一颗钉子（谚语）]]<br />
<br />
* [[Interdependent networks]]<br />
* [[相互依赖的网络]]<br />
<br />
* [[Kessler Syndrome]]<br />
* [[凯斯勒综合症]]<br />
<br />
* [[Percolation theory]]<br />
* [[渗流理论]]<br />
<br />
* [[Progressive collapse]]<br />
* [[渐进式崩溃]]<br />
<br />
* [[Virtuous circle and vicious circle]]<br />
*[[良性循环和恶性循环]]<br />
<br />
* [[Wicked problem]]<br />
* [[抗解问题]]<br />
<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== References ==<br />
参考<br />
<br />
<br />
{{reflist}}<br />
<br />
<br />
<br />
== Further reading ==<br />
进一步阅读<br />
<br />
<br />
* {{cite web <br />
<br />
|url=http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf <br />
<br />
|url=http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf <br />
<br />
Http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf<br />
<br />
|title=Comparison of defense strategies for cascade breakdown on SF networks with degree correlations <br />
<br />
|title=Comparison of defense strategies for cascade breakdown on SF networks with degree correlations <br />
<br />
具有度相关性的 SF 网络级联故障的防御策略比较<br />
<br />
|author=Toshiyuki Miyazaki <br />
<br />
|author=Toshiyuki Miyazaki <br />
<br />
|author=Toshiyuki Miyazaki<br />
<br />
|date=1 March 2005 <br />
<br />
|date=1 March 2005 <br />
<br />
日期 = 2005年3月1日<br />
<br />
|url-status=dead <br />
<br />
|url-status=dead <br />
<br />
地位 = 死亡<br />
<br />
|archiveurl=https://web.archive.org/web/20090220024018/http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf <br />
<br />
|archiveurl=https://web.archive.org/web/20090220024018/http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf <br />
<br />
2012年3月24日 | archiveurl = https://web.archive.org/web/20090220024018/http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf<br />
<br />
|archivedate=2009-02-20 <br />
<br />
|archivedate=2009-02-20 <br />
<br />
| archivedate = 2009-02-20<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite web<br />
<br />
|url=http://redmondmag.com/columns/print.asp?EditorialsID=1000 <br />
<br />
|url=http://redmondmag.com/columns/print.asp?EditorialsID=1000 <br />
<br />
1000 http://redmondmag.com/columns/print.asp<br />
<br />
|title=(In)Secure Shell? <br />
<br />
|title=(In)Secure Shell? <br />
<br />
| title = (In) Secure Shell? ？<br />
<br />
|accessdate=2007-09-08 <br />
<br />
|accessdate=2007-09-08 <br />
<br />
2007-09-08<br />
<br />
|author=Russ Cooper <br />
<br />
|author=Russ Cooper <br />
<br />
作者: Russ Cooper<br />
<br />
|date=1 June 2005 <br />
<br />
|date=1 June 2005 <br />
<br />
日期 = 2005年6月1日<br />
<br />
|publisher=RedmondMag.com <br />
<br />
|publisher=RedmondMag.com <br />
<br />
| publisher = RedmondMag.com<br />
<br />
|archiveurl=https://web.archive.org/web/20070928164525/http://redmondmag.com/columns/print.asp?EditorialsID=1000 <br />
<br />
|archiveurl=https://web.archive.org/web/20070928164525/http://redmondmag.com/columns/print.asp?EditorialsID=1000 <br />
<br />
1000 https://web.archive.org/web/20070928164525/http://redmondmag.com/columns/print.asp<br />
<br />
|archivedate=2007-09-28 <br />
<br />
|archivedate=2007-09-28 <br />
<br />
| archivedate = 2007-09-28<br />
<br />
|url-status=dead <br />
<br />
|url-status=dead <br />
<br />
地位 = 死亡<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite web <br />
<br />
|url=http://www.chds.us/?research/software&d=list <br />
<br />
|url=http://www.chds.us/?research/software&d=list <br />
<br />
Http://www.chds.us/?research/software&d=list<br />
<br />
|title=Cascade Net (simulation program) <br />
<br />
|title=Cascade Net (simulation program) <br />
<br />
| title = Cascade Net (仿真程序)<br />
<br />
|accessdate=2007-09-08 <br />
<br />
|accessdate=2007-09-08 <br />
<br />
2007-09-08<br />
<br />
|author=US Department of Homeland Security <br />
<br />
|author=US Department of Homeland Security <br />
<br />
美国国土安全部<br />
<br />
|date=5 February 2007 <br />
<br />
|date=5 February 2007 <br />
<br />
| 日期 = 2007年2月5日<br />
<br />
|publisher=Center for Homeland Defense and Security <br />
<br />
|publisher=Center for Homeland Defense and Security <br />
<br />
| publisher = 国土安全防御中心<br />
<br />
|url-status=dead <br />
<br />
|url-status=dead <br />
<br />
地位 = 死亡<br />
<br />
|archiveurl=https://web.archive.org/web/20081228044520/http://www.chds.us/?research%2Fsoftware&d=list <br />
<br />
|archiveurl=https://web.archive.org/web/20081228044520/http://www.chds.us/?research%2Fsoftware&d=list <br />
<br />
2012年3月24日 | archiveurl = https://web.archive.org/web/20081228044520/http://www.chds.us/?research%2fsoftware&d=list<br />
<br />
|archivedate=2008-12-28 <br />
<br />
|archivedate=2008-12-28 <br />
<br />
| archivedate = 2008-12-28<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
== External links ==<br />
<br />
* [https://web.archive.org/web/20060827050151/http://www.windows.ucar.edu/spaceweather/blackout.html Space Weather: Blackout — Massive Power Grid Failure]<br />
<br />
* [https://web.archive.org/web/20071022110507/http://vlab.infotech.monash.edu.au/simulations/networks/cascading-failure/ Cascading failure demo applet] (Monash University's Virtual Lab)<br />
<br />
* A. E. Motter and Y.-C. Lai, [http://chaos1.la.asu.edu/~yclai/papers/PRE_02_ML_3.pdf ''Cascade-based attacks on complex networks,''] Physical Review E (Rapid Communications) 66, 065102 (2002).<br />
<br />
* P. Crucitti, V. Latora and M. Marchiori, [https://pdfs.semanticscholar.org/aeda/97ccce03a5979dd4196fb7544ee0dc546f18.pdf ''Model for cascading failures in complex networks,''] Physical Review E (Rapid Communications) 69, 045104 (2004).<br />
<br />
* [https://web.archive.org/web/20040704132003/http://www.epri.com/programHigh.asp?objid=261741 Protection Strategies for Cascading Grid Failures — A Shortcut Approach]<br />
<br />
* I. Dobson, B. A. Carreras, and D. E. Newman, [https://web.archive.org/web/20060222073252/http://eceserv0.ece.wisc.edu/~dobson/PAPERS/dobsonPEIS05.pdf preprint] A loading-dependent model of probabilistic cascading failure, Probability in the Engineering and Informational Sciences, vol. 19, no. 1, January 2005, pp.&nbsp;15–32.<br />
<br />
* [https://www.pbs.org/wgbh/nova/transcripts/3105_aircrash.html Nova: Crash of Flight 111] on September 2, 1998. [[Swissair Flight 111]] flying from New York to Geneva slammed into the Atlantic Ocean off the coast of Nova Scotia with 229 people aboard. Originally believed a terrorist act. After $39 million investigation, insurance settlement of $1.5 billion and more than four years, investigators unravel the puzzle: cascading failure. What is the legacy of Swissair 111? "We have a window into the internal structure of design, checks and balances, protection, and safety." -David Evans, Editor-in-Chief of Air Safety Week.<br />
<br />
* PhysicsWeb story: [http://physicsweb.org/articles/news/5/11/9 Accident grounds neutrino lab]<br />
<br />
* [http://necsi.edu/affiliates/braha/StructureandDynamics.htm The Structure and Dynamics of Large Scale Organizational Networks (Dan Braha, New England Complex Systems Institute)]<br />
<br />
*From Single Network to Network of Networks http://havlin.biu.ac.il/Pdf/Bremen070715a.pdf<br />
<br />
<br />
<br />
{{Electricity delivery}}<br />
<br />
<br />
<br />
[[Category:Failure]]<br />
<br />
Category:Failure<br />
<br />
类别: 失败<br />
<br />
[[Category:Reliability engineering]]<br />
<br />
Category:Reliability engineering<br />
<br />
类别: 可靠度<br />
<br />
[[Category:Electric power transmission]]<br />
<br />
Category:Electric power transmission<br />
<br />
类别: 输电系统<br />
<br />
[[Category:Systemic risk]]<br />
<br />
Category:Systemic risk<br />
<br />
类别: 系统性风险<br />
<br />
[[Category:Systems science]]<br />
<br />
Category:Systems science<br />
<br />
类别: 系统科学<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Cascading failure]]. Its edit history can be viewed at [[级联故障/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E5%B8%95%E7%B4%AF%E6%89%98%E6%9C%80%E4%BC%98_Pareto_optimality&diff=14735帕累托最优 Pareto optimality2020-10-04T07:34:22Z<p>趣木木：</p>
<hr />
<div>此词条由袁一博翻译，未经人工整理和审校，带来阅读不便，请见谅。<br />
<br />
{{short description|State in which no reallocation of resources can make everyone at least as well off}}<br />
<br />
{{Use mdy dates|date=January 2016}}<br />
<br />
<br />
<br />
'''Pareto efficiency''' or '''Pareto optimality''' is a situation that cannot be modified so as to make any one individual or preference criterion better off without making at least one individual or preference criterion worse off. The concept is named after [[Vilfredo Pareto]] (1848–1923), Italian engineer and economist, who used the concept in his studies of [[economic efficiency]] and [[income distribution]]. The following three concepts are closely related:<br />
<br />
Pareto efficiency or Pareto optimality is a situation that cannot be modified so as to make any one individual or preference criterion better off without making at least one individual or preference criterion worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related:<br />
<br />
帕累托效率或帕累托最优是一种不能被修改的情况，它使得任何个体或优先准则变得更好而不使至少一个个体或一项优先准则变得更差。这个概念是以意大利工程师、经济学家维尔弗雷多·帕累托（1848-1923）的名字命名的。他在研究'''<font color="#ff8000">经济效率</font>'''和'''<font color="#ff8000">收入分配</font>'''时使用了这个概念。以下三个概念密切相关：<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）专有名词与疑难句 后面需要附上英文<br />
<br />
<br />
* Given an initial situation, a '''Pareto improvement''' is a new situation which is weakly preferred by all agents, and strictly preferred by at least one agent. In a sense, it is a unanimously-agreed improvement: if we move to the new situation, some agents will gain, and no agents will lose.<br />
<br />
* A situation is called '''Pareto dominated''' if it has a Pareto improvement. <br />
<br />
* A situation is called '''Pareto optimal''' or '''Pareto efficient''' if it is not Pareto dominated.<br />
<br />
* 在一个给定的初始条件下，一个帕累托改进指的是一种不为大多数主体所喜爱但被至少一个主体喜爱的状况。在某种意义上，它是一种一致同意的改进：如果我们处于这种新的情况下，某些主体可能获利，且没有主体会蒙受损失。<br />
*一种状况如果拥有一个帕累托改进，那么它被称作受帕累托支配的。<br />
*一种状况如果是不受帕累托支配的，那么它被称作帕累托最优的或帕累托有效的。<br />
<br />
<br />
<br />
The '''Pareto frontier''' is the set of all Pareto efficient allocations, conventionally shown [[Chart|graphically]]. It also is variously known as the '''Pareto front''' or '''Pareto set'''.<ref>{{Cite web|url=http://www.cenaero.be/Page.asp?docid=27103&|title=Pareto Front|last=proximedia|website=www.cenaero.be|access-date=2018-10-08}}</ref><br />
<br />
The Pareto frontier is the set of all Pareto efficient allocations, conventionally shown graphically. It also is variously known as the Pareto front or Pareto set.<br />
<br />
帕累托边界是所有帕累托有效分配的集合，按惯例以图表形式表示它。它也被称为帕累托前沿或帕累托集。<br />
<br />
<br />
<br />
"Pareto efficiency" is considered as a minimal notion of efficiency that does not necessarily result in a socially desirable distribution of resources: it makes no statement about [[Social equality|equality]], or the overall well-being of a society.<ref>{{cite journal |authorlink=Amartya Sen |first=A. |last=Sen |title=Markets and freedom: Achievements and limitations of the market mechanism in promoting individual freedoms |journal=Oxford Economic Papers |volume=45 |issue=4 |pages=519–541 |date=October 1993 |jstor=2663703 |url=http://www.cs.princeton.edu/courses/archive/spr06/cos444/papers/sen.pdf |doi=10.1093/oxfordjournals.oep.a042106 }}</ref><ref>{{cite book |first=N. |last=Barr |author-link=Nicholas Barr|chapter=3.2.2 The relevance of efficiency to different theories of society |title=Economics of the Welfare State |year=2012 |publisher=[[Oxford University Press]] |isbn=978-0-19-929781-8 |pages=[https://books.google.com/books?id=DOg0BM1XiqQC&pg=PA46 46–49] |edition=5th}}</ref>{{rp|46–49}} It is a necessary, but not sufficient, condition of efficiency.<br />
<br />
"Pareto efficiency" is considered as a minimal notion of efficiency that does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society. It is a necessary, but not sufficient, condition of efficiency.<br />
<br />
“帕累托最优”被认为是一种狭义的效率，它不一定产生社会所期望的资源分配: 它没有为平等或一个社会的总体福祉发声。它是效率的必要不充分条件。<br />
<br />
<br />
<br />
In addition to the context of efficiency in ''allocation'', the concept of Pareto efficiency also arises in the context of [[productive efficiency|''efficiency in production'']] vs. ''[[x-inefficiency]]'': a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.<ref>[[John D. Black|Black, J. D.]], Hashimzade, N., & [[Gareth Myles|Myles, G.]], eds., ''A Dictionary of Economics'', 5th ed. (Oxford: Oxford University Press, 2017), [https://books.google.com/books?id=WyvYDQAAQBAJ&pg=PT459 p. 459].</ref>{{rp|459}}<br />
<br />
In addition to the context of efficiency in allocation, the concept of Pareto efficiency also arises in the context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.<br />
<br />
除了分配效率的背景之外，帕累托最优的概念也出现在'''<font color="#ff8000">生产效率</font>'''对比于'''<font color="#ff8000">x-低效率</font>'''的背景之下，即如果生产投入没有可行的再分配，或者说一种产品的产出增加，而所有其他产品的产出增加或保持不变，那么一组产品的产出就是帕累托有效的。<br />
<br />
<br />
<br />
Besides economics, the notion of Pareto efficiency has been applied to the selection of alternatives in [[engineering]] and [[biology]]. Each option is first assessed, under multiple criteria, and then a subset of options is ostensibly identified with the property that no other option can categorically outperform the specified option. It is a statement of impossibility of improving one variable without harming other variables in the subject of [[multi-objective optimization]] (also termed '''Pareto optimization''').<br />
<br />
Besides economics, the notion of Pareto efficiency has been applied to the selection of alternatives in engineering and biology. Each option is first assessed, under multiple criteria, and then a subset of options is ostensibly identified with the property that no other option can categorically outperform the specified option. It is a statement of impossibility of improving one variable without harming other variables in the subject of multi-objective optimization (also termed Pareto optimization).<br />
<br />
除了经济学，帕累托最优的概念已经应用到工程和生物学中的替代品的选择。首先根据多项标准对每个选项进行评估，然后确定选项子集，其中的任何元素都具有没有其他选项可以明确胜过该元素的属性。在'''<font color="#ff8000">多目标优化</font>'''(又称帕累托优化)中，这是一种对在不损害其他变量的情况下改进一个变量的不可能性的陈述。<br />
<br />
<br />
<br />
== Overview 综述 ==<br />
<br />
<br />
<br />
<br />
"Pareto optimality" is a formally defined concept used to describe when an [[resource allocation|allocation]] is optimal. An allocation is ''not'' Pareto optimal if there is an alternative allocation where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a transfer that satisfies this condition, the reallocation is called a "Pareto improvement". When no further Pareto improvements are possible, the allocation is a "Pareto optimum".<br />
<br />
"Pareto optimality" is a formally defined concept used to describe when an allocation is optimal. An allocation is not Pareto optimal if there is an alternative allocation where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a transfer that satisfies this condition, the reallocation is called a "Pareto improvement". When no further Pareto improvements are possible, the allocation is a "Pareto optimum".<br />
<br />
“帕累托最优”是一个正式定义的概念，用来描述一个分配何时是最优的。如果有一种替代性的分配方式可以在不降低任何其他参与者福祉的情况下改善至少一个参与者的福祉，那么这种分配就不是帕累托最优的。如果有一个转移满足这个条件，这个再分配就被称为“帕累托改进”。当无法进一步实现帕累托改进时，这个分配就是“帕累托最优”。<br />
<br />
<br />
<br />
The formal presentation of the concept in an economy is as follows: Consider an economy with <math> n</math> agents and <math> k </math> goods. Then an allocation <math> \{x_1, ..., x_n\} </math>, where <math> x_i \in \mathbb{R}^k </math> for all ''i'', is ''Pareto optimal'' if there is no other feasible allocation <math> \{x_1', ..., x_n'\} </math> such that, for utility function <math> u_i </math> for each agent <math> i </math>, <math> u_i(x_i') \geq u_i(x_i) </math> for all <math> i \in \{1, ..., n\} </math> with <math> u_i(x_i') > u_i(x_i) </math> for some <math> i</math>.<ref name="AndreuMas95">{{citation|author-link=Andreu Mas-Colell|last1=Mas-Colell|first1=A.|first2=Michael D.|last2=Whinston|first3=Jerry R.|last3=Green|year=1995|title=Microeconomic Theory|chapter=Chapter 16: Equilibrium and its Basic Welfare Properties|publisher=Oxford University Press|isbn=978-0-19-510268-0|url-access=registration|url=https://archive.org/details/isbn_9780198089537}}</ref> Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption [[Vector space|vector]]s and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced.<br />
<br />
The formal presentation of the concept in an economy is as follows: Consider an economy with <math> n</math> agents and <math> k </math> goods. Then an allocation <math> \{x_1, ..., x_n\} </math>, where <math> x_i \in \mathbb{R}^k </math> for all i, is Pareto optimal if there is no other feasible allocation <math> \{x_1', ..., x_n'\} </math> such that, for utility function <math> u_i </math> for each agent <math> i </math>, <math> u_i(x_i') \geq u_i(x_i) </math> for all <math> i \in \{1, ..., n\} </math> with <math> u_i(x_i') > u_i(x_i) </math> for some <math> i</math>. Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced.<br />
<br />
这个概念在一个经济体系中的正式表现如下: 考虑一个有''n''个主体和''k''个商品的经济体系，如果没有其他可行的分配'''<font color="#32CD32">此处需插入公式</font>'''使得对于效用函数对任意主体''i''满足'''<font color="#32CD32">此处需插入公式</font>'''，它对某些个体''i''满足'''<font color="#32CD32">此处需插入公式</font>'''，那么一个分配'''<font color="#32CD32">此处需插入公式</font>'''，是 Pareto 最优的，其中对任意''i''，'''<font color="#32CD32">此处需插入公式</font>'''。在这个简单的经济体系中，“可行性”是指每种商品的分配总额不超过该经济体系中所有商品的总额。在一个有生产能力的更为复杂的经济体中，一个分配将包括消费载体和生产载体，且可行性要求每种消费品的总量不大于初始禀赋加上生产总量。<br />
<br />
<br />
<br />
In principle, a change from a generally inefficient economic allocation to an efficient one is not necessarily considered to be a Pareto improvement. Even when there are overall gains in the economy, if a single agent is disadvantaged by the reallocation, the allocation is not Pareto optimal. For instance, if a change in economic policy eliminates a monopoly and that market subsequently becomes competitive, the gain to others may be large. However, since the monopolist is disadvantaged, this is not a Pareto improvement. In theory, if the gains to the economy are larger than the loss to the monopolist, the monopolist could be compensated for its loss while still leaving a net gain for others in the economy, allowing for a Pareto improvement. Thus, in practice, to ensure that nobody is disadvantaged by a change aimed at achieving Pareto efficiency, [[compensation principle|compensation]] of one or more parties may be required. It is acknowledged, in the real world, that such compensations may have [[unintended consequences]] leading to incentive distortions over time, as agents supposedly anticipate such compensations and change their actions accordingly.<ref>See [[Ricardian equivalence]]</ref><br />
<br />
In principle, a change from a generally inefficient to an efficient one is not necessarily considered to be a Pareto improvement. Even when there are overall gains in the economy, if a single agent is disadvantaged by the reallocation, the allocation is not Pareto optimal. For instance, if a change in economic policy eliminates a monopoly and that market subsequently becomes competitive, the gain to others may be large. However, since the monopolist is disadvantaged, this is not a Pareto improvement. In theory, if the gains to the economy are larger than the loss to the monopolist, the monopolist could be compensated for its loss while still leaving a net gain for others in the economy, a Pareto improvement. Thus, in practice, to ensure that nobody is disadvantaged by a change aimed at achieving Pareto efficiency, compensation of one or more parties may be required. It is acknowledged, in the real world, that such compensations may have unintended consequences leading to incentive distortions over time, as agents supposedly anticipate such compensations and change their actions accordingly.<br />
<br />
原则上，从一个普遍低效率的经济分配到一个高效率的经济分配的转变不一定被认为是一个帕累托改进。即使经济总体是获益的，如果一个主体在再分配中处于不利地位，这个分配也不是帕累托最优的。例如，如果经济政策的某个改变消除了垄断，市场随后变得具有竞争力，那么其他主体的收益可能很大。然而，由于垄断者处于不利地位，这不是一个帕累托改善。理论上，如果经济体系的收益大于垄断者的损失，考虑到帕累托改善，垄断者可以在为经济体系中的其他主体留下净收益的情况下得到补偿。因此，在实践中，为了确保没有人会因为旨在实现帕累托最优的改变而处于不利地位，可能需要对一个或多个当事方进行补偿。在现实世界中，因为代理人可能预期这种补偿并相应地改变他们的行为，随着时间的推移，这种补偿可能会造成意外的后果以及动机的扭曲。<br />
<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“帕累托改善”“帕累托改进”名词注意统一<br />
Under the idealized conditions of the [[first welfare theorem]], a system of [[free market]]s, also called a "[[competitive equilibrium]]", leads to a Pareto-efficient outcome. It was first demonstrated mathematically by economists [[Kenneth Arrow]] and [[Gérard Debreu]].<br />
<br />
Under the idealized conditions of the first welfare theorem, a system of free markets, also called a "competitive equilibrium", leads to a Pareto-efficient outcome. It was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu.<br />
<br />
在福利经济学第一定理的理想条件下，一个自由市场系统，也称为“竞争均衡” ，对应一个帕累托有效的结果。经济学家肯尼斯·阿罗(Kenneth Arrow)和杰拉德·迪布鲁(Gérard Debreu)首先用数学方法证明了这一点。<br />
<br />
<br />
<br />
However, the result only holds under the restrictive assumptions necessary for the proof: markets exist for all possible goods, so there are no [[externality|externalities]]; all markets are in full equilibrium; markets are perfectly competitive; transaction costs are negligible; and market participants have [[perfect information]].<br />
<br />
However, the result only holds under the restrictive assumptions necessary for the proof: markets exist for all possible goods, so there are no externalities; all markets are in full equilibrium; markets are perfectly competitive; transaction costs are negligible; and market participants have perfect information.<br />
<br />
然而，这个结果只有在证明所需的限制性假设下才成立，即所有可能的商品都存在市场，因此不存在外部效应; 所有市场都处于完全均衡状态; 市场是完全竞争的; 交易成本是可忽略的; 市场参与者拥有完全的信息。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）在博弈论中有“完全的信息”为完全信息<br />
<br />
<br />
In the absence of perfect information or complete markets, outcomes will generally be Pareto inefficient, per the [[Joseph Stiglitz#Information asymmetry|Greenwald-Stiglitz theorem]].<ref>{{Cite journal |doi=10.2307/1891114 |last1=Greenwald |first1=B. |last2=Stiglitz |first2=J. E. |author1-link=Bruce Greenwald |author2-link=Joseph E. Stiglitz |journal=Quarterly Journal of Economics |volume=101 |issue=2 |pages=229–64 |year=1986 |title=Externalities in economies with imperfect information and incomplete markets |jstor=1891114}}</ref><br />
<br />
In the absence of perfect information or complete markets, outcomes will generally be Pareto inefficient, per the Greenwald-Stiglitz theorem.<br />
<br />
根据 Greenwald-Stiglitz 定理，在缺乏完全信息或完全市场的情况下，这个结果通常是帕累托低效的。<br />
<br />
<br />
<br />
The [[second welfare theorem]] is essentially the reverse of the first welfare-theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some [[competitive equilibrium]], or [[free market]] system, although it may also require a [[lump-sum]] transfer of wealth.<ref name="AndreuMas95"/><br />
<br />
The second welfare theorem is essentially the reverse of the first welfare-theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some competitive equilibrium, or free market system, although it may also require a lump-sum transfer of wealth.<br />
<br />
福利经济学第二定理实质上是福利经济学第一定理的逆转。它指出，在类似的理想假设下，任何帕累托最优都可以通过某种竞争均衡或自由市场制度获得，尽管它可能也需要一次性转移财富。<br />
<br />
<br />
<br />
== Weak Pareto efficiency{{anchor|weak}} 弱帕累托效率 ==d<br />
<br />
<br />
'''Weak Pareto optimality''' is a situation that cannot be strictly improved for ''every'' individual.<ref>{{Cite book | doi=10.1007/978-1-4020-9160-5_341|chapter = Pareto Optimality|title = Encyclopedia of Global Justice| pages=808–809|year = 2011|last1 = Mock|first1 = William B T.| isbn=978-1-4020-9159-9}}</ref> <br />
<br />
Weak Pareto optimality is a situation that cannot be strictly improved for every individual. <br />
<br />
弱帕累托最优是一种不能严格地改善每个个体的情况。<br />
<br />
<br />
<br />
Formally, we define a '''strong pareto improvement''' as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good). A situation is '''weak Pareto-optimal''' if it has no strong Pareto-improvements.<br />
<br />
Formally, we define a strong pareto improvement as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good). A situation is weak Pareto-optimal if it has no strong Pareto-improvements.<br />
<br />
在形式上，我们将强帕累托改善定义为所有主体严格处于较好状态的情况(与之相对的只是“帕累托改进” ，它要求一个主体严格处于较好状态，而其他主体至少同样良好)。没有强帕累托改进的情况是弱帕累托最优的。<br />
<br />
<br />
<br />
Any strong Pareto-improvement is also a weak Pareto-improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at 10, 0 and George values at 5, 5. Consider the allocation giving all resources to Alice, where the utility profile is (10,0).<br />
<br />
Any strong Pareto-improvement is also a weak Pareto-improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at 10, 0 and George values at 5, 5. Consider the allocation giving all resources to Alice, where the utility profile is (10,0).<br />
<br />
任何强帕累托改进也是弱帕累托改进。反之则不然; 例如，考虑一个包含两个资源的资源分配问题，Alice值为10,0，George值为5,5。考虑将所有资源分配给 Alice 的分配，它的'''<font color="#32CD32">分配方案</font>'''为(10,0)。<br />
<br />
<br />
<br />
* It is a weak-PO, since no other allocation is strictly better to both agents (there are no strong Pareto improvements). <br />
<br />
* But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5)<br />
* 它是一个弱帕累托最优，因为没有其他任何分配对上述两个主体是更优的（没有强帕累托改进）。<br />
* 但它不是一个强帕累托最优，因为这个George在其中得到第二顺位的资源的分配对George是严格更优的且对Alice是弱更优的（它是一个弱帕累托改进），它的'''<font color="#32CD32">分配方案</font>'''为(10,5)<br />
<br />
<br />
<br />
A market doesn't require [[local nonsatiation]] to get to a weak Pareto-optimum.<ref>Markey‐Towler, Brendan and John Foster. "[http://www.uq.edu.au/economics/abstract/476.pdf Why economic theory has little to say about the causes and effects of inequality]", School of Economics, [[University of Queensland]], Australia, 21 February 2013, RePEc:qld:uq2004:476</ref><br />
<br />
A market doesn't require local nonsatiation to get to a weak Pareto-optimum.<br />
<br />
市场不需要局部不饱和就能达到弱帕累托最优。<br />
<br />
<br />
<br />
== Constrained Pareto efficiency {{anchor|Constrained Pareto efficiency}} 受约束的帕累托效率 ==<br />
<br />
'''Constrained Pareto optimality''' is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.<ref>Magill, M., & [[Martine Quinzii|Quinzii, M.]], ''Theory of Incomplete Markets'', MIT Press, 2002, [https://books.google.com/books?id=d66GXq2F2M0C&pg=PA104#v=onepage&q&f=false p. 104].</ref>{{rp|104}}<br />
<br />
Constrained Pareto optimality is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.<br />
<br />
受约束的帕累托最优是帕累托最优的弱化，因为一个潜在的规划者(比如政府)可能无法改善分散市场的结果，即使这个结果是低效的。如果它受到与独立主体相同的信息或机构约束的限制，就会发生这种情况。<br />
<br />
<br />
<br />
An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in [[moral hazard]] or an [[adverse selection]] and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see [[Lindahl prices]]). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".<br />
<br />
− <br />
An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in moral hazard or an adverse selection and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see Lindahl prices). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".<br />
<br />
例如，个人拥有私人信息的情况(例如，劳动力市场中工人自己的生产率为工人所知，而潜在雇主却不知道，或者二手车市场中汽车的质量为卖方所知，而非买方所知)导致道德风险或逆向选择和次优结果。在这种情况下，希望改善局面的规划者不太可能获得市场参与者没有的任何信息。因此，计划者不能执行基于个人特质的分配规则; 例如，”如果一个人属于 a 型，他们支付 p1的价格，但如果属于 b 型，他们支付 p2的价格”(见林达尔价格)。基本上，只有隐性规则(类似于“每个人都支付价格 p”)或基于可观察行为的规则被允许; “如果任何人以价格 px 选择 x，那么他们将得到10美元的补贴，除此之外什么也得不到”。如果不存在能够成功改善市场结果的允许规则，那么该结果被称为是“受约束的帕累托最优的”。<br />
<br />
<br />
<br />
The concept of constrained Pareto optimality assumes benevolence on the part of the planner and hence is distinct from the concept of [[government failure]], which occurs when the policy making politicians fail to achieve an optimal outcome simply because they are not necessarily acting in the public's best interest.<br />
<br />
The concept of constrained Pareto optimality assumes benevolence on the part of the planner and hence is distinct from the concept of government failure, which occurs when the policy making politicians fail to achieve an optimal outcome simply because they are not necessarily acting in the public's best interest.<br />
<br />
受约束的帕累托最优的概念假定了计划者的仁慈，因此不同于政府失灵的概念。政府失灵在制定政策的政客仅仅因为他们的行为不一定符合公众的最佳利益而未能取得最佳结果时会出现。<br />
<br />
<br />
<br />
== Fractional Pareto efficiency{{anchor|fractional}} 部分帕累托效率 ==<br />
<br />
'''Fractional Pareto optimality''' is a strengthening of Pareto-optimality in the context of [[fair item allocation]]. An allocation of indivisible items is '''fractionally Pareto-optimal (fPO)''' if it is not Pareto-dominated even by an allocation in which some items are split between agents. This is in contrast to standard Pareto-optimality, which only considers domination by feasible (discrete) allocations.<ref>Barman, S., Krishnamurthy, S. K., & Vaish, R., [https://arxiv.org/pdf/1707.04731.pdf "Finding Fair and Efficient Allocations"], ''EC '18: Proceedings of the 2018 ACM Conference on Economics and Computation'', June 2018.</ref><br />
<br />
Fractional Pareto optimality is a strengthening of Pareto-optimality in the context of fair item allocation. An allocation of indivisible items is fractionally Pareto-optimal (fPO) if it is not Pareto-dominated even by an allocation in which some items are split between agents. This is in contrast to standard Pareto-optimality, which only considers domination by feasible (discrete) allocations.<br />
<br />
部分帕累托最优是在物品公平分配的背景下对帕累托最优的一个加强。 即使是在一个分配过程中，一些物品在主体之间被分配，如果一个不可分割的物品的分配不是受帕累托支配的，那么它不是部分帕累托最优(fPO)。这与标准的帕累托最优相反，因为它只考虑可行(离散)分配的控制。<br />
<br />
<br />
<br />
As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1).<br />
<br />
As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1).<br />
<br />
作为一个示例，考虑一个有两个项的项分配问题，Alice 值为3,2，George 值为4,1。考虑将第一个项目分配给 Alice，第二个项目分配给 George，其中'''<font color="#32CD32">分配方案</font>'''为(3,1)。<br />
<br />
<br />
<br />
* It is Pareto-optimal, since any other discrete allocation (without splitting items) makes someone worse-off. <br />
<br />
* However, it is not fractionally-Pareto-optimal, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George - its utility profile is (3.5, 2).<br />
* 它是一个帕累托最优，因为其他任何离散分配（在不分离物品的情况下）都会使得某个主体变差。<br />
* 但是，它不是部分帕累托最优的，因为它是受该分配帕累托支配的。它分配给了Alice第一个资源的一半和第二个资源的全部，分配给了George第一个资源的一半。它的'''<font color="#32CD32">分配方案</font>'''是(3.5,2)。<br />
<br />
<br />
<br />
== Pareto-efficiency and welfare-maximization 帕累托效率和福利最大化==<br />
<br />
{{See also|Pareto-efficient envy-free division 同见帕累托效率与无嫉妒分割}}<br />
<br />
Suppose each agent ''i'' is assigned a positive weight ''a<sub>i</sub>''. For every allocation ''x'', define the ''welfare'' of ''x'' as the weighted sum of utilities of all agents in ''x'', i.e.:<br />
<br />
Suppose each agent i is assigned a positive weight a<sub>i</sub>. For every allocation x, define the welfare of x as the weighted sum of utilities of all agents in x, i.e.:<br />
<br />
假设每个主体 ''i'' 被赋予一个正权重。对于每个分配 ''x'' ，将 ''x'' 的福利定义为 ''x'' 中所有主体的配置的加权和，即。:<br />
<br />
<br />
<br />
<math>W_a(x) := \sum_{i=1}^n a_i u_i(x)</math>.<br />
<br />
<br />
<br />
<br />
Let ''x<sub>a</sub>'' be an allocation that maximizes the welfare over all allocations, i.e.:<br />
<br />
假设是一个在所有分配中使福利最大化的分配，即:<br />
<br />
<br />
<br />
<math>x_a \in \arg \max_{x} W_a(x)</math>.<br />
<br />
<br />
<br />
<br />
It is easy to show that the allocation ''x<sub>a</sub>'' is Pareto-efficient: since all weights are positive, any Pareto-improvement would increase the sum, contradicting the definition of ''x<sub>a</sub>''.<br />
<br />
<br />
很容易证明分配是帕累托有效的: 因为所有'''<font color="#32CD32">此处需插入公式</font>'''的权重都是正的，任何帕累托改进都会增加加权和，这与'''<font color="#32CD32">此处需插入公式</font>'''的定义相矛盾。<br />
<br />
<br />
<br />
Japanese neo-[[Léon_Walras#General_equilibrium_theory|Walrasian]] economist [[Takashi Negishi]] proved<ref>{{cite journal |last=Negishi |first=Takashi |date=1960 |title=Welfare Economics and Existence of an Equilibrium for a Competitive Economy |journal=Metroeconomica |volume=12 |issue=2–3 |pages=92–97 |doi=10.1111/j.1467-999X.1960.tb00275.x }}</ref> that, under certain assumptions, the opposite is also true: for ''every'' Pareto-efficient allocation ''x'', there exists a positive vector ''a'' such that ''x'' maximizes ''W''<sub>a</sub>. A shorter proof is provided by [[Hal Varian]].<ref>{{cite journal |doi=10.1016/0047-2727(76)90018-9 |title=Two problems in the theory of fairness |journal=Journal of Public Economics |volume=5 |issue=3–4 |pages=249–260 |year=1976 |last1=Varian |first1=Hal R. |hdl=1721.1/64180 |hdl-access=free }}</ref><br />
<br />
Japanese neo-Walrasian economist Takashi Negishi proved that, under certain assumptions, the opposite is also true: for every Pareto-efficient allocation x, there exists a positive vector a such that x maximizes W<sub>a</sub>. A shorter proof is provided by Hal Varian.<br />
<br />
日本新瓦尔拉斯经济学家根岸隆史(Takashi Negishi)证明，在某些假设下,该命题的逆命题也成立，即对于每一个帕累托有效配置''x''，都存在一个正向量''a''，使最大化。哈尔·瓦里安提供了一个较短的证明。<br />
<br />
<br />
<br />
== Use in engineering 工程学上的应用==<br />
<br />
The notion of Pareto efficiency has been used in engineering.<ref>Goodarzi, E., Ziaei, M., & Hosseinipour, E. Z., ''Introduction to Optimization Analysis in Hydrosystem Engineering'' ([[Berlin]]/[[Heidelberg]]: [[Springer Science+Business Media|Springer]], 2014), [https://books.google.com/books?id=WjS8BAAAQBAJ&pg=PT111 pp. 111–148].</ref>{{rp|111–148}} Given a set of choices and a way of valuing them, the '''Pareto frontier''' or '''Pareto set''' or '''Pareto front''' is the set of choices that are Pareto efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make [[Trade-off|tradeoffs]] within this set, rather than considering the full range of every parameter.<ref>Jahan, A., Edwards, K. L., & Bahraminasab, M., ''Multi-criteria Decision Analysis'', 2nd ed. ([[Amsterdam]]: [[Elsevier]], 2013), [https://books.google.com/books?id=3mreBgAAQBAJ&pg=PA63 pp. 63–65].</ref>{{rp|63–65}}<br />
<br />
The notion of Pareto efficiency has been used in engineering. Given a set of choices and a way of valuing them, the Pareto frontier or Pareto set or Pareto front is the set of choices that are Pareto efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make tradeoffs within this set, rather than considering the full range of every parameter.<br />
<br />
帕累托最优的概念已经在工程中得到了应用。给定一组选择和一种评估它们的方法，帕累托边界、帕累托解集或帕累托前沿就是帕累托有效的选择集。通过将注意力限制在帕累托有效的选择集上，设计者可以在这个集合中进行权衡，而不是考虑每个参数的全部范围。<br />
<br />
<br />
<br />
[[File:Front pareto.svg|thumb|300px|Example of a Pareto frontier. The boxed points represent feasible choices, and smaller values are preferred to larger ones. Point ''C'' is not on the Pareto frontier because it is dominated by both point ''A'' and point ''B''. Points ''A'' and ''B'' are not strictly dominated by any other, and hence lie on the frontier.]] <br />
<br />
Example of a Pareto frontier. The boxed points represent feasible choices, and smaller values are preferred to larger ones. Point C is not on the Pareto frontier because it is dominated by both point A and point B. Points A and B are not strictly dominated by any other, and hence lie on the frontier. <br />
<br />
帕累托边界的例子。集合中的点表示可行的选择，较小的值比较大的值更好。点''C''不在帕累托边界上，因为它同时被点 ''A'' 和点 ''B'' 支配。点''A''和点''B''不受任何其他点严格控制，因此位于边界上。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）图片的格式按照[图1：英文＋译文来]<br />
<br />
[[File:Pareto Efficient Frontier 1024x1024.png|thumb|256px|A [[production-possibility frontier]]. The red line is an example of a Pareto-efficient frontier, where the frontier and the area left and below it are a continuous set of choices. The red points on the frontier are examples of Pareto-optimal choices of production. Points off the frontier, such as N and K, are not Pareto-efficient, since there exist points on the frontier which Pareto-dominate them.]]<br />
<br />
A [[production-possibility frontier. The red line is an example of a Pareto-efficient frontier, where the frontier and the area left and below it are a continuous set of choices. The red points on the frontier are examples of Pareto-optimal choices of production. Points off the frontier, such as N and K, are not Pareto-efficient, since there exist points on the frontier which Pareto-dominate them.]]<br />
<br />
生产可能性边界。红线是帕累托有效边界的一个例子，边界和左下方的区域是一个连续的选择集。边界上的红点是生产的帕累托最优选择的例子。边界外的点，如 ''N'' 和''K''，不是帕累托有效率，因为在边界上存在着受帕累托支配的点<br />
<br />
<br />
<br />
=== Pareto frontier 帕累托边界 ===<br />
<br />
For a given system, the '''Pareto frontier''' or '''Pareto set''' is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused [[Trade-off|tradeoffs]] within this constrained set of parameters, rather than needing to consider the full ranges of parameters.<ref>Costa, N. R., & Lourenço, J. A., "Exploring Pareto Frontiers in the Response Surface Methodology", in G.-C. Yang, S.-I. Ao, & L. Gelman, eds., ''Transactions on Engineering Technologies: World Congress on Engineering 2014'' (Berlin/Heidelberg: Springer, 2015), [https://books.google.com/books?id=eMElCQAAQBAJ&pg=PA398 pp. 399–412].</ref>{{rp|399–412}}<br />
<br />
For a given system, the Pareto frontier or Pareto set is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused tradeoffs within this constrained set of parameters, rather than needing to consider the full ranges of parameters.<br />
<br />
对于一个给定的系统，帕累托边界或帕累托集是所有帕累托有效的参数化(分配)的集合。找到帕累托前沿在工程学中特别有用。通过产生所有潜在的最优解决方案，设计师可以在这个受限的参数集中进行集中的权衡，而不需要考虑所有的参数。<br />
<br />
<br />
<br />
The Pareto frontier, ''P''(''Y''), may be more formally described as follows. Consider a system with function <math>f: \mathbb{R}^n \rightarrow \mathbb{R}^m</math>, where ''X'' is a [[compact space|compact set]] of feasible decisions in the [[metric space]] <math>\mathbb{R}^n</math>, and ''Y'' is the feasible set of criterion vectors in <math>\mathbb{R}^m</math>, such that <math>Y = \{ y \in \mathbb{R}^m:\; y = f(x), x \in X\;\}</math>.<br />
<br />
The Pareto frontier, P(Y), may be more formally described as follows. Consider a system with function <math>f: \mathbb{R}^n \rightarrow \mathbb{R}^m</math>, where X is a compact set of feasible decisions in the metric space <math>\mathbb{R}^n</math>, and Y is the feasible set of criterion vectors in <math>\mathbb{R}^m</math>, such that <math>Y = \{ y \in \mathbb{R}^m:\; y = f(x), x \in X\;\}</math>.<br />
<br />
帕累托边界, ''P''(''Y'') ，可以更正式地描述如下。考虑一个包含函数'''<font color="#32CD32">此处需插入公式</font>'''的系统，其中''X''是度量空间'''<font color="#32CD32">此处需插入公式</font>'''中可行决策的紧集，''Y''是'''<font color="#32CD32">此处需插入公式</font>'''中标准向量的可行集，使得'''<font color="#32CD32">此处需插入公式</font>'''。<br />
<br />
<br />
<br />
We assume that the preferred directions of criteria values are known. A point <math>y^{\prime\prime} \in \mathbb{R}^m</math> is preferred to (strictly dominates) another point <math>y^{\prime} \in \mathbb{R}^m</math>, written as <math>y^{\prime\prime} \succ y^{\prime}</math>. The Pareto frontier is thus written as:<br />
<br />
We assume that the preferred directions of criteria values are known. A point <math>y^{\prime\prime} \in \mathbb{R}^m</math> is preferred to (strictly dominates) another point <math>y^{\prime} \in \mathbb{R}^m</math>, written as <math>y^{\prime\prime} \succ y^{\prime}</math>. The Pareto frontier is thus written as:<br />
<br />
我们假设标准值的最优方向是已知的。'''<font color="#32CD32">此处需插入公式</font>'''中的一个点'''<font color="#32CD32">此处需插入公式</font>'''优于中的另一个点'''<font color="#32CD32">此处需插入公式</font>'''，写作'''<font color="#32CD32">此处需插入公式</font>'''。因此，帕累托边界可以被描述为:<br />
<br />
<br />
<br />
: <math>P(Y) = \{ y^\prime \in Y: \; \{y^{\prime\prime} \in Y:\; y^{\prime\prime} \succ y^{\prime}, y^\prime \neq y^{\prime\prime} \; \} = \empty \}. </math><br />
<br />
<math>P(Y) = \{ y^\prime \in Y: \; \{y^{\prime\prime} \in Y:\; y^{\prime\prime} \succ y^{\prime}, y^\prime \neq y^{\prime\prime} \; \} = \empty \}. </math><br />
<br />
<br />
<br />
<br />
=== Marginal rate of substitution 边际替代率 ===<br />
<br />
A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the [[marginal rate of substitution]] is the same for all consumers. A formal statement can be derived by considering a system with ''m'' consumers and ''n'' goods, and a utility function of each consumer as <math>z_i=f^i(x^i)</math> where <math>x^i=(x_1^i, x_2^i, \ldots, x_n^i)</math> is the vector of goods, both for all ''i''. The feasibility constraint is <math>\sum_{i=1}^m x_j^i = b_j</math> for <math>j=1,\ldots,n</math>. To find the Pareto optimal allocation, we maximize the [[Lagrangian mechanics|Lagrangian]]:<br />
<br />
A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the marginal rate of substitution is the same for all consumers. A formal statement can be derived by considering a system with m consumers and n goods, and a utility function of each consumer as <math>z_i=f^i(x^i)</math> where <math>x^i=(x_1^i, x_2^i, \ldots, x_n^i)</math> is the vector of goods, both for all i. The feasibility constraint is <math>\sum_{i=1}^m x_j^i = b_j</math> for <math>j=1,\ldots,n</math>. To find the Pareto optimal allocation, we maximize the Lagrangian:<br />
<br />
经济学中，帕累托边界的一个重要方面是在帕累托有效分配中，所有消费者的边际替代率是相同的。一个正式的陈述可以通过考虑一个有''m''个消费者和''n''个商品的系统，以及每个消费者的效用函数'''<font color="#32CD32">此处需插入公式</font>'''来推导出。在这个效用方程中，对所有的''i''，'''<font color="#32CD32">此处需插入公式</font>'''是商品的矢量。可行性约束为'''<font color="#32CD32">此处需插入公式</font>'''。为了找到帕累托最优分配，我们最大化拉格朗日函数:<br />
<br />
<br />
<br />
: <math>L_i((x_j^k)_{k,j}, (\lambda_k)_k, (\mu_j)_j)=f^i(x^i)+\sum_{k=2}^m \lambda_k(z_k- f^k(x^k))+\sum_{j=1}^n \mu_j \left( b_j-\sum_{k=1}^m x_j^k \right)</math><br />
<br />
<math>L_i((x_j^k)_{k,j}, (\lambda_k)_k, (\mu_j)_j)=f^i(x^i)+\sum_{k=2}^m \lambda_k(z_k- f^k(x^k))+\sum_{j=1}^n \mu_j \left( b_j-\sum_{k=1}^m x_j^k \right)</math><br />
<br />
<br />
<br />
where <math>(\lambda_k)_k</math> and <math>(\mu_j)_j</math> are the vectors of multipliers. Taking the partial derivative of the Lagrangian with respect to each good <math>x_j^k</math> for <math>j=1,\ldots,n</math> and <math>k=1,\ldots, m</math> and gives the following system of first-order conditions:<br />
<br />
where <math>(\lambda_k)_k</math> and <math>(\mu_j)_j</math> are the vectors of multipliers. Taking the partial derivative of the Lagrangian with respect to each good <math>x_j^k</math> for <math>j=1,\ldots,n</math> and <math>k=1,\ldots, m</math> and gives the following system of first-order conditions:<br />
<br />
其中'''<font color="#32CD32">此处需插入公式</font>'''和'''<font color="#32CD32">此处需插入公式</font>'''是乘子的向量。采用关于商品的拉格朗日函数的偏导数，其中，并给出以下一阶条件系统:<br />
<br />
<br />
<br />
: <math>\frac{\partial L_i}{\partial x_j^i} = f_{x^i_j}^1-\mu_j=0\text{ for }j=1,\ldots,n,</math><br />
<br />
<math>\frac{\partial L_i}{\partial x_j^i} = f_{x^i_j}^1-\mu_j=0\text{ for }j=1,\ldots,n,</math><br />
<br />
1，ldots，n，math<br />
<br />
<br />
<br />
: <math>\frac{\partial L_i}{\partial x_j^k} = -\lambda_k f_{x^k_j}^i-\mu_j=0 \text{ for }k= 2,\ldots,m \text{ and }j=1,\ldots,n,</math><br />
<br />
<math>\frac{\partial L_i}{\partial x_j^k} = -\lambda_k f_{x^k_j}^i-\mu_j=0 \text{ for }k= 2,\ldots,m \text{ and }j=1,\ldots,n,</math><br />
<br />
2，ldots，m text { and }1，ldots，n，/ math<br />
<br />
<br />
<br />
where <math>f_{x^i_j}</math> denotes the partial derivative of <math>f</math> with respect to <math>x_j^i</math>. Now, fix any <math>k\neq i</math> and <math>j,s\in \{1,\ldots,n\}</math>. The above first-order condition imply that<br />
<br />
where <math>f_{x^i_j}</math> denotes the partial derivative of <math>f</math> with respect to <math>x_j^i</math>. Now, fix any <math>k\neq i</math> and <math>j,s\in \{1,\ldots,n\}</math>. The above first-order condition imply that<br />
<br />
其中'''<font color="#32CD32">此处需插入公式</font>'''表示'''<font color="#32CD32">此处需插入公式</font>'''的偏导数。现给定'''<font color="#32CD32">此处需插入公式</font>'''。上述一阶条件意味着<br />
<br />
<br />
<br />
: <math>\frac{f_{x_j^i}^i}{f_{x_s^i}^i}=\frac{\mu_j}{\mu_s}=\frac{f_{x_j^k}^k}{f_{x_s^k}^k}.</math><br />
<br />
<math>\frac{f_{x_j^i}^i}{f_{x_s^i}^i}=\frac{\mu_j}{\mu_s}=\frac{f_{x_j^k}^k}{f_{x_s^k}^k}.</math><br />
<br />
Math frac { x ^ i } i }{ x s ^ i }} frac { mu s } f { x ^ k } ^ k } . / math<br />
<br />
<br />
<br />
Thus, in a Pareto-optimal allocation, the marginal rate of substitution must be the same for all consumers.<ref>Wilkerson, T., ''Advanced Economic Theory'' ([[Waltham Abbey]]: Edtech Press, 2018), [https://books.google.com/books?id=UtW_DwAAQBAJ&pg=PA114 p. 114].</ref>{{rp|114}}<br />
<br />
Thus, in a Pareto-optimal allocation, the marginal rate of substitution must be the same for all consumers.<br />
<br />
因此，在帕累托最优分配中，所有消费者的边际替代率必须相同。<br />
<br />
<br />
<br />
=== Computation 计算===<br />
<br />
[[Algorithm]]s for computing the Pareto frontier of a finite set of alternatives have been studied in [[computer science]] and power engineering.<ref>{{cite journal |doi=10.3390/en6031439 |last1=Tomoiagă |first1=Bogdan |last2=Chindriş |first2=Mircea |last3=Sumper |first3=Andreas |last4=Sudria-Andreu |first4=Antoni |last5=Villafafila-Robles |first5=Roberto |title=Pareto Optimal Reconfiguration of Power Distribution Systems Using a Genetic Algorithm Based on NSGA-II |journal=Energies |year=2013 |volume=6 |issue=3 |pages=1439–55 |doi-access=free }}</ref> They include:<br />
<br />
Algorithms for computing the Pareto frontier of a finite set of alternatives have been studied in computer science and power engineering. They include:<br />
<br />
计算机科学和动力工程给出了计算有限个方案集的帕累托边界的算法。它们包括:<br />
<br />
<br />
<br />
* "The maximum vector problem" or the [[Skyline operator|skyline query]].<ref>{{cite journal |doi=10.1016/0020-0190(96)00116-0 |last1=Nielsen |first1=Frank |title=Output-sensitive peeling of convex and maximal layers |journal=Information Processing Letters |volume=59 |pages=255–9 |year=1996 |issue=5 |citeseerx=10.1.1.259.1042 }}</ref><ref>{{cite journal |doi=10.1145/321906.321910 |last1=Kung |first1=H. T. |last2=Luccio |first2=F. |last3=Preparata |first3=F.P. |title=On finding the maxima of a set of vectors |journal=Journal of the ACM |volume=22 |pages=469–76 |year=1975 |issue=4 }}</ref><ref>{{cite journal |doi=10.1007/s00778-006-0029-7 |last1=Godfrey |first1=P. |last2=Shipley |first2=R. |last3=Gryz |first3=J. |journal=VLDB Journal |volume=16 |pages=5–28 |year=2006 |title=Algorithms and Analyses for Maximal Vector Computation |citeseerx=10.1.1.73.6344 }}</ref><br />
* “最大向量问题”，或称轮廓查询。<br />
<br />
* "The scalarization algorithm" or the method of weighted sums.<ref name="Kimde Weck2005">{{cite journal|last1=Kim|first1=I. Y.|last2=de Weck|first2=O. L.|title=Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation|journal=Structural and Multidisciplinary Optimization|volume=31|issue=2|year=2005|pages=105–116|issn=1615-147X|doi=10.1007/s00158-005-0557-6}}</ref><ref name="MarlerArora2009">{{cite journal|last1=Marler|first1=R. Timothy|last2=Arora|first2=Jasbir S.|title=The weighted sum method for multi-objective optimization: new insights|journal=Structural and Multidisciplinary Optimization|volume=41|issue=6|year=2009|pages=853–862|issn=1615-147X|doi=10.1007/s00158-009-0460-7}}</ref><br />
* “标量化算法”，或称加权求和法。<br />
<br />
<br />
<br />
* "The <math>\epsilon</math>-constraints method".<ref>{{cite journal|title=On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization|journal=IEEE Transactions on Systems, Man, and Cybernetics|volume=SMC-1|issue=3|year=1971|pages=296–297|issn=0018-9472|doi=10.1109/TSMC.1971.4308298}}</ref><ref name="Mavrotas2009">{{cite journal|last1=Mavrotas|first1=George|title=Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems|journal=Applied Mathematics and Computation|volume=213|issue=2|year=2009|pages=455–465|issn=00963003|doi=10.1016/j.amc.2009.03.037}}</ref><br />
* “ϵ-约束法”。<br />
<br />
<br />
<br />
== Use in biology 在生物学中的应用==<br />
<br />
Pareto optimisation has also been studied in biological processes.<ref>Moore, J. H., Hill, D. P., Sulovari, A., & Kidd, L. C., "Genetic Analysis of Prostate Cancer Using Computational Evolution, Pareto-Optimization and Post-processing", in R. Riolo, E. Vladislavleva, M. D. Ritchie, & J. H. Moore, eds., ''Genetic Programming Theory and Practice X'' (Berlin/Heidelberg: Springer, 2013), [https://books.google.co.il/books?id=YZZAAAAAQBAJ&pg=PA86 pp. 87–102].</ref>{{rp|87–102}} In bacteria, genes were shown to be either inexpensive to make (resource efficient) or easier to read (translation efficient). Natural selection acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency. Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).<ref>{{Cite journal|doi=10.1186/s13059-018-1480-7|pmid=30064467|last1=Seward|first1=Emily A. |last2=Kelly|first2=Steven|title=Selection-driven cost-efficiency optimization of transcripts modulates gene evolutionary rate in bacteria.|journal=Genome Biology|volume=19|issue=1|pages=102|year=2018|pmc=6066932}}</ref><br />
<br />
Pareto optimisation has also been studied in biological processes. In bacteria, genes were shown to be either inexpensive to make (resource efficient) or easier to read (translation efficient). Natural selection acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency. Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).<br />
<br />
帕累托最优化在生物过程中也有研究。在细菌中，基因要么生成成本低廉(资源节约型) ，要么更容易被读取(翻译效率型)。自然选择将高表达的基因推向资源利用和翻译效率的帕累托边界。帕累托边界附近基因的进化速度也较慢(这表明它们提供了一种选择优势)。<br />
<br />
<br />
<br />
== Criticism 批判 ==<br />
<br />
It would be incorrect to treat Pareto efficiency as equivalent to societal optimization,<ref>[[Jacques Drèze|Drèze, J.]], ''Essays on Economic Decisions Under Uncertainty'' ([[Cambridge]]: [[Cambridge University Press]], 1987), [https://books.google.com/books?id=LWE4AAAAIAAJ&pg=PA358 pp. 358–364]</ref>{{rp|358–364}} as the latter is a [[normative]] concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution.<ref>Backhaus, J. G., ''The Elgar Companion to Law and Economics'' ([[Cheltenham|Cheltenham, UK]] / [[Northampton, MA]]: [[Edward Elgar Publishing|Edward Elgar]], 2005), [https://books.google.com/books?id=EtguKoWHUHYC&lpg=PP1&hl=de&pg=PA10 pp. 10–15].</ref>{{rp|10–15}} An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.<ref>Paulsen, M. B., "The Economics of the Public Sector: The Nature and Role of Public Policy in the Finance of Higher Education", in M. B. Paulsen, J. C. Smart, eds. ''The Finance of Higher Education: Theory, Research, Policy, and Practice'' (New York: Agathon Press, 2001), [https://books.google.com/books?id=BlkPAy-gb8sC&pg=PA95 pp. 95–132].</ref>{{rp|95–132}}<br />
<br />
It would be incorrect to treat Pareto efficiency as equivalent to societal optimization, as the latter is a normative concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution. An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.<br />
<br />
把帕累托最优等同于社会优化是不正确的，因为后者是一个规范性概念，是一个典型的解释问题，可以解释分配不平等程度的后果。一个例子就是对一个财产税收入较低的学区和另一个财政收入较高的学区的解释，这表明在政府再分配的帮助下实现了更加平等的分配。<br />
<br />
<br />
<br />
Pareto efficiency does not require a totally equitable distribution of wealth.<ref>Bhushi, K., ed., ''Farm to Fingers: The Culture and Politics of Food in Contemporary India'' (Cambridge: Cambridge University Press, 2018), [https://books.google.com/books?id=NYJIDwAAQBAJ&pg=PA222 p. 222].</ref>{{rp|222}} An economy in which a wealthy few hold the [[Wealth condensation|vast majority of resources]] can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; often the [[status quo]] is Pareto efficient regardless of the degree to which wealth is equitably distributed. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded.<ref>Wittman, D., ''Economic Foundations of Law and Organization'' (Cambridge: Cambridge University Press, 2006), [https://books.google.com/books?id=fOolQOtKM7QC&pg=PA18 p. 18].</ref>{{rp|18}} The origin (and utility value) of the pie is conceived as immaterial in these examples. In such cases, whereby a "windfall" is gained that none of the potential distributees actually produced (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation. Wealth consolidation may exclude others from wealth accumulation because of bars to market entry, etc.<br />
<br />
Pareto efficiency does not require a totally equitable distribution of wealth. An economy in which a wealthy few hold the vast majority of resources can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; often the status quo is Pareto efficient regardless of the degree to which wealth is equitably distributed. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded. The origin (and utility value) of the pie is conceived as immaterial in these examples. In such cases, whereby a "windfall" is gained that none of the potential distributees actually produced (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation. Wealth consolidation may exclude others from wealth accumulation because of bars to market entry, etc.<br />
<br />
帕累托最优并不需要完全公平的财富分配。一个少数富人拥有绝大多数资源的经济体系可以是帕累托有效的。这种可能性是帕累托最优的固有定义; 通常情况下，无论财富的公平分配程度如何，现状都是帕累托有效的。一个简单的例子是在三个人之间分配馅饼。最公平的分配将分配给每个人三分之一。<br />
<br />
--[[用户:粲兰|袁一博]]（[[用户讨论:粲兰|讨论]]） <br />
<br />
<br />
另一种分配是两个人各占半部分，第三个人不占分毫。然而，尽管这种分配并不公平，它也是帕累托最优的，因为没有一个受者能够在不减少其他人的份额的情况下得到更优的收益; 还有其他许多这样的分配例子。帕累托无效率的馅饼分配的一个例子是三者中的每一个分得馅饼的四分之一，剩下的部分丢弃。在这些示例中，馅饼的缘由(和实用价值)被认为是无关紧要的。在这种情况下，由于潜在的分配者都没有实际生产，却获得了“意外之财”(例如，土地、继承的财产、广播频谱的一部分或其他资源) ，帕累托最优的标准并不能决定唯一的一个最优分配。由于市场准入门槛等原因，财产整合可能会将他者排除在财产积累之外。<br />
<br />
<br />
<br />
The [[liberal paradox]] elaborated by [[Amartya Sen]] shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.<ref>Sen, A., ''Rationality and Freedom'' ([[Cambridge, Massachusetts|Cambridge, MA]] / London: [[Harvard University Press|Belknep Press]], 2004), [https://books.google.cz/books?id=DaOY4DQ-MKAC&pg=PA92 pp. 92–94].</ref>{{rp|92–94}}<br />
<br />
The liberal paradox elaborated by Amartya Sen shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.<br />
<br />
阿马蒂亚·森(Amartya Sen)阐述的自由主义悖论表明，当人们对他人的行为有偏好时，帕累托最优的目标可能与个人自由的目标发生冲突。<br />
<br />
<br />
<br />
==See also 请参阅 ==<br />
<br />
* [[Admissible decision rule]], analog in [[decision theory]] 可容许决策规则，决策理论中的类比<br />
<br />
* [[Arrow's impossibility theorem]] 阿罗不可能定理<br />
<br />
* [[Bayesian efficiency]] 贝叶斯效率<br />
<br />
* [[Fundamental theorems of welfare economics]] 福利经济学基本定理<br />
<br />
* [[Deadweight loss]] 无谓损失<br />
<br />
* [[Economic efficiency]] 经济效益<br />
<br />
* [[Highest and best use]] 最佳使用<br />
<br />
* [[Kaldor–Hicks efficiency]] 卡尔多-希克斯效率<br />
<br />
* [[Market failure]], when a market result is not Pareto optimal 市场失灵，即市场结果非帕累托最优的时刻<br />
<br />
* [[Maximal element]], concept in [[order theory]] 极大元，阶理论中的概念<br />
<br />
* [[Maxima of a point set]] 点集极大值<br />
<br />
* [[Multi-objective optimization]] 多目标优化<br />
<br />
* [[Pareto-efficient envy-free division]] 帕累托有效的无嫉妒分割<br />
<br />
* ''[[Social Choice and Individual Values]]'' for the '(weak) Pareto principle' 关于弱帕累托原则的社会选择与个人价值<br />
<br />
* [[Trade-off talking rational economic person|TOTREP]] 讲究权衡的理性经济人<br />
<br />
* [[Welfare economics]] 福利经济<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）需附上编者推荐<br />
<br />
==References 参考文献==<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
== Further reading 延伸阅读 ==<br />
<br />
* {{Cite Fudenberg Tirole 1991|pages=[https://books.google.com/books?id=pFPHKwXro3QC&pg=PA18 18–23]}}<br />
<br />
* {{Cite journal |last1=Bendor | first1=Jonathan |last2= Mookherjee | first2=Dilip | title = Communitarian versus Universalistic norms | journal = [[Quarterly Journal of Political Science]] | volume = 3 | issue = 1 | pages = 33–61 | doi = 10.1561/100.00007028 | date = April 2008 | ref = harv }}<br />
<br />
* {{Cite journal | last = Kanbur | first = Ravi| author-link = Ravi Kanbur | title = Pareto's revenge | journal = Journal of Social and Economic Development | volume = 7 | issue = 1 | pages = 1–11 | date = January–June 2005 | url = http://www.arts.cornell.edu/poverty/kanbur/ParRev.pdf | ref = harv }}<br />
<br />
* {{cite book | last = Ng | first = Yew-Kwang | author-link = Yew-Kwang Ng | title = Welfare economics towards a more complete analysis | url=https://books.google.com/books?id=o-2GDAAAQBAJ&printsec=frontcover| publisher = Palgrave Macmillan | location = Basingstoke, Hampshire New York | year = 2004 | isbn = 9780333971215 }}<br />
<br />
* {{Citation | author-first1=Ariel | author-last1=Rubinstein | author-first2=Martin J. | author-last2=Osborne | author-link1 = Ariel Rubinstein | contribution = Introduction | editor-first1=Ariel | editor-last1=Rubinstein | editor-first2=Martin J. | editor-last2=Osborne | editor-link1 = Ariel Rubinstein | title = A course in game theory | pages = 6–7 | publisher = MIT Press | location = Cambridge, Massachusetts | year = 1994 | isbn = 9780262650403 }} [https://books.google.com/books?id=5ntdaYX4LPkC&pg=PA6 Book preview.]<br />
<br />
* {{Cite journal | last = Mathur | first = Vijay K. | title = How well do we know Pareto optimality? | journal = The Journal of Economic Education | volume = 22 | issue = 2 | pages = 172–178 | doi = 10.2307/1182422 | date = Spring 1991 | ref = harv | jstor = 1182422 }}<br />
<br />
* {{Cite journal | last1 = Newbery | first1 = David M.G. | last2 = Stiglitz | first2 = Joseph E. | author-link1 = David Newbery | author-link2 = Joseph Stiglitz | title = Pareto inferior trade | journal = Review of Economic Studies | volume = 51 | issue = 1 | pages = 1–12 | doi = 10.2307/2297701 | date = January 1984 | ref = harv | jstor = 2297701 }}<br />
<br />
<br />
<br />
{{Economics}}<br />
<br />
{{Game theory}}<br />
<br />
{{Voting systems}}<br />
<br />
<br />
<br />
{{Authority control}}<br />
<br />
<br />
<br />
{{DEFAULTSORT:Pareto Efficiency}}<br />
<br />
[[Category:Game theory]]<br />
<br />
Category:Game theory<br />
<br />
范畴: 博弈论<br />
<br />
[[Category:Law and economics]]<br />
<br />
Category:Law and economics<br />
<br />
类别: 法律和经济学<br />
<br />
[[Category:Welfare economics]]<br />
<br />
Category:Welfare economics<br />
<br />
类别: 福利经济学<br />
<br />
[[Category:Pareto efficiency]]<br />
<br />
Category:Pareto efficiency<br />
<br />
类别: 帕累托最优<br />
<br />
[[Category:Mathematical optimization]]<br />
<br />
Category:Mathematical optimization<br />
<br />
类别: 最优化<br />
<br />
[[Category:Electoral system criteria]]<br />
<br />
Category:Electoral system criteria<br />
<br />
类别: 选举制度标准<br />
<br />
[[Category:Vilfredo Pareto]]<br />
<br />
Category:Vilfredo Pareto<br />
<br />
类别: Vilfredo Pareto<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Pareto efficiency]]. Its edit history can be viewed at [[帕累托最优/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E7%BA%A7%E8%81%94%E5%A4%B1%E6%95%88&diff=14730级联失效2020-10-04T06:59:18Z<p>趣木木：</p>
<hr />
<div>本词条由11初步翻译<br />
<br />
{{short description|System of interconnected parts in which the failure of one or few parts can trigger the failure of others}}<br />
<br />
[[Image:Networkfailure.gif|thumb|right|An animation demonstrating how a single failure may result in other failures throughout a network.]]<br />
<br />
[[Image:Networkfailure.gif|thumb|right|演示单个故障如何导致整个网络中其他故障的动画]]<br />
<br />
An animation demonstrating how a single failure may result in other failures throughout a network.<br />
<br />
演示单个故障如何导致整个网络中其他故障的动画。<br />
<br />
A cascading failure is a process in a system of [[interconnection|interconnected]] parts in which the failure of one or few parts can trigger the failure of other parts and so on. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, transportation systems, organisms, the human body, and ecosystems.<br />
<br />
A cascading failure is a process in a system of interconnected parts in which the failure of one or few parts can trigger the failure of other parts and so on. Such a failure may happen in many types of systems, including power transmission, computer networking, finance, transportation systems, organisms, the human body, and ecosystems.<br />
<br />
'''<font color="#ff8000"> 级联故障 Cascading Failure</font>'''是一个相互连接的部件系统中的一个或几个部件的故障可以引发其他部件的故障等过程。这种故障可能发生在许多类型的系统中，包括电力输送、计算机网络、金融、交通系统、微生物、人体和生态系统。<br />
<br />
<br />
<br />
Cascading failures may occur when one part of the system fails. When this happens, other parts must then compensate for the failed component. This in turn overloads these nodes, causing them to fail as well, prompting additional nodes to fail one after another.<br />
<br />
Cascading failures may occur when one part of the system fails. When this happens, other parts must then compensate for the failed component. This in turn overloads these nodes, causing them to fail as well, prompting additional nodes to fail one after another.<br />
<br />
当系统的一部分发生故障时，可能会发生级联故障。当这种情况发生时，其他部分必须对发生故障的部分进行补偿，这反过来又使这些节点超载，导致它们也发生故障，促使更多的节点相继发生故障。<br />
<br />
<br />
<br />
== In power transmission ==<br />
在电力输送中<br />
<br />
<br />
<br />
Cascading failure is common in [[power grid]]s when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. Those nearby elements are then pushed beyond their capacity so they become overloaded and shift their load onto other elements. Cascading failure is a common effect seen in [[high voltage]] systems, where a [[single point of failure]] (SPF) on a fully loaded or slightly overloaded system results in a sudden spike across all nodes of the system. This surge current can induce the already overloaded nodes into failure, setting off more overloads and thereby taking down the entire system in a very short time.<br />
<br />
Cascading failure is common in power grids when one of the elements fails (completely or partially) and shifts its load to nearby elements in the system. Those nearby elements are then pushed beyond their capacity so they become overloaded and shift their load onto other elements. Cascading failure is a common effect seen in high voltage systems, where a single point of failure (SPF) on a fully loaded or slightly overloaded system results in a sudden spike across all nodes of the system. This surge current can induce the already overloaded nodes into failure, setting off more overloads and thereby taking down the entire system in a very short time.<br />
<br />
级联故障在电网中很常见，当其中一个元件(完全或部分)发生故障并将其负荷转移到系统中附近的元件时，就会推动那些附近的元件超出其容量，从而过载，并将其负荷转移到其他元件上。级联故障在高压系统中也很常见，在一个满载或轻度过载的系统中，一个'''<font color="#ff8000"> 单点故障 Single Point of Failure (SPF)</font>'''会导致系统所有节点突然出现尖峰。这种'''<font color="#ff8000"> 浪涌电流 <br />
Surge Current</font>'''可能会导致已经超载的节点发生故障，引发更多过载，从而在很短的时间内使整个系统瘫痪。<br />
<br />
<br />
<br />
This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. For example, under certain conditions a large power grid can collapse after the failure of a single transformer.<br />
<br />
This failure process cascades through the elements of the system like a ripple on a pond and continues until substantially all of the elements in the system are compromised and/or the system becomes functionally disconnected from the source of its load. For example, under certain conditions a large power grid can collapse after the failure of a single transformer.<br />
<br />
这个故障过程就像池塘上的涟漪一样，在系统的各个元件中层层叠加，直到系统中的所有元件都受到损害和/或系统在功能上与负载源断开。例如，在某些情况下，一个大型电网可能因为单个变压器的故障而崩溃。<br />
<br />
<br />
<br />
Monitoring the operation of a system, in [[real-time computing|real-time]], and judicious disconnection of parts can help stop a cascade. Another common technique is to calculate a safety margin for the system by computer simulation of possible failures, to establish safe operating levels below which none of the calculated scenarios is predicted to cause cascading failure, and to identify the parts of the network which are most likely to cause cascading failures.<ref name="chao">{{cite arXiv |last1=Zhai |first1=Chao |title=Modeling and Identification of Worst-Case Cascading Failures in Power Systems |eprint=1703.05232 |class=cs.SY |year=2017}}</ref><br />
<br />
Monitoring the operation of a system, in real-time, and judicious disconnection of parts can help stop a cascade. Another common technique is to calculate a safety margin for the system by computer simulation of possible failures, to establish safe operating levels below which none of the calculated scenarios is predicted to cause cascading failure, and to identify the parts of the network which are most likely to cause cascading failures.<br />
<br />
实时监测系统的运行情况，并明智地断开部件的连接，有助于阻止级联。 另一种常见的技术是通过计算机模拟可能发生的故障来计算系统的安全边际，确定安全运行水平，在此水平之下，预计计算出的任何一种情况都不会引起级联故障，并确定网络中最有可能引起级联故障的部分。<br />
<br />
<br />
<br />
One of the primary problems with preventing electrical grid failures is that the speed of the control signal is no faster than the speed of the propagating power overload, i.e. since both the control signal and the electrical power are moving at the same speed, it is not possible to isolate the outage by sending a warning ahead to isolate the element.<br />
<br />
One of the primary problems with preventing electrical grid failures is that the speed of the control signal is no faster than the speed of the propagating power overload, i.e. since both the control signal and the electrical power are moving at the same speed, it is not possible to isolate the outage by sending a warning ahead to isolate the element.<br />
<br />
防止电网故障的主要问题之一是，控制信号的速度不快于传播功率过载的速度，即由于控制信号和电力都以同样的速度运动，所以无法通过提前发出警告来隔离元件从而隔离停电。<br />
<br />
<br />
<br />
The question if power grid failures are correlated have been studied in Daqing Li et al.<ref>{{Cite journal|last=Daqing|first=Li|last2=Yinan|first2=Jiang|last3=Rui|first3=Kang|last4=Havlin|first4=Shlomo|date=2014-06-20|title=Spatial correlation analysis of cascading failures: Congestions and Blackouts|journal=Scientific Reports|language=En|volume=4|issue=1|pages=5381|doi=10.1038/srep05381|pmid=24946927|pmc=4064325|issn=2045-2322|bibcode=2014NatSR...4E5381D}}</ref> as well as by Paul DH Hines et al.<ref>{{Cite journal|last=Hines|first=Paul D. H.|last2=Dobson|first2=Ian|last3=Rezaei|first3=Pooya|date=2016|title=Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology|arxiv=1508.01775|journal=IEEE Transactions on Power Systems|pages=1|doi=10.1109/TPWRS.2016.2578259|issn=0885-8950}}</ref><br />
<br />
The question if power grid failures are correlated have been studied in Daqing Li et al. as well as by Paul DH Hines et al.<br />
<br />
电网故障是否具有相关性的问题，李大庆等人以及Paul DH Hines等人都有研究。<br />
<br />
<br />
=== Examples ===<br />
案例<br />
<br />
Cascading failure caused the following [[power outage]]s:<br />
<br />
Cascading failure caused the following power outages:<br />
<br />
级联故障曾导致以下停电:<br />
<br />
* [[Northeast blackout of 1965|Blackout in Northeast America in 1965]]<br />
* [[1965年东北大停电|1965年美国东北大停电]]<br />
<br />
* [[1999 Southern Brazil blackout|Blackout in Southern Brazil in 1999]]<br />
* [[1999年巴西南部停电|1999年巴西南部停电]]<br />
<br />
* [[Northeast blackout of 2003|Blackout in Northeast America in 2003]]<br />
* [[2003年东北大停电|2003年美国东北大停电]]<br />
<br />
* [[2003 Italy blackout|Blackout in Italy in 2003]]<br />
* [[2003年意大利停电|2003年意大利停电]]<br />
<br />
* [[2003 London blackout|Blackout in London in 2003]]<br />
* [[2003年伦敦大停电|2003年伦敦大停电]]<br />
<br />
* [[2006 European blackout|European Blackout in 2006]]<br />
* [[2006年欧洲停电|2006年欧洲停电]]<br />
<br />
* [[2012 northern India power grid failure|Blackout in Northern India in 2012]]<br />
* [[2012年印度北部电网故障|2012年印度北部停电]]<br />
<br />
* [[2016 South Australian blackout|Blackout in South Australia in 2016]]<br />
* [[2016年南澳停电|2016年南澳停电]]<br />
<br />
* [[2019 Argentina, Paraguay and Uruguay blackout|Blackout in southeast South America in 2019]]<br />
* [[2019年阿根廷、巴拉圭和乌拉圭停电|2019年南美洲东南部停电]]<br />
<br />
<br />
<br />
== In computer networks ==<br />
在计算机网络中<br />
<br />
<br />
<br />
<br />
Cascading failures can also occur in [[computer network]]s (such as the [[Internet]]) in which [[Network traffic control|network traffic]] is severely impaired or halted to or between larger sections of the network, caused by failing or disconnected hardware or software. In this context, the cascading failure is known by the term '''cascade failure'''. A cascade failure can affect large groups of people and systems.<br />
<br />
Cascading failures can also occur in computer networks (such as the Internet) in which network traffic is severely impaired or halted to or between larger sections of the network, caused by failing or disconnected hardware or software. In this context, the cascading failure is known by the term cascade failure. A cascade failure can affect large groups of people and systems.<br />
<br />
级联故障也可能发生在计算机网络(如因特网)中，由于硬件或软件的故障或断开，导致网络中较大部分的网络通信严重受损或停止。在这种情况下，级联故障被称为术语级联故障。级联故障会影响到大批人员和系统。<br />
<br />
<br />
<br />
The cause of a cascade failure is usually the overloading of a single, crucial [[Router (computing)|router]] or node, which causes the node to go down, even briefly. It can also be caused by taking a node down for maintenance or upgrades. In either case, traffic is [[routing|routed]] to or through another (alternative) path. This alternative path, as a result, becomes overloaded, causing it to go down, and so on. It will also affect systems which depend on the node for regular operation.<br />
<br />
The cause of a cascade failure is usually the overloading of a single, crucial router or node, which causes the node to go down, even briefly. It can also be caused by taking a node down for maintenance or upgrades. In either case, traffic is routed to or through another (alternative) path. This alternative path, as a result, becomes overloaded, causing it to go down, and so on. It will also affect systems which depend on the node for regular operation.<br />
<br />
级联故障的原因通常是一个单个关键的路由器或节点的超载，导致节点宕机或短暂地宕机。它也可能是由于为了维护或升级而关闭一个节点引起的。在这两种情况下，流量都被路由到或通过另一条(替代)路径。结果，这条替代路径变得过载，导致它宕机，等等。它还会影响依赖该节点正常运行的系统。<br />
<br />
<br />
<br />
=== Symptoms ===<br />
症状<br />
<br />
<br />
<br />
The symptoms of a cascade failure include: [[packet loss]] and high network [[lag|latency]], not just to single systems, but to whole sections of a network or the internet. The high latency and packet loss is caused by the nodes that fail to operate due to [[congestion collapse]], which causes them to still be present in the network but without much or any useful communication going through them. As a result, routes can still be considered valid, without them actually providing communication.<br />
<br />
The symptoms of a cascade failure include: packet loss and high network latency, not just to single systems, but to whole sections of a network or the internet. The high latency and packet loss is caused by the nodes that fail to operate due to congestion collapse, which causes them to still be present in the network but without much or any useful communication going through them. As a result, routes can still be considered valid, without them actually providing communication.<br />
<br />
级联故障的症状包括: 数据包丢失和高网络延迟，不仅仅是对单个系统，而是对整个网络或互联网部分。高延迟和数据包丢失是由于网络拥塞崩溃导致节点无法正常运行，这使得它们仍然存在于网络中，但是没有太多或任何有用的通信通过它们。因此，路由仍然可被认为是有效的，而实际上它们并没有提供通信。<br />
<br />
<br />
<br />
If enough routes go down because of a cascade failure, a complete section of the network or internet can become unreachable. Although undesired, this can help speed up the recovery from this failure as connections will time out, and other nodes will give up trying to establish connections to the section(s) that have become cut off, decreasing load on the involved nodes.<br />
<br />
If enough routes go down because of a cascade failure, a complete section of the network or internet can become unreachable. Although undesired, this can help speed up the recovery from this failure as connections will time out, and other nodes will give up trying to establish connections to the section(s) that have become cut off, decreasing load on the involved nodes.<br />
<br />
如果有足够多的路由因为级联故障而中断，网络或互联网的一个完整部分就会无法访问。尽管我们不希望出现这种情况，但这有助于加快从故障中恢复的速度，因为连接会超时，其他节点会放弃尝试与被切断的部分建立连接，从而减少相关节点的负载。<br />
<br />
<br />
<br />
A common occurrence during a cascade failure is a '''walking failure''', where sections go down, causing the next section to fail, after which the first section comes back up. This '''ripple''' can make several passes through the same sections or connecting nodes before stability is restored.<br />
<br />
A common occurrence during a cascade failure is a walking failure, where sections go down, causing the next section to fail, after which the first section comes back up. This ripple can make several passes through the same sections or connecting nodes before stability is restored.<br />
<br />
在级联故障中，一个常见的现象是行走故障，即各段下行，导致下一段故障，之后第一段回升。在恢复稳定之前，这种波纹可能会在相同的区段或连接节点上进行多次传递。<br />
<br />
<br />
=== History ===<br />
历史<br />
<br />
<br />
<br />
Cascade failures are a relatively recent development, with the massive increase in traffic and the high interconnectivity between systems and networks. The term was first applied in this context in the late 1990s by a Dutch IT professional and has slowly become a relatively common term for this kind of large-scale failure.{{Citation needed|date=January 2009}}<br />
<br />
Cascade failures are a relatively recent development, with the massive increase in traffic and the high interconnectivity between systems and networks. The term was first applied in this context in the late 1990s by a Dutch IT professional and has slowly become a relatively common term for this kind of large-scale failure.<br />
<br />
级联故障是一个相对较新的发展，随着流量的大量增加和系统与网络之间的高度互连性而出现。这个术语最早是在90年代末由一位荷兰的IT专业人员在此情况下使用的，后来慢慢成为这种大规模故障的一个比较常见的术语。<br />
<br />
<br />
<br />
<br />
=== Example ===<br />
案例<br />
<br />
<br />
<br />
Network failures typically start when a single network node fails. Initially, the traffic that would normally go through the node is stopped. Systems and users get errors about not being able to reach hosts. Usually, the redundant systems of an ISP respond very quickly, choosing another path through a different backbone. The routing path through this alternative route is longer, with more [[Hop (telecommunications)|hops]] and subsequently going through more systems that normally do not process the amount of traffic suddenly offered.<br />
<br />
Network failures typically start when a single network node fails. Initially, the traffic that would normally go through the node is stopped. Systems and users get errors about not being able to reach hosts. Usually, the redundant systems of an ISP respond very quickly, choosing another path through a different backbone. The routing path through this alternative route is longer, with more hops and subsequently going through more systems that normally do not process the amount of traffic suddenly offered.<br />
<br />
网络故障通常在单个网络节点故障时开始。最初，正常情况下会经过该节点的流量被停止。系统和用户会得到无法到达主机的错误。通常，ISP的冗余系统会很快做出反应，选择另一条通过不同骨干网的路径。通过这条替代路径的路由路径更长，跳数更多，随后要经过更多的系统，而这些系统通常不会处理突然提供的流量。<br />
<br />
<br />
<br />
This can cause one or more systems along the alternative route to go down, creating similar problems of their own.<br />
<br />
This can cause one or more systems along the alternative route to go down, creating similar problems of their own.<br />
<br />
这可能会导致替代路线上的一个或多个系统瘫痪，造成自身的类似问题。<br />
<br />
<br />
<br />
Also, related systems are affected in this case. As an example, [[Domain name system|DNS]] resolution might fail and what would normally cause systems to be interconnected, might break connections that are not even directly involved in the actual systems that went down. This, in turn, may cause seemingly unrelated nodes to develop problems, that can cause another cascade failure all on its own.<br />
<br />
Also, related systems are affected in this case. As an example, DNS resolution might fail and what would normally cause systems to be interconnected, might break connections that are not even directly involved in the actual systems that went down. This, in turn, may cause seemingly unrelated nodes to develop problems, that can cause another cascade failure all on its own.<br />
<br />
此外，在这种情况下，相关系统也会受到影响。例如，DNS解析可能会失败，通常会导致系统互连的情况可能会破坏甚至没有直接参与实际系统故障的连接。而这又可能导致看似不相关的节点出现问题，从而导致另一个级联故障的发生。<br />
<br />
<br />
<br />
In December 2012, a partial loss (40%) of [[Gmail]] service occurred globally, for 18 minutes. This loss of service was caused by a routine update of load balancing software which contained faulty logic—in this case, the error was caused by logic using an [https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ inappropriate ''all'' instead of the more appropriate ''some''.] The cascading error was fixed by fully updating a single node in the network instead of partially updating all nodes at one time.<br />
<br />
In December 2012, a partial loss (40%) of Gmail service occurred globally, for 18 minutes. This loss of service was caused by a routine update of load balancing software which contained faulty logic—in this case, the error was caused by logic using an [https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ inappropriate all instead of the more appropriate some.] The cascading error was fixed by fully updating a single node in the network instead of partially updating all nodes at one time.<br />
<br />
2012年12月，Gmail服务在全球范围内出现了部分损失(40%)，持续了18分钟。这次服务损失是由包含错误逻辑的负载平衡软件的例行更新引起的--在这种情况下，该错误是由使用[https://arstechnica.com/information-technology/2012/12/why-gmail-went-down-google-misconfigured-chromes-sync-server/ 不合适的all而不是更合适的some]的逻辑引起的。通过完全更新网络中的一个节点，而不是一次部分更新所有节点，修复了级联错误。<br />
<br />
<br />
<br />
== Cascading structural failure ==<br />
级联结构故障<br />
<br />
Certain load-bearing structures with discrete structural components can be subject to the "zipper effect", where the failure of a single structural member increases the load on adjacent members. In the case of the [[Hyatt Regency walkway collapse]], a suspended walkway (which was already overstressed due to an error in construction) failed when a single vertical suspension rod failed, overloading the neighboring rods which failed sequentially (i.e. like a [[zipper]]). A bridge that can have such a failure is called fracture critical, and numerous bridge collapses have been caused by the failure of a single part. Properly designed structures use an adequate [[factor of safety]] and/or alternate load paths to prevent this type of mechanical cascade failure.<ref name="petroski">{{cite book| title=To Engineer Is Human: The Role of Failure in Structural Design| first=Henry| last=Petroski| year=1992| isbn=978-0-679-73416-1| publisher=Vintage| place=| url-access=registration| url=https://archive.org/details/toengineerishuma00petr}}</ref><br />
<br />
Certain load-bearing structures with discrete structural components can be subject to the "zipper effect", where the failure of a single structural member increases the load on adjacent members. In the case of the Hyatt Regency walkway collapse, a suspended walkway (which was already overstressed due to an error in construction) failed when a single vertical suspension rod failed, overloading the neighboring rods which failed sequentially (i.e. like a zipper). A bridge that can have such a failure is called fracture critical, and numerous bridge collapses have been caused by the failure of a single part. Properly designed structures use an adequate factor of safety and/or alternate load paths to prevent this type of mechanical cascade failure.<br />
<br />
某些具有离散结构构件的承重结构可能会出现 "拉链效应"，即单个结构构件的失效会增加相邻构件的荷载。 在凯悦酒店人行道坍塌事件中，当单根垂直悬杆失效时，悬空的人行道（由于施工中的错误，人行道已经过度受力）失效，使相邻的悬杆超载，相邻的悬杆依次失效（像拉链一样）。一座可能发生这种破坏的桥梁被称为断裂临界桥梁，许多桥梁的坍塌都是由单一部件的故障引起的。正确设计的结构使用足够的安全系数和/或交替的荷载路径来防止这种类型的机械级联失效。<br />
<br />
<br />
<br />
== Other examples ==<br />
其他例子<br />
<br />
<br />
<br />
=== Biology ===<br />
生物<br />
<br />
<br />
[[Biochemical cascade]]s exist in biology, where a small reaction can have system-wide implications. One negative example is [[ischemic cascade]], in which a small [[ischemia|ischemic]] attack releases [[toxin]]s which kill off far more cells than the initial damage, resulting in more toxins being released. Current research is to find a way to block this cascade in [[stroke]] patients to minimize the damage.<br />
<br />
Biochemical cascades exist in biology, where a small reaction can have system-wide implications. One negative example is ischemic cascade, in which a small ischemic attack releases toxins which kill off far more cells than the initial damage, resulting in more toxins being released. Current research is to find a way to block this cascade in stroke patients to minimize the damage.<br />
<br />
生物学中存在着生化级联，一个小的反应就会对整个系统产生影响。一个负面的例子是缺血性级联反应，在这种反应中，一个小的缺血性发作释放出的毒素比最初的损伤杀死更多的细胞，导致更多的毒素被释放。目前的研究正在寻找一种方法来阻断中风患者的这种级联反应，以最大限度地减少损伤。<br />
<br />
<br />
<br />
In the study of extinction, sometimes the extinction of one species will cause many other extinctions to happen. Such a species is known as a [[keystone species]].<br />
<br />
In the study of extinction, sometimes the extinction of one species will cause many other extinctions to happen. Such a species is known as a keystone species.<br />
<br />
在物种灭绝的研究中，有时一个物种的灭绝会导致许多其他物种的灭绝。这样的物种被称为关键物种。<br />
<br />
<br />
<br />
=== Electronics ===<br />
电子学<br />
<br />
<br />
Another example is the [[Cockcroft–Walton generator]], which can also experience cascade failures wherein one failed [[diode]] can result in all the diodes failing in a fraction of a second.<br />
<br />
Another example is the Cockcroft–Walton generator, which can also experience cascade failures wherein one failed diode can result in all the diodes failing in a fraction of a second.<br />
<br />
另一个例子是Cockcroft-Walton发电机，它也会发生级联故障，其中一个故障的二极管会导致所有二极管在几分之一秒内发生故障。<br />
<br />
<br />
<br />
Yet another example of this effect in a scientific experiment was the [[Implosion (mechanical process)|implosion]] in 2001 of several thousand fragile glass photomultiplier tubes used in the [[Super-Kamiokande]] experiment, where the shock wave caused by the failure of a single detector appears to have triggered the implosion of the other detectors in a chain reaction.<br />
<br />
Yet another example of this effect in a scientific experiment was the implosion in 2001 of several thousand fragile glass photomultiplier tubes used in the Super-Kamiokande experiment, where the shock wave caused by the failure of a single detector appears to have triggered the implosion of the other detectors in a chain reaction.<br />
<br />
在科学实验中，这种效应的另一个例子是2001年用于超级神冈探测器实验中使用的几千支易碎的玻璃光电倍增管发生内爆，其中一个探测器的故障造成的冲击波似乎引发了连锁反应中其他探测器的内爆。<br />
<br />
<br />
=== Finance ===<br />
金融<br />
<br />
<br />
{{main|Systemic risk}} {{main|Cascades in financial networks}}<br />
{{主要}系统性风险}} {{主要}金融网络中的级联}}}<br />
<br />
<br />
In [[finance]], the risk of cascading failures of financial institutions is referred to as ''[[systemic risk]]:'' the failure of one financial institution may cause other financial institutions (its [[Counterparty|counterparties]]) to fail, cascading throughout the system.<ref name="HuangVodenska2013">{{cite journal|last1=Huang|first1=Xuqing|last2=Vodenska|first2=Irena|last3=Havlin|first3=Shlomo|last4=Stanley|first4=H. Eugene|title=Cascading Failures in Bi-partite Graphs: Model for Systemic Risk Propagation|journal=Scientific Reports|volume=3|pages=1219|year=2013|issn=2045-2322|doi=10.1038/srep01219|pmid=23386974|pmc=3564037|arxiv=1210.4973|bibcode=2013NatSR...3E1219H}}</ref><br />
<br />
In finance, the risk of cascading failures of financial institutions is referred to as systemic risk: the failure of one financial institution may cause other financial institutions (its counterparties) to fail, cascading throughout the system.<br />
<br />
在金融领域，金融机构连锁倒闭的风险被称为系统性风险：一家金融机构的倒闭可能会引起其他金融机构（其交易对手）的倒闭，在整个系统中连锁倒闭。<br />
<br />
Institutions that are believed to pose systemic risk are deemed either "[[too big to fail]]" (TBTF) or "too interconnected to fail" (TICTF), depending on why they appear to pose a threat.<br />
<br />
Institutions that are believed to pose systemic risk are deemed either "too big to fail" (TBTF) or "too interconnected to fail" (TICTF), depending on why they appear to pose a threat.<br />
<br />
那些被认为构成系统性风险的机构要么被视为“太大而不能倒”(TBTF) ，要么被视为“太相关而不能倒闭”(TICTF) ，这取决于它们为什么会构成威胁。<br />
<br />
<br />
<br />
Note however that systemic risk is not due to individual institutions per se, but due to the interconnections. For detailed models in economics and finance, see Elliott et al. (2014) and Acemoglu et al. (2015).<ref name="Acemoglu Ozdaglar Tahbaz-Salehi 2015 pp. 564–608">{{cite journal | last=Acemoglu | first=Daron | last2=Ozdaglar | first2=Asuman | last3=Tahbaz-Salehi | first3=Alireza | title=Systemic Risk and Stability in Financial Networks | journal=American Economic Review | publisher=American Economic Association | volume=105 | issue=2 | year=2015 | issn=0002-8282 | doi=10.1257/aer.20130456 | pages=564–608| hdl=1721.1/100979 | hdl-access=free }}</ref><ref name="Elliott Golub Jackson 2014 pp. 3115–3153">{{cite journal | last=Elliott | first=Matthew | last2=Golub | first2=Benjamin | last3=Jackson | first3=Matthew O. | title=Financial Networks and Contagion | journal=American Economic Review | publisher=American Economic Association | volume=104 | issue=10 | year=2014 | issn=0002-8282 | doi=10.1257/aer.104.10.3115 | pages=3115–3153}}</ref><br />
<br />
Note however that systemic risk is not due to individual institutions per se, but due to the interconnections. For detailed models in economics and finance, see Elliott et al. (2014) and Acemoglu et al. (2015).<br />
<br />
但请注意，系统性风险不是由于单个机构本身造成的，而是由于它们相互之间的联系。关于经济学和金融学的详细模型，请参阅Elliott等人（2014）和Acemoglu等人（2015）的文章。<br />
<br />
<br />
<br />
A related (though distinct) type of cascading failure in finance occurs in the stock market, exemplified by the [[2010 Flash Crash]].<br />
<br />
A related (though distinct) type of cascading failure in finance occurs in the stock market, exemplified by the 2010 Flash Crash.<br />
<br />
金融领域的一种相关的（但不同的）级联失败发生在股票市场，2010年的闪电崩盘就是一个例子。<br />
<br />
<br />
<br />
For another framework to study and predict the effect of cascading failures in finance see <ref>{{cite journal|last1=Li|first1=W|last2=Kenett|first2=DY|last3=Yamasaki|first3=K|last4=Stanley|first4=HE|last5=Havlin|first5=S|title=Ranking the economic importance of countries and industries|journal=Journal of Network Theory in Finance|volume=3|pages=1–17|year=2017|issn=2055-7795|doi=10.21314/JNTF.2017.031|arxiv=1408.0443}}</ref><ref name="HuangVodenska2013"/><br />
<br />
For another framework to study and predict the effect of cascading failures in finance see <br />
<br />
有关研究和预测金融连锁反应影响的另一个框架，请参见<br />
<br />
<br />
<br />
== Interdependent cascading failures ==<br />
相互依赖的级联故障<br />
<br />
<br />
[[File:Interdependent_relationship_among_different_infrastructures.tif|thumb|right|Fig. 1: Illustration of the interdependent relationship among different infrastructures]]<br />
<br />
Fig. 1: Illustration of the interdependent relationship among different infrastructures<br />
<br />
图1: 不同基础设施之间的相互依存关系的说明<br />
<br />
[[File:Schematic_demonstration_of_first-_and_second-order_percolation_transitions.tif|thumb|right|Fig. 2. Schematic demonstration of first- and second-order percolation transitions. In the second-order case, the giant component is continuously approaching zero at the percolation threshold p = p_c. In the first-order case, the giant component approaches zero discontinuously]]<br />
<br />
Fig. 2. Schematic demonstration of first- and second-order percolation transitions. In the second-order case, the giant component is continuously approaching zero at the percolation threshold p = p_c. In the first-order case, the giant component approaches zero discontinuously<br />
<br />
图2： 一阶和二阶渗流过渡的示意图。在二阶情况下，'''<font color="#32CD32">最大连通分支 giant component</font>'''在渗流阈值p=p_c时不断接近零。在一阶情况下，最大连通分支不连续地接近零。<br />
<br />
<br />
<br />
Diverse [[infrastructure]]s such as [[water supply]], [[transportation]], fuel and [[power station]]s are coupled together and depend on each other for functioning, see Fig. 1. Owing to this coupling, interdependent networks are extremely sensitive to random failures, and in particular to [[Targeted threat|targeted attacks]], such that a failure of a small fraction of nodes in one network can triger an iterative cascade of failures in several interdependent networks.<ref>{{cite web|title=Report of the Commission to Assess the Threat to the United States from Electromagnetic Pulse (EMP) Attack|url=http://empcommission.org/docs/A2473-EMP_Commission-7MB.pdf}}</ref><ref>{{Cite journal|last=Rinaldi|first=S.M.|last2=Peerenboom|first2=J.P.|last3=Kelly|first3=T.K.|date=2001|title=Identifying, understanding, and analyzing critical infrastructure interdependencies|url=|journal= IEEE Control Systems Magazine|volume=21|pages=11–25|via=}}</ref> [[Power outage|Electrical blackouts]] frequently result from a cascade of failures between interdependent networks, and the problem has been dramatically exemplified by the several large-scale blackouts that have occurred in recent years. Blackouts are a fascinating demonstration of the important role played by the dependencies between networks. For example, the [[2003 Italy blackout]] resulted in a widespread failure of the [[Rail transport|railway network]], [[Health system|health care systems]], and [[financial services]] and, in addition, severely influenced the [[telecommunication network]]s. The partial failure of the communication system in turn further impaired the [[electrical grid]] management system, thus producing a positive feedback on the power grid.<ref>{{cite journal|last=V. Rosato |first=Issacharoff, L., Tiriticco, F., Meloni, S., Porcellinis, S.D., & Setola, R. |title=Modelling interdependent infrastructures using interacting dynamical models |journal=International Journal of Critical Infrastructures |year=2008 |volume=4 |pages=63–79 |doi=10.1504/IJCIS.2008.016092 }}</ref> This example emphasizes how inter-dependence can significantly magnify the damage in an interacting network system. A framework to study the cascading failures between coupled networks based on percolation theory was developed recently.<ref>{{cite journal|last=S. V. Buldyrev|first=R. Parshani, G. Paul, H. E. Stanley, S. Havlin|title=Catastrophic cascade of failures in interdependent networks|journal=Nature|year=2010|volume=464|pages=1025–8|doi=10.1038/nature08932|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291<br />
<br />
Diverse infrastructures such as water supply, transportation, fuel and power stations are coupled together and depend on each other for functioning, see Fig. 1. Owing to this coupling, interdependent networks are extremely sensitive to random failures, and in particular to targeted attacks, such that a failure of a small fraction of nodes in one network can triger an iterative cascade of failures in several interdependent networks. Electrical blackouts frequently result from a cascade of failures between interdependent networks, and the problem has been dramatically exemplified by the several large-scale blackouts that have occurred in recent years. Blackouts are a fascinating demonstration of the important role played by the dependencies between networks. For example, the 2003 Italy blackout resulted in a widespread failure of the railway network, health care systems, and financial services and, in addition, severely influenced the telecommunication networks. The partial failure of the communication system in turn further impaired the electrical grid management system, thus producing a positive feedback on the power grid. This example emphasizes how inter-dependence can significantly magnify the damage in an interacting network system. A framework to study the cascading failures between coupled networks based on percolation theory was developed recently.<ref>{{cite journal|last=S. V. Buldyrev|first=R. Parshani, G. Paul, H. E. Stanley, S. Havlin|title=Catastrophic cascade of failures in interdependent networks|journal=Nature|year=2010|volume=464|pages=1025–8|doi=10.1038/nature08932|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291<br />
<br />
诸如供水、运输、燃料和发电站等多种基础设施都是耦合在一起的，并相互依赖着运行，见图1。 由于这种耦合，相互依存的网络对随机故障，特别是对有针对性的攻击极为敏感，因此，一个网络中一小部分节点的故障就会导致几个相互依存的网络中出现一连串的故障。电气停电经常是由相互依赖的网络之间的故障级联造成的，近年来发生的几次大规模停电事件就极大地说明了这个问题。停电是网络之间的依存关系所起的重要作用的一个引人入胜的证明。例如，2003年意大利大停电导致铁路网、医疗系统、金融服务大面积瘫痪，此外，还严重影响了电信网络。通信系统的部分故障又进一步损害了电网管理系统，从而对电网产生了正反馈。这个例子强调了在一个相互影响的网络系统中，相互依赖性是如何显著放大损害的。基于'''<font color="#ff8000"> 渗流理论 Percolation Theory</font>'''，最近发展了一个研究耦合网络之间级联故障的框架。1 = r.在相互依赖的网络中灾难性的级联故障 | 杂志 = 自然 | 年 = 2010 | 卷 = 464 | 页 = 1025-8 | doi = 10.1038/nature08932 | url = http://Havlin.biu.ac.il/publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all|pmid=20393559|issue=7291<br />
<br />
|arxiv=1012.0206|bibcode=2010Natur.464.1025B}}</ref> The cascading failures can lead to abrupt collapse compare to percolation in a single network where the breakdown of the network is continuous, see Fig. 2.<br />
<br />
|arxiv=1012.0206|bibcode=2010Natur.464.1025B}}</ref> The cascading failures can lead to abrupt collapse compare to percolation in a single network where the breakdown of the network is continuous, see Fig. 2.<br />
<br />
与级联故障可能会导致突然崩溃相比，在单一网络中，网络的崩溃是连续的，见图2。<br />
<br />
Cascading failures in spatially embedded systems have been<br />
<br />
Cascading failures in spatially embedded systems have been<br />
<br />
空间嵌入式系统中的级联故障已经成为当前研究的热点。<br />
<br />
shown to lead to extreme vulnerability.<ref name="BashanBerezin2013">{{cite journal|last1=Bashan|first1=Amir|last2=Berezin|first2=Yehiel|last3=Buldyrev|first3=Sergey V.|last4=Havlin|first4=Shlomo|title=The extreme vulnerability of interdependent spatially embedded networks|journal=Nature Physics|year=2013|issn=1745-2473|doi=10.1038/nphys2727|volume=9|issue=10|pages=667–672|arxiv=1206.2062|bibcode=2013NatPh...9..667B}}</ref> For the dynamic process of cascading failures see ref.<ref>{{Cite journal|last=Zhou|first=D.|last2=Bashan|first2=A.|last3=Cohen|first3=R.|last4=Berezin|first4=Y.|last5=Shnerb|first5=N.|last6=Havlin|first6=S.|date=2014|title=Simultaneous first- and second-order percolation transitions in interdependent networks|url=|journal=Phys. Rev. E|volume=90|issue=1|pages=012803|bibcode=2014PhRvE..90a2803Z|doi=10.1103/PhysRevE.90.012803|pmid=25122338|arxiv=1211.2330}}</ref> A model for repairing failures in order to avoid cascading failures was developed by Di Muro et al.<ref>{{Cite journal|last=Di Muro|first=M. A.|last2=La Rocca|first2=C. E.|last3=Stanley|first3=H. E.|last4=Havlin|first4=S.|last5=Braunstein|first5=L. A.|date=2016-03-09|title=Recovery of Interdependent Networks|journal=Scientific Reports|language=En|volume=6|issue=1|pages=22834|doi=10.1038/srep22834|pmid=26956773|pmc=4783785|issn=2045-2322|arxiv=1512.02555|bibcode=2016NatSR...622834D}}</ref><br />
<br />
shown to lead to extreme vulnerability. For the dynamic process of cascading failures see ref. A model for repairing failures in order to avoid cascading failures was developed by Di Muro et al.<br />
<br />
显示会导致极端的脆弱性。关于级联故障的动态过程见参考文献。Di Muro等人开发了一个修复故障的模型，以避免级联故障。<br />
<br />
<br />
Furthermore, it was shown that such systems when embedded in space are extremely vulnerable to localized attacks or failures. Above a critical radius of damage, the failure may spread to the entire system.<ref>{{Cite journal|last=Berezin|first=Yehiel|last2=Bashan|first2=Amir|last3=Danziger|first3=Michael M.|last4=Li|first4=Daqing|last5=Havlin|first5=Shlomo|date=2015-03-11|title=Localized attacks on spatially embedded networks with dependencies|journal=Scientific Reports|language=en|volume=5|issue=1|pages=8934|doi=10.1038/srep08934|pmid=25757572|pmc=4355725|issn=2045-2322|bibcode=2015NatSR...5E8934B}}</ref><br />
<br />
Furthermore, it was shown that such systems when embedded in space are extremely vulnerable to localized attacks or failures. Above a critical radius of damage, the failure may spread to the entire system.<br />
<br />
此外，研究表明，当这种系统嵌入空间时，极易受到局部攻击或故障的影响。超过临界损伤半径，故障可能扩散到整个系统。<br />
<br />
<br />
<br />
== Model for overload cascading failures ==<br />
过载级联故障模型<br />
<br />
A model for cascading failures due to overload propagation is the Motter–Lai model.<ref>{{Cite journal|last=Motter|first=A. E.|last2=Lai|first2=Y. C.|date=2002|title=Cascade-based attacks on complex networks|url=|journal=Phys. Rev. E|volume=66|issue=6 Pt 2|pages=065102|doi=10.1103/PhysRevE.66.065102|pmid=12513335|bibcode=2002PhRvE..66f5102M|arxiv=cond-mat/0301086}}</ref> The tempo-spatial propagation of such failures have been studied by Jichang Zhao et al.<ref>{{Cite journal|last=Zhao|first=J.|last2=Li|first2=D.|last3=Sanhedrai|first3=H.|last4=Cohen|first4=R.|last5=Havlin|first5=S.|date=2016|title=Spatio-temporal propagation of cascading overload failures in spatially embedded networks|url=|journal=Nature Communications|volume=7|pages=10094|bibcode=2016NatCo...710094Z|doi=10.1038/ncomms10094|pmid=26754065|pmc=4729926}}</ref><br />
<br />
A model for cascading failures due to overload propagation is the Motter–Lai model. The tempo-spatial propagation of such failures have been studied by Jichang Zhao et al.<br />
<br />
过载传播导致的级联故障的模型是Motter-Lai模型。赵继昌等人对这种故障的速度空间传播进行了研究。<br />
<br />
<br />
<br />
== See also ==<br />
请参阅<br />
<br />
{{div col}}<br />
<br />
* [[Power outage|Blackouts]]<br />
*[[停电|停电]]。<br />
<br />
* [[Brittle system]]<br />
* [[脆性系统]]<br />
<br />
* [[Butterfly effect]]<br />
* [[蝴蝶效应]]<br />
<br />
* [[Byzantine failure]]<br />
* [[拜占庭故障]]<br />
<br />
* [[Cascading rollback]]<br />
* [[级联回滚]]<br />
<br />
* [[Chain reaction]]<br />
* [[连锁反应]]<br />
<br />
* [[Chaos theory]]<br />
* [[混沌理论]]<br />
<br />
* [[Cache stampede]]<br />
* [[缓存雪崩]]<br />
<br />
<br />
* [[Congestion collapse]]<br />
* [[拥堵崩溃]]<br />
<br />
* [[Domino effect]]<br />
* [[多米诺效应]]<br />
<br />
* [[For Want of a Nail (proverb)]]<br />
* [[只因少了一颗钉子（谚语）]]<br />
<br />
* [[Interdependent networks]]<br />
* [[相互依赖的网络]]<br />
<br />
* [[Kessler Syndrome]]<br />
* [[凯斯勒综合症]]<br />
<br />
* [[Percolation theory]]<br />
* [[渗流理论]]<br />
<br />
* [[Progressive collapse]]<br />
* [[渐进式崩溃]]<br />
<br />
* [[Virtuous circle and vicious circle]]<br />
*[[良性循环和恶性循环]]<br />
<br />
* [[Wicked problem]]<br />
* [[抗解问题]]<br />
<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== References ==<br />
参考<br />
<br />
<br />
{{reflist}}<br />
<br />
<br />
<br />
== Further reading ==<br />
进一步阅读<br />
<br />
<br />
* {{cite web <br />
<br />
|url=http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf <br />
<br />
|url=http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf <br />
<br />
Http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf<br />
<br />
|title=Comparison of defense strategies for cascade breakdown on SF networks with degree correlations <br />
<br />
|title=Comparison of defense strategies for cascade breakdown on SF networks with degree correlations <br />
<br />
具有度相关性的 SF 网络级联故障的防御策略比较<br />
<br />
|author=Toshiyuki Miyazaki <br />
<br />
|author=Toshiyuki Miyazaki <br />
<br />
|author=Toshiyuki Miyazaki<br />
<br />
|date=1 March 2005 <br />
<br />
|date=1 March 2005 <br />
<br />
日期 = 2005年3月1日<br />
<br />
|url-status=dead <br />
<br />
|url-status=dead <br />
<br />
地位 = 死亡<br />
<br />
|archiveurl=https://web.archive.org/web/20090220024018/http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf <br />
<br />
|archiveurl=https://web.archive.org/web/20090220024018/http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf <br />
<br />
2012年3月24日 | archiveurl = https://web.archive.org/web/20090220024018/http://www.jaist.ac.jp/library/thesis/ks-master-2005/abstract/tmiyazak/abstract.pdf<br />
<br />
|archivedate=2009-02-20 <br />
<br />
|archivedate=2009-02-20 <br />
<br />
| archivedate = 2009-02-20<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite web<br />
<br />
|url=http://redmondmag.com/columns/print.asp?EditorialsID=1000 <br />
<br />
|url=http://redmondmag.com/columns/print.asp?EditorialsID=1000 <br />
<br />
1000 http://redmondmag.com/columns/print.asp<br />
<br />
|title=(In)Secure Shell? <br />
<br />
|title=(In)Secure Shell? <br />
<br />
| title = (In) Secure Shell? ？<br />
<br />
|accessdate=2007-09-08 <br />
<br />
|accessdate=2007-09-08 <br />
<br />
2007-09-08<br />
<br />
|author=Russ Cooper <br />
<br />
|author=Russ Cooper <br />
<br />
作者: Russ Cooper<br />
<br />
|date=1 June 2005 <br />
<br />
|date=1 June 2005 <br />
<br />
日期 = 2005年6月1日<br />
<br />
|publisher=RedmondMag.com <br />
<br />
|publisher=RedmondMag.com <br />
<br />
| publisher = RedmondMag.com<br />
<br />
|archiveurl=https://web.archive.org/web/20070928164525/http://redmondmag.com/columns/print.asp?EditorialsID=1000 <br />
<br />
|archiveurl=https://web.archive.org/web/20070928164525/http://redmondmag.com/columns/print.asp?EditorialsID=1000 <br />
<br />
1000 https://web.archive.org/web/20070928164525/http://redmondmag.com/columns/print.asp<br />
<br />
|archivedate=2007-09-28 <br />
<br />
|archivedate=2007-09-28 <br />
<br />
| archivedate = 2007-09-28<br />
<br />
|url-status=dead <br />
<br />
|url-status=dead <br />
<br />
地位 = 死亡<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
* {{cite web <br />
<br />
|url=http://www.chds.us/?research/software&d=list <br />
<br />
|url=http://www.chds.us/?research/software&d=list <br />
<br />
Http://www.chds.us/?research/software&d=list<br />
<br />
|title=Cascade Net (simulation program) <br />
<br />
|title=Cascade Net (simulation program) <br />
<br />
| title = Cascade Net (仿真程序)<br />
<br />
|accessdate=2007-09-08 <br />
<br />
|accessdate=2007-09-08 <br />
<br />
2007-09-08<br />
<br />
|author=US Department of Homeland Security <br />
<br />
|author=US Department of Homeland Security <br />
<br />
美国国土安全部<br />
<br />
|date=5 February 2007 <br />
<br />
|date=5 February 2007 <br />
<br />
| 日期 = 2007年2月5日<br />
<br />
|publisher=Center for Homeland Defense and Security <br />
<br />
|publisher=Center for Homeland Defense and Security <br />
<br />
| publisher = 国土安全防御中心<br />
<br />
|url-status=dead <br />
<br />
|url-status=dead <br />
<br />
地位 = 死亡<br />
<br />
|archiveurl=https://web.archive.org/web/20081228044520/http://www.chds.us/?research%2Fsoftware&d=list <br />
<br />
|archiveurl=https://web.archive.org/web/20081228044520/http://www.chds.us/?research%2Fsoftware&d=list <br />
<br />
2012年3月24日 | archiveurl = https://web.archive.org/web/20081228044520/http://www.chds.us/?research%2fsoftware&d=list<br />
<br />
|archivedate=2008-12-28 <br />
<br />
|archivedate=2008-12-28 <br />
<br />
| archivedate = 2008-12-28<br />
<br />
}}<br />
<br />
}}<br />
<br />
}}<br />
<br />
<br />
<br />
== External links ==<br />
<br />
* [https://web.archive.org/web/20060827050151/http://www.windows.ucar.edu/spaceweather/blackout.html Space Weather: Blackout — Massive Power Grid Failure]<br />
<br />
* [https://web.archive.org/web/20071022110507/http://vlab.infotech.monash.edu.au/simulations/networks/cascading-failure/ Cascading failure demo applet] (Monash University's Virtual Lab)<br />
<br />
* A. E. Motter and Y.-C. Lai, [http://chaos1.la.asu.edu/~yclai/papers/PRE_02_ML_3.pdf ''Cascade-based attacks on complex networks,''] Physical Review E (Rapid Communications) 66, 065102 (2002).<br />
<br />
* P. Crucitti, V. Latora and M. Marchiori, [https://pdfs.semanticscholar.org/aeda/97ccce03a5979dd4196fb7544ee0dc546f18.pdf ''Model for cascading failures in complex networks,''] Physical Review E (Rapid Communications) 69, 045104 (2004).<br />
<br />
* [https://web.archive.org/web/20040704132003/http://www.epri.com/programHigh.asp?objid=261741 Protection Strategies for Cascading Grid Failures — A Shortcut Approach]<br />
<br />
* I. Dobson, B. A. Carreras, and D. E. Newman, [https://web.archive.org/web/20060222073252/http://eceserv0.ece.wisc.edu/~dobson/PAPERS/dobsonPEIS05.pdf preprint] A loading-dependent model of probabilistic cascading failure, Probability in the Engineering and Informational Sciences, vol. 19, no. 1, January 2005, pp.&nbsp;15–32.<br />
<br />
* [https://www.pbs.org/wgbh/nova/transcripts/3105_aircrash.html Nova: Crash of Flight 111] on September 2, 1998. [[Swissair Flight 111]] flying from New York to Geneva slammed into the Atlantic Ocean off the coast of Nova Scotia with 229 people aboard. Originally believed a terrorist act. After $39 million investigation, insurance settlement of $1.5 billion and more than four years, investigators unravel the puzzle: cascading failure. What is the legacy of Swissair 111? "We have a window into the internal structure of design, checks and balances, protection, and safety." -David Evans, Editor-in-Chief of Air Safety Week.<br />
<br />
* PhysicsWeb story: [http://physicsweb.org/articles/news/5/11/9 Accident grounds neutrino lab]<br />
<br />
* [http://necsi.edu/affiliates/braha/StructureandDynamics.htm The Structure and Dynamics of Large Scale Organizational Networks (Dan Braha, New England Complex Systems Institute)]<br />
<br />
*From Single Network to Network of Networks http://havlin.biu.ac.il/Pdf/Bremen070715a.pdf<br />
<br />
<br />
<br />
{{Electricity delivery}}<br />
<br />
<br />
<br />
[[Category:Failure]]<br />
<br />
Category:Failure<br />
<br />
类别: 失败<br />
<br />
[[Category:Reliability engineering]]<br />
<br />
Category:Reliability engineering<br />
<br />
类别: 可靠度<br />
<br />
[[Category:Electric power transmission]]<br />
<br />
Category:Electric power transmission<br />
<br />
类别: 输电系统<br />
<br />
[[Category:Systemic risk]]<br />
<br />
Category:Systemic risk<br />
<br />
类别: 系统性风险<br />
<br />
[[Category:Systems science]]<br />
<br />
Category:Systems science<br />
<br />
类别: 系统科学<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Cascading failure]]. Its edit history can be viewed at [[级联故障/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E5%B8%95%E7%B4%AF%E6%89%98%E6%9C%80%E4%BC%98_Pareto_optimality&diff=14687帕累托最优 Pareto optimality2020-10-01T15:44:02Z<p>趣木木：</p>
<hr />
<div>此词条由袁一博翻译，未经人工整理和审校，带来阅读不便，请见谅。<br />
<br />
{{short description|State in which no reallocation of resources can make everyone at least as well off}}<br />
<br />
{{Use mdy dates|date=January 2016}}<br />
<br />
<br />
<br />
'''Pareto efficiency''' or '''Pareto optimality''' is a situation that cannot be modified so as to make any one individual or preference criterion better off without making at least one individual or preference criterion worse off. The concept is named after [[Vilfredo Pareto]] (1848–1923), Italian engineer and economist, who used the concept in his studies of [[economic efficiency]] and [[income distribution]]. The following three concepts are closely related:<br />
<br />
Pareto efficiency or Pareto optimality is a situation that cannot be modified so as to make any one individual or preference criterion better off without making at least one individual or preference criterion worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related:<br />
<br />
帕累托效率或帕累托最优是一种不能被修改的情况，它使得任何个体或优先准则变得更好而不使至少一个个体或一项优先准则变得更差。这个概念是以意大利工程师、经济学家维尔弗雷多·帕累托（1848-1923）的名字命名的。他在研究'''<font color="#ff8000">经济效率</font>'''和'''<font color="#ff8000">收入分配</font>'''时使用了这个概念。以下三个概念密切相关：<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）专有名词与疑难句 后面需要附上英文<br />
<br />
<br />
* Given an initial situation, a '''Pareto improvement''' is a new situation which is weakly preferred by all agents, and strictly preferred by at least one agent. In a sense, it is a unanimously-agreed improvement: if we move to the new situation, some agents will gain, and no agents will lose.<br />
<br />
* A situation is called '''Pareto dominated''' if it has a Pareto improvement. <br />
<br />
* A situation is called '''Pareto optimal''' or '''Pareto efficient''' if it is not Pareto dominated.<br />
<br />
* 在一个给定的初始条件下，一个帕累托改进指的是一种不为大多数主体所喜爱但被至少一个主体喜爱的状况。在某种意义上，它是一种一致同意的改进：如果我们处于这种新的情况下，某些主体可能获利，且没有主体会蒙受损失。<br />
*一种状况如果拥有一个帕累托改进，那么它被称作受帕累托支配的。<br />
*一种状况如果是不受帕累托支配的，那么它被称作帕累托最优的或帕累托有效的。<br />
<br />
<br />
<br />
The '''Pareto frontier''' is the set of all Pareto efficient allocations, conventionally shown [[Chart|graphically]]. It also is variously known as the '''Pareto front''' or '''Pareto set'''.<ref>{{Cite web|url=http://www.cenaero.be/Page.asp?docid=27103&|title=Pareto Front|last=proximedia|website=www.cenaero.be|access-date=2018-10-08}}</ref><br />
<br />
The Pareto frontier is the set of all Pareto efficient allocations, conventionally shown graphically. It also is variously known as the Pareto front or Pareto set.<br />
<br />
帕累托边界是所有帕累托有效分配的集合，按惯例以图表形式表示它。它也被称为帕累托前沿或帕累托集。<br />
<br />
<br />
<br />
"Pareto efficiency" is considered as a minimal notion of efficiency that does not necessarily result in a socially desirable distribution of resources: it makes no statement about [[Social equality|equality]], or the overall well-being of a society.<ref>{{cite journal |authorlink=Amartya Sen |first=A. |last=Sen |title=Markets and freedom: Achievements and limitations of the market mechanism in promoting individual freedoms |journal=Oxford Economic Papers |volume=45 |issue=4 |pages=519–541 |date=October 1993 |jstor=2663703 |url=http://www.cs.princeton.edu/courses/archive/spr06/cos444/papers/sen.pdf |doi=10.1093/oxfordjournals.oep.a042106 }}</ref><ref>{{cite book |first=N. |last=Barr |author-link=Nicholas Barr|chapter=3.2.2 The relevance of efficiency to different theories of society |title=Economics of the Welfare State |year=2012 |publisher=[[Oxford University Press]] |isbn=978-0-19-929781-8 |pages=[https://books.google.com/books?id=DOg0BM1XiqQC&pg=PA46 46–49] |edition=5th}}</ref>{{rp|46–49}} It is a necessary, but not sufficient, condition of efficiency.<br />
<br />
"Pareto efficiency" is considered as a minimal notion of efficiency that does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society. It is a necessary, but not sufficient, condition of efficiency.<br />
<br />
“帕累托最优”被认为是一种狭义的效率，它不一定产生社会所期望的资源分配: 它没有为平等或一个社会的总体福祉发声。它是效率的必要不充分条件。<br />
<br />
<br />
<br />
In addition to the context of efficiency in ''allocation'', the concept of Pareto efficiency also arises in the context of [[productive efficiency|''efficiency in production'']] vs. ''[[x-inefficiency]]'': a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.<ref>[[John D. Black|Black, J. D.]], Hashimzade, N., & [[Gareth Myles|Myles, G.]], eds., ''A Dictionary of Economics'', 5th ed. (Oxford: Oxford University Press, 2017), [https://books.google.com/books?id=WyvYDQAAQBAJ&pg=PT459 p. 459].</ref>{{rp|459}}<br />
<br />
In addition to the context of efficiency in allocation, the concept of Pareto efficiency also arises in the context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.<br />
<br />
除了分配效率的背景之外，帕累托最优的概念也出现在'''<font color="#ff8000">生产效率</font>'''对比于'''<font color="#ff8000">x-低效率</font>'''的背景之下，即如果生产投入没有可行的再分配，或者说一种产品的产出增加，而所有其他产品的产出增加或保持不变，那么一组产品的产出就是帕累托有效的。<br />
<br />
<br />
<br />
Besides economics, the notion of Pareto efficiency has been applied to the selection of alternatives in [[engineering]] and [[biology]]. Each option is first assessed, under multiple criteria, and then a subset of options is ostensibly identified with the property that no other option can categorically outperform the specified option. It is a statement of impossibility of improving one variable without harming other variables in the subject of [[multi-objective optimization]] (also termed '''Pareto optimization''').<br />
<br />
Besides economics, the notion of Pareto efficiency has been applied to the selection of alternatives in engineering and biology. Each option is first assessed, under multiple criteria, and then a subset of options is ostensibly identified with the property that no other option can categorically outperform the specified option. It is a statement of impossibility of improving one variable without harming other variables in the subject of multi-objective optimization (also termed Pareto optimization).<br />
<br />
除了经济学，帕累托最优的概念已经应用到工程和生物学中的替代品的选择。首先根据多项标准对每个选项进行评估，然后确定选项子集，其中的任何元素都具有没有其他选项可以明确胜过该元素的属性。在'''<font color="#ff8000">多目标优化</font>'''(又称帕累托优化)中，这是一种对在不损害其他变量的情况下改进一个变量的不可能性的陈述。<br />
<br />
<br />
<br />
== Overview 综述 ==<br />
<br />
<br />
<br />
<br />
"Pareto optimality" is a formally defined concept used to describe when an [[resource allocation|allocation]] is optimal. An allocation is ''not'' Pareto optimal if there is an alternative allocation where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a transfer that satisfies this condition, the reallocation is called a "Pareto improvement". When no further Pareto improvements are possible, the allocation is a "Pareto optimum".<br />
<br />
"Pareto optimality" is a formally defined concept used to describe when an allocation is optimal. An allocation is not Pareto optimal if there is an alternative allocation where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a transfer that satisfies this condition, the reallocation is called a "Pareto improvement". When no further Pareto improvements are possible, the allocation is a "Pareto optimum".<br />
<br />
“帕累托最优”是一个正式定义的概念，用来描述一个分配何时是最优的。如果有一种替代性的分配方式可以在不降低任何其他参与者福祉的情况下改善至少一个参与者的福祉，那么这种分配就不是帕累托最优的。如果有一个转移满足这个条件，这个再分配就被称为“帕累托改进”。当无法进一步实现帕累托改进时，这个分配就是“帕累托最优”。<br />
<br />
<br />
<br />
The formal presentation of the concept in an economy is as follows: Consider an economy with <math> n</math> agents and <math> k </math> goods. Then an allocation <math> \{x_1, ..., x_n\} </math>, where <math> x_i \in \mathbb{R}^k </math> for all ''i'', is ''Pareto optimal'' if there is no other feasible allocation <math> \{x_1', ..., x_n'\} </math> such that, for utility function <math> u_i </math> for each agent <math> i </math>, <math> u_i(x_i') \geq u_i(x_i) </math> for all <math> i \in \{1, ..., n\} </math> with <math> u_i(x_i') > u_i(x_i) </math> for some <math> i</math>.<ref name="AndreuMas95">{{citation|author-link=Andreu Mas-Colell|last1=Mas-Colell|first1=A.|first2=Michael D.|last2=Whinston|first3=Jerry R.|last3=Green|year=1995|title=Microeconomic Theory|chapter=Chapter 16: Equilibrium and its Basic Welfare Properties|publisher=Oxford University Press|isbn=978-0-19-510268-0|url-access=registration|url=https://archive.org/details/isbn_9780198089537}}</ref> Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption [[Vector space|vector]]s and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced.<br />
<br />
The formal presentation of the concept in an economy is as follows: Consider an economy with <math> n</math> agents and <math> k </math> goods. Then an allocation <math> \{x_1, ..., x_n\} </math>, where <math> x_i \in \mathbb{R}^k </math> for all i, is Pareto optimal if there is no other feasible allocation <math> \{x_1', ..., x_n'\} </math> such that, for utility function <math> u_i </math> for each agent <math> i </math>, <math> u_i(x_i') \geq u_i(x_i) </math> for all <math> i \in \{1, ..., n\} </math> with <math> u_i(x_i') > u_i(x_i) </math> for some <math> i</math>. Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced.<br />
<br />
这个概念在一个经济体系中的正式表现如下: 考虑一个有''n''个主体和''k''个商品的经济体系，如果没有其他可行的分配'''<font color="#32CD32">此处需插入公式</font>'''使得对于效用函数对任意主体''i''满足'''<font color="#32CD32">此处需插入公式</font>'''，它对某些个体''i''满足'''<font color="#32CD32">此处需插入公式</font>'''，那么一个分配'''<font color="#32CD32">此处需插入公式</font>'''，是 Pareto 最优的，其中对任意''i''，'''<font color="#32CD32">此处需插入公式</font>'''。在这个简单的经济体系中，“可行性”是指每种商品的分配总额不超过该经济体系中所有商品的总额。在一个有生产能力的更为复杂的经济体中，一个分配将包括消费载体和生产载体，且可行性要求每种消费品的总量不大于初始禀赋加上生产总量。<br />
<br />
<br />
<br />
In principle, a change from a generally inefficient economic allocation to an efficient one is not necessarily considered to be a Pareto improvement. Even when there are overall gains in the economy, if a single agent is disadvantaged by the reallocation, the allocation is not Pareto optimal. For instance, if a change in economic policy eliminates a monopoly and that market subsequently becomes competitive, the gain to others may be large. However, since the monopolist is disadvantaged, this is not a Pareto improvement. In theory, if the gains to the economy are larger than the loss to the monopolist, the monopolist could be compensated for its loss while still leaving a net gain for others in the economy, allowing for a Pareto improvement. Thus, in practice, to ensure that nobody is disadvantaged by a change aimed at achieving Pareto efficiency, [[compensation principle|compensation]] of one or more parties may be required. It is acknowledged, in the real world, that such compensations may have [[unintended consequences]] leading to incentive distortions over time, as agents supposedly anticipate such compensations and change their actions accordingly.<ref>See [[Ricardian equivalence]]</ref><br />
<br />
In principle, a change from a generally inefficient to an efficient one is not necessarily considered to be a Pareto improvement. Even when there are overall gains in the economy, if a single agent is disadvantaged by the reallocation, the allocation is not Pareto optimal. For instance, if a change in economic policy eliminates a monopoly and that market subsequently becomes competitive, the gain to others may be large. However, since the monopolist is disadvantaged, this is not a Pareto improvement. In theory, if the gains to the economy are larger than the loss to the monopolist, the monopolist could be compensated for its loss while still leaving a net gain for others in the economy, a Pareto improvement. Thus, in practice, to ensure that nobody is disadvantaged by a change aimed at achieving Pareto efficiency, compensation of one or more parties may be required. It is acknowledged, in the real world, that such compensations may have unintended consequences leading to incentive distortions over time, as agents supposedly anticipate such compensations and change their actions accordingly.<br />
<br />
原则上，从一个普遍低效率的经济分配到一个高效率的经济分配的转变不一定被认为是一个帕累托改进。即使经济总体是获益的，如果一个主体在再分配中处于不利地位，这个分配也不是帕累托最优的。例如，如果经济政策的某个改变消除了垄断，市场随后变得具有竞争力，那么其他主体的收益可能很大。然而，由于垄断者处于不利地位，这不是一个帕累托改善。理论上，如果经济体系的收益大于垄断者的损失，考虑到帕累托改善，垄断者可以在为经济体系中的其他主体留下净收益的情况下得到补偿。因此，在实践中，为了确保没有人会因为旨在实现帕累托最优的改变而处于不利地位，可能需要对一个或多个当事方进行补偿。在现实世界中，因为代理人可能预期这种补偿并相应地改变他们的行为，随着时间的推移，这种补偿可能会造成意外的后果以及动机的扭曲。<br />
<br />
<br />
<br />
Under the idealized conditions of the [[first welfare theorem]], a system of [[free market]]s, also called a "[[competitive equilibrium]]", leads to a Pareto-efficient outcome. It was first demonstrated mathematically by economists [[Kenneth Arrow]] and [[Gérard Debreu]].<br />
<br />
Under the idealized conditions of the first welfare theorem, a system of free markets, also called a "competitive equilibrium", leads to a Pareto-efficient outcome. It was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu.<br />
<br />
在福利经济学第一定理的理想条件下，一个自由市场系统，也称为“竞争均衡” ，对应一个帕累托有效的结果。经济学家肯尼斯·阿罗(Kenneth Arrow)和杰拉德·迪布鲁(Gérard Debreu)首先用数学方法证明了这一点。<br />
<br />
<br />
<br />
However, the result only holds under the restrictive assumptions necessary for the proof: markets exist for all possible goods, so there are no [[externality|externalities]]; all markets are in full equilibrium; markets are perfectly competitive; transaction costs are negligible; and market participants have [[perfect information]].<br />
<br />
However, the result only holds under the restrictive assumptions necessary for the proof: markets exist for all possible goods, so there are no externalities; all markets are in full equilibrium; markets are perfectly competitive; transaction costs are negligible; and market participants have perfect information.<br />
<br />
然而，这个结果只有在证明所需的限制性假设下才成立，即所有可能的商品都存在市场，因此不存在外部效应; 所有市场都处于完全均衡状态; 市场是完全竞争的; 交易成本是可忽略的; 市场参与者拥有完全的信息。<br />
<br />
<br />
<br />
In the absence of perfect information or complete markets, outcomes will generally be Pareto inefficient, per the [[Joseph Stiglitz#Information asymmetry|Greenwald-Stiglitz theorem]].<ref>{{Cite journal |doi=10.2307/1891114 |last1=Greenwald |first1=B. |last2=Stiglitz |first2=J. E. |author1-link=Bruce Greenwald |author2-link=Joseph E. Stiglitz |journal=Quarterly Journal of Economics |volume=101 |issue=2 |pages=229–64 |year=1986 |title=Externalities in economies with imperfect information and incomplete markets |jstor=1891114}}</ref><br />
<br />
In the absence of perfect information or complete markets, outcomes will generally be Pareto inefficient, per the Greenwald-Stiglitz theorem.<br />
<br />
根据 Greenwald-Stiglitz 定理，在缺乏完全信息或完全市场的情况下，这个结果通常是帕累托低效的。<br />
<br />
<br />
<br />
The [[second welfare theorem]] is essentially the reverse of the first welfare-theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some [[competitive equilibrium]], or [[free market]] system, although it may also require a [[lump-sum]] transfer of wealth.<ref name="AndreuMas95"/><br />
<br />
The second welfare theorem is essentially the reverse of the first welfare-theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some competitive equilibrium, or free market system, although it may also require a lump-sum transfer of wealth.<br />
<br />
福利经济学第二定理实质上是福利经济学第一定理的逆转。它指出，在类似的理想假设下，任何帕累托最优都可以通过某种竞争均衡或自由市场制度获得，尽管它可能也需要一次性转移财富。<br />
<br />
<br />
<br />
== Weak Pareto efficiency{{anchor|weak}} 弱帕累托效率 ==d<br />
<br />
<br />
'''Weak Pareto optimality''' is a situation that cannot be strictly improved for ''every'' individual.<ref>{{Cite book | doi=10.1007/978-1-4020-9160-5_341|chapter = Pareto Optimality|title = Encyclopedia of Global Justice| pages=808–809|year = 2011|last1 = Mock|first1 = William B T.| isbn=978-1-4020-9159-9}}</ref> <br />
<br />
Weak Pareto optimality is a situation that cannot be strictly improved for every individual. <br />
<br />
弱帕累托最优是一种不能严格地改善每个个体的情况。<br />
<br />
<br />
<br />
Formally, we define a '''strong pareto improvement''' as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good). A situation is '''weak Pareto-optimal''' if it has no strong Pareto-improvements.<br />
<br />
Formally, we define a strong pareto improvement as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good). A situation is weak Pareto-optimal if it has no strong Pareto-improvements.<br />
<br />
在形式上，我们将强帕累托改善定义为所有主体严格处于较好状态的情况(与之相对的只是“帕累托改进” ，它要求一个主体严格处于较好状态，而其他主体至少同样良好)。没有强帕累托改进的情况是弱帕累托最优的。<br />
<br />
<br />
<br />
Any strong Pareto-improvement is also a weak Pareto-improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at 10, 0 and George values at 5, 5. Consider the allocation giving all resources to Alice, where the utility profile is (10,0).<br />
<br />
Any strong Pareto-improvement is also a weak Pareto-improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at 10, 0 and George values at 5, 5. Consider the allocation giving all resources to Alice, where the utility profile is (10,0).<br />
<br />
任何强帕累托改进也是弱帕累托改进。反之则不然; 例如，考虑一个包含两个资源的资源分配问题，Alice值为10,0，George值为5,5。考虑将所有资源分配给 Alice 的分配，它的'''<font color="#32CD32">分配方案</font>'''为(10,0)。<br />
<br />
<br />
<br />
* It is a weak-PO, since no other allocation is strictly better to both agents (there are no strong Pareto improvements). <br />
<br />
* But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5)<br />
* 它是一个弱帕累托最优，因为没有其他任何分配对上述两个主体是更优的（没有强帕累托改进）。<br />
* 但它不是一个强帕累托最优，因为这个George在其中得到第二顺位的资源的分配对George是严格更优的且对Alice是弱更优的（它是一个弱帕累托改进），它的'''<font color="#32CD32">分配方案</font>'''为(10,5)<br />
<br />
<br />
<br />
A market doesn't require [[local nonsatiation]] to get to a weak Pareto-optimum.<ref>Markey‐Towler, Brendan and John Foster. "[http://www.uq.edu.au/economics/abstract/476.pdf Why economic theory has little to say about the causes and effects of inequality]", School of Economics, [[University of Queensland]], Australia, 21 February 2013, RePEc:qld:uq2004:476</ref><br />
<br />
A market doesn't require local nonsatiation to get to a weak Pareto-optimum.<br />
<br />
市场不需要局部不饱和就能达到弱的帕累托最优。<br />
<br />
<br />
<br />
== Constrained Pareto efficiency {{anchor|Constrained Pareto efficiency}} 受约束的帕累托效率 ==<br />
<br />
'''Constrained Pareto optimality''' is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.<ref>Magill, M., & [[Martine Quinzii|Quinzii, M.]], ''Theory of Incomplete Markets'', MIT Press, 2002, [https://books.google.com/books?id=d66GXq2F2M0C&pg=PA104#v=onepage&q&f=false p. 104].</ref>{{rp|104}}<br />
<br />
Constrained Pareto optimality is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.<br />
<br />
受约束的帕累托最优是帕累托最优的弱化，因为一个潜在的规划者(比如政府)可能无法改善分散市场的结果，即使这个结果是低效的。如果它受到与独立主体相同的信息或机构约束的限制，就会发生这种情况。<br />
<br />
<br />
<br />
An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in [[moral hazard]] or an [[adverse selection]] and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see [[Lindahl prices]]). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".<br />
<br />
− <br />
An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in moral hazard or an adverse selection and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see Lindahl prices). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".<br />
<br />
例如，个人拥有私人信息的情况(例如，劳动力市场中工人自己的生产率为工人所知，而潜在雇主却不知道，或者二手车市场中汽车的质量为卖方所知，而非买方所知)导致道德风险或逆向选择和次优结果。在这种情况下，希望改善局面的规划者不太可能获得市场参与者没有的任何信息。因此，计划者不能执行基于个人特质的分配规则; 例如，”如果一个人属于 a 型，他们支付 p1的价格，但如果属于 b 型，他们支付 p2的价格”(见林达尔价格)。基本上，只有隐性规则(类似于“每个人都支付价格 p”)或基于可观察行为的规则被允许; “如果任何人以价格 px 选择 x，那么他们将得到10美元的补贴，除此之外什么也得不到”。如果不存在能够成功改善市场结果的允许规则，那么该结果被称为是“受约束的帕累托最优的”。<br />
<br />
<br />
<br />
The concept of constrained Pareto optimality assumes benevolence on the part of the planner and hence is distinct from the concept of [[government failure]], which occurs when the policy making politicians fail to achieve an optimal outcome simply because they are not necessarily acting in the public's best interest.<br />
<br />
The concept of constrained Pareto optimality assumes benevolence on the part of the planner and hence is distinct from the concept of government failure, which occurs when the policy making politicians fail to achieve an optimal outcome simply because they are not necessarily acting in the public's best interest.<br />
<br />
受约束的帕累托最优的概念假定了计划者的仁慈，因此不同于政府失灵的概念。政府失灵在制定政策的政客仅仅因为他们的行为不一定符合公众的最佳利益而未能取得最佳结果时会出现。<br />
<br />
<br />
<br />
== Fractional Pareto efficiency{{anchor|fractional}} 部分帕累托效率 ==<br />
<br />
'''Fractional Pareto optimality''' is a strengthening of Pareto-optimality in the context of [[fair item allocation]]. An allocation of indivisible items is '''fractionally Pareto-optimal (fPO)''' if it is not Pareto-dominated even by an allocation in which some items are split between agents. This is in contrast to standard Pareto-optimality, which only considers domination by feasible (discrete) allocations.<ref>Barman, S., Krishnamurthy, S. K., & Vaish, R., [https://arxiv.org/pdf/1707.04731.pdf "Finding Fair and Efficient Allocations"], ''EC '18: Proceedings of the 2018 ACM Conference on Economics and Computation'', June 2018.</ref><br />
<br />
Fractional Pareto optimality is a strengthening of Pareto-optimality in the context of fair item allocation. An allocation of indivisible items is fractionally Pareto-optimal (fPO) if it is not Pareto-dominated even by an allocation in which some items are split between agents. This is in contrast to standard Pareto-optimality, which only considers domination by feasible (discrete) allocations.<br />
<br />
部分帕累托最优是在物品公平分配的背景下对帕累托最优的一个加强。 即使是在一个分配过程中，一些物品在主体之间被分配，如果一个不可分割的物品的分配不是受帕累托支配的，那么它不是部分帕累托最优(fPO)。这与标准的帕累托最优相反，因为它只考虑可行(离散)分配的控制。<br />
<br />
<br />
<br />
As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1).<br />
<br />
As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1).<br />
<br />
作为一个示例，考虑一个有两个项的项分配问题，Alice 值为3,2，George 值为4,1。考虑将第一个项目分配给 Alice，第二个项目分配给 George，其中'''<font color="#32CD32">分配方案</font>'''为(3,1)。<br />
<br />
<br />
<br />
* It is Pareto-optimal, since any other discrete allocation (without splitting items) makes someone worse-off. <br />
<br />
* However, it is not fractionally-Pareto-optimal, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George - its utility profile is (3.5, 2).<br />
* 它是一个帕累托最优，因为其他任何离散分配（在不分离物品的情况下）都会使得某个主体变差。<br />
* 但是，它不是部分帕累托最优的，因为它是受该分配帕累托支配的。它分配给了Alice第一个资源的一半和第二个资源的全部，分配给了George第一个资源的一半。它的'''<font color="#32CD32">分配方案</font>'''是(3.5,2)。<br />
<br />
<br />
<br />
== Pareto-efficiency and welfare-maximization 帕累托效率和福利最大化==<br />
<br />
{{See also|Pareto-efficient envy-free division 同见帕累托效率与无嫉妒分割}}<br />
<br />
Suppose each agent ''i'' is assigned a positive weight ''a<sub>i</sub>''. For every allocation ''x'', define the ''welfare'' of ''x'' as the weighted sum of utilities of all agents in ''x'', i.e.:<br />
<br />
Suppose each agent i is assigned a positive weight a<sub>i</sub>. For every allocation x, define the welfare of x as the weighted sum of utilities of all agents in x, i.e.:<br />
<br />
假设每个主体 ''i'' 被赋予一个正权重。对于每个分配 ''x'' ，将 ''x'' 的福利定义为 ''x'' 中所有主体的配置的加权和，即。:<br />
<br />
<br />
<br />
<math>W_a(x) := \sum_{i=1}^n a_i u_i(x)</math>.<br />
<br />
<br />
<br />
<br />
Let ''x<sub>a</sub>'' be an allocation that maximizes the welfare over all allocations, i.e.:<br />
<br />
假设是一个在所有分配中使福利最大化的分配，即:<br />
<br />
<br />
<br />
<math>x_a \in \arg \max_{x} W_a(x)</math>.<br />
<br />
<br />
<br />
<br />
It is easy to show that the allocation ''x<sub>a</sub>'' is Pareto-efficient: since all weights are positive, any Pareto-improvement would increase the sum, contradicting the definition of ''x<sub>a</sub>''.<br />
<br />
<br />
很容易证明分配是帕累托有效的: 因为所有'''<font color="#32CD32">此处需插入公式</font>'''的权重都是正的，任何帕累托改进都会增加加权和，这与'''<font color="#32CD32">此处需插入公式</font>'''的定义相矛盾。<br />
<br />
<br />
<br />
Japanese neo-[[Léon_Walras#General_equilibrium_theory|Walrasian]] economist [[Takashi Negishi]] proved<ref>{{cite journal |last=Negishi |first=Takashi |date=1960 |title=Welfare Economics and Existence of an Equilibrium for a Competitive Economy |journal=Metroeconomica |volume=12 |issue=2–3 |pages=92–97 |doi=10.1111/j.1467-999X.1960.tb00275.x }}</ref> that, under certain assumptions, the opposite is also true: for ''every'' Pareto-efficient allocation ''x'', there exists a positive vector ''a'' such that ''x'' maximizes ''W''<sub>a</sub>. A shorter proof is provided by [[Hal Varian]].<ref>{{cite journal |doi=10.1016/0047-2727(76)90018-9 |title=Two problems in the theory of fairness |journal=Journal of Public Economics |volume=5 |issue=3–4 |pages=249–260 |year=1976 |last1=Varian |first1=Hal R. |hdl=1721.1/64180 |hdl-access=free }}</ref><br />
<br />
Japanese neo-Walrasian economist Takashi Negishi proved that, under certain assumptions, the opposite is also true: for every Pareto-efficient allocation x, there exists a positive vector a such that x maximizes W<sub>a</sub>. A shorter proof is provided by Hal Varian.<br />
<br />
日本新瓦尔拉斯经济学家根岸隆史(Takashi Negishi)证明，在某些假设下,该命题的逆命题也成立，即对于每一个帕累托有效配置''x''，都存在一个正向量''a''，使最大化。哈尔·瓦里安提供了一个较短的证明。<br />
<br />
<br />
<br />
== Use in engineering 工程学上的应用==<br />
<br />
The notion of Pareto efficiency has been used in engineering.<ref>Goodarzi, E., Ziaei, M., & Hosseinipour, E. Z., ''Introduction to Optimization Analysis in Hydrosystem Engineering'' ([[Berlin]]/[[Heidelberg]]: [[Springer Science+Business Media|Springer]], 2014), [https://books.google.com/books?id=WjS8BAAAQBAJ&pg=PT111 pp. 111–148].</ref>{{rp|111–148}} Given a set of choices and a way of valuing them, the '''Pareto frontier''' or '''Pareto set''' or '''Pareto front''' is the set of choices that are Pareto efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make [[Trade-off|tradeoffs]] within this set, rather than considering the full range of every parameter.<ref>Jahan, A., Edwards, K. L., & Bahraminasab, M., ''Multi-criteria Decision Analysis'', 2nd ed. ([[Amsterdam]]: [[Elsevier]], 2013), [https://books.google.com/books?id=3mreBgAAQBAJ&pg=PA63 pp. 63–65].</ref>{{rp|63–65}}<br />
<br />
The notion of Pareto efficiency has been used in engineering. Given a set of choices and a way of valuing them, the Pareto frontier or Pareto set or Pareto front is the set of choices that are Pareto efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make tradeoffs within this set, rather than considering the full range of every parameter.<br />
<br />
帕累托最优的概念已经在工程中得到了应用。给定一组选择和一种评估它们的方法，帕累托边界、帕累托解集或帕累托前沿就是帕累托有效的选择集。通过将注意力限制在帕累托有效的选择集上，设计者可以在这个集合中进行权衡，而不是考虑每个参数的全部范围。<br />
<br />
<br />
<br />
[[File:Front pareto.svg|thumb|300px|Example of a Pareto frontier. The boxed points represent feasible choices, and smaller values are preferred to larger ones. Point ''C'' is not on the Pareto frontier because it is dominated by both point ''A'' and point ''B''. Points ''A'' and ''B'' are not strictly dominated by any other, and hence lie on the frontier.]] <br />
<br />
Example of a Pareto frontier. The boxed points represent feasible choices, and smaller values are preferred to larger ones. Point C is not on the Pareto frontier because it is dominated by both point A and point B. Points A and B are not strictly dominated by any other, and hence lie on the frontier. <br />
<br />
帕累托边界的例子。集合中的点表示可行的选择，较小的值比较大的值更好。点''C''不在帕累托边界上，因为它同时被点 ''A'' 和点 ''B'' 支配。点''A''和点''B''不受任何其他点严格控制，因此位于边界上。<br />
<br />
[[File:Pareto Efficient Frontier 1024x1024.png|thumb|256px|A [[production-possibility frontier]]. The red line is an example of a Pareto-efficient frontier, where the frontier and the area left and below it are a continuous set of choices. The red points on the frontier are examples of Pareto-optimal choices of production. Points off the frontier, such as N and K, are not Pareto-efficient, since there exist points on the frontier which Pareto-dominate them.]]<br />
<br />
A [[production-possibility frontier. The red line is an example of a Pareto-efficient frontier, where the frontier and the area left and below it are a continuous set of choices. The red points on the frontier are examples of Pareto-optimal choices of production. Points off the frontier, such as N and K, are not Pareto-efficient, since there exist points on the frontier which Pareto-dominate them.]]<br />
<br />
生产可能性边界。红线是帕累托有效边界的一个例子，边界和左下方的区域是一个连续的选择集。边界上的红点是生产的帕累托最优选择的例子。边界外的点，如 ''N'' 和''K''，不是帕累托有效率，因为在边界上存在着受帕累托支配的点<br />
<br />
<br />
<br />
=== Pareto frontier 帕累托边界 ===<br />
<br />
For a given system, the '''Pareto frontier''' or '''Pareto set''' is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused [[Trade-off|tradeoffs]] within this constrained set of parameters, rather than needing to consider the full ranges of parameters.<ref>Costa, N. R., & Lourenço, J. A., "Exploring Pareto Frontiers in the Response Surface Methodology", in G.-C. Yang, S.-I. Ao, & L. Gelman, eds., ''Transactions on Engineering Technologies: World Congress on Engineering 2014'' (Berlin/Heidelberg: Springer, 2015), [https://books.google.com/books?id=eMElCQAAQBAJ&pg=PA398 pp. 399–412].</ref>{{rp|399–412}}<br />
<br />
For a given system, the Pareto frontier or Pareto set is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused tradeoffs within this constrained set of parameters, rather than needing to consider the full ranges of parameters.<br />
<br />
对于一个给定的系统，帕累托边界或帕累托集是所有帕累托有效的参数化(分配)的集合。找到帕累托前沿在工程学中特别有用。通过产生所有潜在的最优解决方案，设计师可以在这个受限的参数集中进行集中的权衡，而不需要考虑所有的参数。<br />
<br />
<br />
<br />
The Pareto frontier, ''P''(''Y''), may be more formally described as follows. Consider a system with function <math>f: \mathbb{R}^n \rightarrow \mathbb{R}^m</math>, where ''X'' is a [[compact space|compact set]] of feasible decisions in the [[metric space]] <math>\mathbb{R}^n</math>, and ''Y'' is the feasible set of criterion vectors in <math>\mathbb{R}^m</math>, such that <math>Y = \{ y \in \mathbb{R}^m:\; y = f(x), x \in X\;\}</math>.<br />
<br />
The Pareto frontier, P(Y), may be more formally described as follows. Consider a system with function <math>f: \mathbb{R}^n \rightarrow \mathbb{R}^m</math>, where X is a compact set of feasible decisions in the metric space <math>\mathbb{R}^n</math>, and Y is the feasible set of criterion vectors in <math>\mathbb{R}^m</math>, such that <math>Y = \{ y \in \mathbb{R}^m:\; y = f(x), x \in X\;\}</math>.<br />
<br />
帕累托边界, ''P''(''Y'') ，可以更正式地描述如下。考虑一个包含函数'''<font color="#32CD32">此处需插入公式</font>'''的系统，其中''X''是度量空间'''<font color="#32CD32">此处需插入公式</font>'''中可行决策的紧集，''Y''是'''<font color="#32CD32">此处需插入公式</font>'''中标准向量的可行集，使得'''<font color="#32CD32">此处需插入公式</font>'''。<br />
<br />
<br />
<br />
We assume that the preferred directions of criteria values are known. A point <math>y^{\prime\prime} \in \mathbb{R}^m</math> is preferred to (strictly dominates) another point <math>y^{\prime} \in \mathbb{R}^m</math>, written as <math>y^{\prime\prime} \succ y^{\prime}</math>. The Pareto frontier is thus written as:<br />
<br />
We assume that the preferred directions of criteria values are known. A point <math>y^{\prime\prime} \in \mathbb{R}^m</math> is preferred to (strictly dominates) another point <math>y^{\prime} \in \mathbb{R}^m</math>, written as <math>y^{\prime\prime} \succ y^{\prime}</math>. The Pareto frontier is thus written as:<br />
<br />
我们假设标准值的最优方向是已知的。'''<font color="#32CD32">此处需插入公式</font>'''中的一个点'''<font color="#32CD32">此处需插入公式</font>'''优于中的另一个点'''<font color="#32CD32">此处需插入公式</font>'''，写作'''<font color="#32CD32">此处需插入公式</font>'''。因此，帕累托边界可以被描述为:<br />
<br />
<br />
<br />
: <math>P(Y) = \{ y^\prime \in Y: \; \{y^{\prime\prime} \in Y:\; y^{\prime\prime} \succ y^{\prime}, y^\prime \neq y^{\prime\prime} \; \} = \empty \}. </math><br />
<br />
<math>P(Y) = \{ y^\prime \in Y: \; \{y^{\prime\prime} \in Y:\; y^{\prime\prime} \succ y^{\prime}, y^\prime \neq y^{\prime\prime} \; \} = \empty \}. </math><br />
<br />
<br />
<br />
<br />
=== Marginal rate of substitution 边际替代率 ===<br />
<br />
A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the [[marginal rate of substitution]] is the same for all consumers. A formal statement can be derived by considering a system with ''m'' consumers and ''n'' goods, and a utility function of each consumer as <math>z_i=f^i(x^i)</math> where <math>x^i=(x_1^i, x_2^i, \ldots, x_n^i)</math> is the vector of goods, both for all ''i''. The feasibility constraint is <math>\sum_{i=1}^m x_j^i = b_j</math> for <math>j=1,\ldots,n</math>. To find the Pareto optimal allocation, we maximize the [[Lagrangian mechanics|Lagrangian]]:<br />
<br />
A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the marginal rate of substitution is the same for all consumers. A formal statement can be derived by considering a system with m consumers and n goods, and a utility function of each consumer as <math>z_i=f^i(x^i)</math> where <math>x^i=(x_1^i, x_2^i, \ldots, x_n^i)</math> is the vector of goods, both for all i. The feasibility constraint is <math>\sum_{i=1}^m x_j^i = b_j</math> for <math>j=1,\ldots,n</math>. To find the Pareto optimal allocation, we maximize the Lagrangian:<br />
<br />
经济学中，帕累托边界的一个重要方面是，在帕累托有效分配中，所有消费者的边际替代率是相同的。一个正式的陈述可以通过考虑一个有''m''个消费者和''n''个商品的系统，以及每个消费者的效用函数'''<font color="#32CD32">此处需插入公式</font>'''来推导出。在这个效用方程中，对所有的''i''，'''<font color="#32CD32">此处需插入公式</font>'''是商品的矢量。可行性约束为'''<font color="#32CD32">此处需插入公式</font>'''。为了找到帕累托最优分配，我们最大化拉格朗日函数:<br />
<br />
<br />
<br />
: <math>L_i((x_j^k)_{k,j}, (\lambda_k)_k, (\mu_j)_j)=f^i(x^i)+\sum_{k=2}^m \lambda_k(z_k- f^k(x^k))+\sum_{j=1}^n \mu_j \left( b_j-\sum_{k=1}^m x_j^k \right)</math><br />
<br />
<math>L_i((x_j^k)_{k,j}, (\lambda_k)_k, (\mu_j)_j)=f^i(x^i)+\sum_{k=2}^m \lambda_k(z_k- f^k(x^k))+\sum_{j=1}^n \mu_j \left( b_j-\sum_{k=1}^m x_j^k \right)</math><br />
<br />
<br />
<br />
where <math>(\lambda_k)_k</math> and <math>(\mu_j)_j</math> are the vectors of multipliers. Taking the partial derivative of the Lagrangian with respect to each good <math>x_j^k</math> for <math>j=1,\ldots,n</math> and <math>k=1,\ldots, m</math> and gives the following system of first-order conditions:<br />
<br />
where <math>(\lambda_k)_k</math> and <math>(\mu_j)_j</math> are the vectors of multipliers. Taking the partial derivative of the Lagrangian with respect to each good <math>x_j^k</math> for <math>j=1,\ldots,n</math> and <math>k=1,\ldots, m</math> and gives the following system of first-order conditions:<br />
<br />
其中'''<font color="#32CD32">此处需插入公式</font>'''和'''<font color="#32CD32">此处需插入公式</font>'''是乘子的向量。采用关于商品的拉格朗日函数的偏导数，其中，并给出以下一阶条件系统:<br />
<br />
<br />
<br />
: <math>\frac{\partial L_i}{\partial x_j^i} = f_{x^i_j}^1-\mu_j=0\text{ for }j=1,\ldots,n,</math><br />
<br />
<math>\frac{\partial L_i}{\partial x_j^i} = f_{x^i_j}^1-\mu_j=0\text{ for }j=1,\ldots,n,</math><br />
<br />
1，ldots，n，math<br />
<br />
<br />
<br />
: <math>\frac{\partial L_i}{\partial x_j^k} = -\lambda_k f_{x^k_j}^i-\mu_j=0 \text{ for }k= 2,\ldots,m \text{ and }j=1,\ldots,n,</math><br />
<br />
<math>\frac{\partial L_i}{\partial x_j^k} = -\lambda_k f_{x^k_j}^i-\mu_j=0 \text{ for }k= 2,\ldots,m \text{ and }j=1,\ldots,n,</math><br />
<br />
2，ldots，m text { and }1，ldots，n，/ math<br />
<br />
<br />
<br />
where <math>f_{x^i_j}</math> denotes the partial derivative of <math>f</math> with respect to <math>x_j^i</math>. Now, fix any <math>k\neq i</math> and <math>j,s\in \{1,\ldots,n\}</math>. The above first-order condition imply that<br />
<br />
where <math>f_{x^i_j}</math> denotes the partial derivative of <math>f</math> with respect to <math>x_j^i</math>. Now, fix any <math>k\neq i</math> and <math>j,s\in \{1,\ldots,n\}</math>. The above first-order condition imply that<br />
<br />
其中'''<font color="#32CD32">此处需插入公式</font>'''表示'''<font color="#32CD32">此处需插入公式</font>'''的偏导数。现给定'''<font color="#32CD32">此处需插入公式</font>'''。上述一阶条件意味着<br />
<br />
<br />
<br />
: <math>\frac{f_{x_j^i}^i}{f_{x_s^i}^i}=\frac{\mu_j}{\mu_s}=\frac{f_{x_j^k}^k}{f_{x_s^k}^k}.</math><br />
<br />
<math>\frac{f_{x_j^i}^i}{f_{x_s^i}^i}=\frac{\mu_j}{\mu_s}=\frac{f_{x_j^k}^k}{f_{x_s^k}^k}.</math><br />
<br />
Math frac { x ^ i } i }{ x s ^ i }} frac { mu s } f { x ^ k } ^ k } . / math<br />
<br />
<br />
<br />
Thus, in a Pareto-optimal allocation, the marginal rate of substitution must be the same for all consumers.<ref>Wilkerson, T., ''Advanced Economic Theory'' ([[Waltham Abbey]]: Edtech Press, 2018), [https://books.google.com/books?id=UtW_DwAAQBAJ&pg=PA114 p. 114].</ref>{{rp|114}}<br />
<br />
Thus, in a Pareto-optimal allocation, the marginal rate of substitution must be the same for all consumers.<br />
<br />
因此，在帕累托最优分配中，所有消费者的边际替代率必须相同。<br />
<br />
<br />
<br />
=== Computation 计算===<br />
<br />
[[Algorithm]]s for computing the Pareto frontier of a finite set of alternatives have been studied in [[computer science]] and power engineering.<ref>{{cite journal |doi=10.3390/en6031439 |last1=Tomoiagă |first1=Bogdan |last2=Chindriş |first2=Mircea |last3=Sumper |first3=Andreas |last4=Sudria-Andreu |first4=Antoni |last5=Villafafila-Robles |first5=Roberto |title=Pareto Optimal Reconfiguration of Power Distribution Systems Using a Genetic Algorithm Based on NSGA-II |journal=Energies |year=2013 |volume=6 |issue=3 |pages=1439–55 |doi-access=free }}</ref> They include:<br />
<br />
Algorithms for computing the Pareto frontier of a finite set of alternatives have been studied in computer science and power engineering. They include:<br />
<br />
计算机科学和动力工程给出了计算有限个方案集的帕累托边界的算法。它们包括:<br />
<br />
<br />
<br />
* "The maximum vector problem" or the [[Skyline operator|skyline query]].<ref>{{cite journal |doi=10.1016/0020-0190(96)00116-0 |last1=Nielsen |first1=Frank |title=Output-sensitive peeling of convex and maximal layers |journal=Information Processing Letters |volume=59 |pages=255–9 |year=1996 |issue=5 |citeseerx=10.1.1.259.1042 }}</ref><ref>{{cite journal |doi=10.1145/321906.321910 |last1=Kung |first1=H. T. |last2=Luccio |first2=F. |last3=Preparata |first3=F.P. |title=On finding the maxima of a set of vectors |journal=Journal of the ACM |volume=22 |pages=469–76 |year=1975 |issue=4 }}</ref><ref>{{cite journal |doi=10.1007/s00778-006-0029-7 |last1=Godfrey |first1=P. |last2=Shipley |first2=R. |last3=Gryz |first3=J. |journal=VLDB Journal |volume=16 |pages=5–28 |year=2006 |title=Algorithms and Analyses for Maximal Vector Computation |citeseerx=10.1.1.73.6344 }}</ref><br />
* “最大向量问题”，或称轮廓查询。<br />
<br />
* "The scalarization algorithm" or the method of weighted sums.<ref name="Kimde Weck2005">{{cite journal|last1=Kim|first1=I. Y.|last2=de Weck|first2=O. L.|title=Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation|journal=Structural and Multidisciplinary Optimization|volume=31|issue=2|year=2005|pages=105–116|issn=1615-147X|doi=10.1007/s00158-005-0557-6}}</ref><ref name="MarlerArora2009">{{cite journal|last1=Marler|first1=R. Timothy|last2=Arora|first2=Jasbir S.|title=The weighted sum method for multi-objective optimization: new insights|journal=Structural and Multidisciplinary Optimization|volume=41|issue=6|year=2009|pages=853–862|issn=1615-147X|doi=10.1007/s00158-009-0460-7}}</ref><br />
* “标量化算法”，或称加权求和法。<br />
<br />
<br />
<br />
* "The <math>\epsilon</math>-constraints method".<ref>{{cite journal|title=On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization|journal=IEEE Transactions on Systems, Man, and Cybernetics|volume=SMC-1|issue=3|year=1971|pages=296–297|issn=0018-9472|doi=10.1109/TSMC.1971.4308298}}</ref><ref name="Mavrotas2009">{{cite journal|last1=Mavrotas|first1=George|title=Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems|journal=Applied Mathematics and Computation|volume=213|issue=2|year=2009|pages=455–465|issn=00963003|doi=10.1016/j.amc.2009.03.037}}</ref><br />
* “ϵ-约束法”。<br />
<br />
<br />
<br />
== Use in biology 在生物学中的应用==<br />
<br />
Pareto optimisation has also been studied in biological processes.<ref>Moore, J. H., Hill, D. P., Sulovari, A., & Kidd, L. C., "Genetic Analysis of Prostate Cancer Using Computational Evolution, Pareto-Optimization and Post-processing", in R. Riolo, E. Vladislavleva, M. D. Ritchie, & J. H. Moore, eds., ''Genetic Programming Theory and Practice X'' (Berlin/Heidelberg: Springer, 2013), [https://books.google.co.il/books?id=YZZAAAAAQBAJ&pg=PA86 pp. 87–102].</ref>{{rp|87–102}} In bacteria, genes were shown to be either inexpensive to make (resource efficient) or easier to read (translation efficient). Natural selection acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency. Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).<ref>{{Cite journal|doi=10.1186/s13059-018-1480-7|pmid=30064467|last1=Seward|first1=Emily A. |last2=Kelly|first2=Steven|title=Selection-driven cost-efficiency optimization of transcripts modulates gene evolutionary rate in bacteria.|journal=Genome Biology|volume=19|issue=1|pages=102|year=2018|pmc=6066932}}</ref><br />
<br />
Pareto optimisation has also been studied in biological processes. In bacteria, genes were shown to be either inexpensive to make (resource efficient) or easier to read (translation efficient). Natural selection acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency. Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).<br />
<br />
帕累托最优化在生物过程中也有研究。在细菌中，基因要么生成成本低廉(资源节约型) ，要么更容易被读取(翻译效率型)。自然选择将高表达的基因推向资源利用和翻译效率的帕累托边界。帕累托边界附近基因的进化速度也较慢(这表明它们提供了一种选择优势)。<br />
<br />
<br />
<br />
== Criticism 批判 ==<br />
<br />
It would be incorrect to treat Pareto efficiency as equivalent to societal optimization,<ref>[[Jacques Drèze|Drèze, J.]], ''Essays on Economic Decisions Under Uncertainty'' ([[Cambridge]]: [[Cambridge University Press]], 1987), [https://books.google.com/books?id=LWE4AAAAIAAJ&pg=PA358 pp. 358–364]</ref>{{rp|358–364}} as the latter is a [[normative]] concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution.<ref>Backhaus, J. G., ''The Elgar Companion to Law and Economics'' ([[Cheltenham|Cheltenham, UK]] / [[Northampton, MA]]: [[Edward Elgar Publishing|Edward Elgar]], 2005), [https://books.google.com/books?id=EtguKoWHUHYC&lpg=PP1&hl=de&pg=PA10 pp. 10–15].</ref>{{rp|10–15}} An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.<ref>Paulsen, M. B., "The Economics of the Public Sector: The Nature and Role of Public Policy in the Finance of Higher Education", in M. B. Paulsen, J. C. Smart, eds. ''The Finance of Higher Education: Theory, Research, Policy, and Practice'' (New York: Agathon Press, 2001), [https://books.google.com/books?id=BlkPAy-gb8sC&pg=PA95 pp. 95–132].</ref>{{rp|95–132}}<br />
<br />
It would be incorrect to treat Pareto efficiency as equivalent to societal optimization, as the latter is a normative concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution. An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.<br />
<br />
把帕累托最优等同于社会优化是不正确的，因为后者是一个规范性概念，是一个典型的解释问题，可以解释分配不平等程度的后果。一个例子就是对一个财产税收入较低的学区和另一个财政收入较高的学区的解释，这表明在政府再分配的帮助下实现了更加平等的分配。<br />
<br />
<br />
<br />
Pareto efficiency does not require a totally equitable distribution of wealth.<ref>Bhushi, K., ed., ''Farm to Fingers: The Culture and Politics of Food in Contemporary India'' (Cambridge: Cambridge University Press, 2018), [https://books.google.com/books?id=NYJIDwAAQBAJ&pg=PA222 p. 222].</ref>{{rp|222}} An economy in which a wealthy few hold the [[Wealth condensation|vast majority of resources]] can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; often the [[status quo]] is Pareto efficient regardless of the degree to which wealth is equitably distributed. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded.<ref>Wittman, D., ''Economic Foundations of Law and Organization'' (Cambridge: Cambridge University Press, 2006), [https://books.google.com/books?id=fOolQOtKM7QC&pg=PA18 p. 18].</ref>{{rp|18}} The origin (and utility value) of the pie is conceived as immaterial in these examples. In such cases, whereby a "windfall" is gained that none of the potential distributees actually produced (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation. Wealth consolidation may exclude others from wealth accumulation because of bars to market entry, etc.<br />
<br />
Pareto efficiency does not require a totally equitable distribution of wealth. An economy in which a wealthy few hold the vast majority of resources can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; often the status quo is Pareto efficient regardless of the degree to which wealth is equitably distributed. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded. The origin (and utility value) of the pie is conceived as immaterial in these examples. In such cases, whereby a "windfall" is gained that none of the potential distributees actually produced (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation. Wealth consolidation may exclude others from wealth accumulation because of bars to market entry, etc.<br />
<br />
帕累托最优并不需要完全公平的财富分配。一个少数富人拥有绝大多数资源的经济体系可以是帕累托有效的。这种可能性是帕累托最优的固有定义; 通常情况下，无论财富的公平分配程度如何，现状都是帕累托有效的。一个简单的例子是在三个人之间分配馅饼。最公平的分配将分配给每个人三分之一。--[[用户:粲兰|袁一博]]（[[用户讨论:粲兰|讨论]]） <br />
另一种分配是两个人各占半部分，第三个人不占分毫。然而，尽管这种分配并不公平，它也是帕累托最优的，因为没有一个受者能够在不减少其他人的份额的情况下得到更优的收益; 还有其他许多这样的分配例子。帕累托无效率的馅饼分配的一个例子是三者中的每一个分得馅饼的四分之一，剩下的部分丢弃。在这些示例中，馅饼的缘由(和实用价值)被认为是无关紧要的。在这种情况下，由于潜在的分配者都没有实际生产，却获得了“意外之财”(例如，土地、继承的财产、广播频谱的一部分或其他资源) ，帕累托最优的标准并不能决定唯一的一个最优分配。由于市场准入门槛等原因，财产整合可能会将他者排除在财产积累之外。<br />
<br />
<br />
<br />
The [[liberal paradox]] elaborated by [[Amartya Sen]] shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.<ref>Sen, A., ''Rationality and Freedom'' ([[Cambridge, Massachusetts|Cambridge, MA]] / London: [[Harvard University Press|Belknep Press]], 2004), [https://books.google.cz/books?id=DaOY4DQ-MKAC&pg=PA92 pp. 92–94].</ref>{{rp|92–94}}<br />
<br />
The liberal paradox elaborated by Amartya Sen shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.<br />
<br />
阿马蒂亚·森(Amartya Sen)阐述的自由主义悖论表明，当人们对他人的行为有偏好时，帕累托最优的目标可能与个人自由的目标发生冲突。<br />
<br />
<br />
<br />
==See also 请参阅 ==<br />
<br />
* [[Admissible decision rule]], analog in [[decision theory]] 可容许决策规则，决策理论中的类比<br />
<br />
* [[Arrow's impossibility theorem]] 阿罗不可能定理<br />
<br />
* [[Bayesian efficiency]] 贝叶斯效率<br />
<br />
* [[Fundamental theorems of welfare economics]] 福利经济学基本定理<br />
<br />
* [[Deadweight loss]] 无谓损失<br />
<br />
* [[Economic efficiency]] 经济效益<br />
<br />
* [[Highest and best use]] 最佳使用<br />
<br />
* [[Kaldor–Hicks efficiency]] 卡尔多-希克斯效率<br />
<br />
* [[Market failure]], when a market result is not Pareto optimal 市场失灵，即市场结果非帕累托最优的时刻<br />
<br />
* [[Maximal element]], concept in [[order theory]] 极大元，阶理论中的概念<br />
<br />
* [[Maxima of a point set]] 点集极大值<br />
<br />
* [[Multi-objective optimization]] 多目标优化<br />
<br />
* [[Pareto-efficient envy-free division]] 帕累托有效的无嫉妒分割<br />
<br />
* ''[[Social Choice and Individual Values]]'' for the '(weak) Pareto principle' 关于弱帕累托原则的社会选择与个人价值<br />
<br />
* [[Trade-off talking rational economic person|TOTREP]] 讲究权衡的理性经济人<br />
<br />
* [[Welfare economics]] 福利经济<br />
<br />
<br />
<br />
==References 参考文献==<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
== Further reading 延伸阅读 ==<br />
<br />
* {{Cite Fudenberg Tirole 1991|pages=[https://books.google.com/books?id=pFPHKwXro3QC&pg=PA18 18–23]}}<br />
<br />
* {{Cite journal |last1=Bendor | first1=Jonathan |last2= Mookherjee | first2=Dilip | title = Communitarian versus Universalistic norms | journal = [[Quarterly Journal of Political Science]] | volume = 3 | issue = 1 | pages = 33–61 | doi = 10.1561/100.00007028 | date = April 2008 | ref = harv }}<br />
<br />
* {{Cite journal | last = Kanbur | first = Ravi| author-link = Ravi Kanbur | title = Pareto's revenge | journal = Journal of Social and Economic Development | volume = 7 | issue = 1 | pages = 1–11 | date = January–June 2005 | url = http://www.arts.cornell.edu/poverty/kanbur/ParRev.pdf | ref = harv }}<br />
<br />
* {{cite book | last = Ng | first = Yew-Kwang | author-link = Yew-Kwang Ng | title = Welfare economics towards a more complete analysis | url=https://books.google.com/books?id=o-2GDAAAQBAJ&printsec=frontcover| publisher = Palgrave Macmillan | location = Basingstoke, Hampshire New York | year = 2004 | isbn = 9780333971215 }}<br />
<br />
* {{Citation | author-first1=Ariel | author-last1=Rubinstein | author-first2=Martin J. | author-last2=Osborne | author-link1 = Ariel Rubinstein | contribution = Introduction | editor-first1=Ariel | editor-last1=Rubinstein | editor-first2=Martin J. | editor-last2=Osborne | editor-link1 = Ariel Rubinstein | title = A course in game theory | pages = 6–7 | publisher = MIT Press | location = Cambridge, Massachusetts | year = 1994 | isbn = 9780262650403 }} [https://books.google.com/books?id=5ntdaYX4LPkC&pg=PA6 Book preview.]<br />
<br />
* {{Cite journal | last = Mathur | first = Vijay K. | title = How well do we know Pareto optimality? | journal = The Journal of Economic Education | volume = 22 | issue = 2 | pages = 172–178 | doi = 10.2307/1182422 | date = Spring 1991 | ref = harv | jstor = 1182422 }}<br />
<br />
* {{Cite journal | last1 = Newbery | first1 = David M.G. | last2 = Stiglitz | first2 = Joseph E. | author-link1 = David Newbery | author-link2 = Joseph Stiglitz | title = Pareto inferior trade | journal = Review of Economic Studies | volume = 51 | issue = 1 | pages = 1–12 | doi = 10.2307/2297701 | date = January 1984 | ref = harv | jstor = 2297701 }}<br />
<br />
<br />
<br />
{{Economics}}<br />
<br />
{{Game theory}}<br />
<br />
{{Voting systems}}<br />
<br />
<br />
<br />
{{Authority control}}<br />
<br />
<br />
<br />
{{DEFAULTSORT:Pareto Efficiency}}<br />
<br />
[[Category:Game theory]]<br />
<br />
Category:Game theory<br />
<br />
范畴: 博弈论<br />
<br />
[[Category:Law and economics]]<br />
<br />
Category:Law and economics<br />
<br />
类别: 法律和经济学<br />
<br />
[[Category:Welfare economics]]<br />
<br />
Category:Welfare economics<br />
<br />
类别: 福利经济学<br />
<br />
[[Category:Pareto efficiency]]<br />
<br />
Category:Pareto efficiency<br />
<br />
类别: 帕累托最优<br />
<br />
[[Category:Mathematical optimization]]<br />
<br />
Category:Mathematical optimization<br />
<br />
类别: 最优化<br />
<br />
[[Category:Electoral system criteria]]<br />
<br />
Category:Electoral system criteria<br />
<br />
类别: 选举制度标准<br />
<br />
[[Category:Vilfredo Pareto]]<br />
<br />
Category:Vilfredo Pareto<br />
<br />
类别: Vilfredo Pareto<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Pareto efficiency]]. Its edit history can be viewed at [[帕累托最优/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6%E5%AE%9A%E5%BE%8B_Laws_of_thermodynamics&diff=14686热力学定律 Laws of thermodynamics2020-10-01T15:42:10Z<p>趣木木：/* History */</p>
<hr />
<div>本词条由Solitude初步翻译<br />
<br />
{{Thermodynamics|cTopic=Laws}}<br><br />
模板：热力学<br />
<br />
The '''laws of thermodynamics''' define physical quantities, such as [[temperature]], [[energy]], and [[entropy]], that characterize [[thermodynamic system]]s at [[thermodynamic equilibrium]]. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as [[perpetual motion]]. In addition to their use in [[thermodynamics]], they are important fundamental [[Physical law|laws]] of [[physics]] in general, and are applicable in other natural [[sciences]].<br />
<br />
The laws of thermodynamics define physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems at thermodynamic equilibrium. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.<br />
<br />
'''<font color="#ff8000"> 热力学定律The laws of thermodynamics</font>'''定义了许多物理量，如'''<font color="#ff8000"> 温度temperature</font>'''、'''<font color="#ff8000"> 能量energy</font>'''和'''<font color="#ff8000">熵 entropy</font>'''，这些物理量表征处于热力学平衡的热力学系统。这些定律描述了这些物理量之间的关系，并构成了排除某些现象的可能性的基础，例如永动机。除了在热力学中的应用之外，它们也是一般物理学中的重要基本定律，也适用于其他自然科学。<br />
<br />
<br />
<br />
<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.<ref name="Guggenheim 1985">Guggenheim, E.A. (1985). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', seventh edition, North Holland, Amsterdam, {{ISBN|0-444-86951-4}}.</ref><ref name="Kittel and Kroemer 1980">Kittel, C. Kroemer, H. (1980). ''Thermal Physics'', second edition, W.H. Freeman, San Francisco, {{ISBN|0-7167-1088-9}}.</ref><ref name="Adkins 1968">Adkins, C.J. (1968). ''Equilibrium Thermodynamics'', McGraw-Hill, London, {{ISBN|0-07-084057-1}}.</ref><ref name="LJCV 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers'', Springer, Berlin, {{ISBN|978-3-540-74252-4}}.</ref><ref>{{cite book |author1=Chris Vuille |author2=Serway, Raymond A. |author3=Faughn, Jerry S. |title=College physics |publisher=Brooks/Cole, Cengage Learning |location=Belmont, CA |year=2009 |isbn=978-0-495-38693-3 |oclc= |doi= |accessdate= | page = 355 |url=https://books.google.com/books?id=CX0u0mIOZ44C&pg=PT355}}</ref>. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
传统上，'''<font color="#ff8000"> 热力学Thermodynamics</font>'''描述了三个基本定律：（简单的按顺序命名为）第一定律、第二定律和第三定律。此外，在前三个定律确立之后，人们认识到可以提出另一个对这三个定律更为基本的定律，即第零定律。<br />
<br />
<br />
<br />
The [[zeroth law of thermodynamics]] defines [[thermal equilibrium]] and forms a basis for the definition of [[temperature]]: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
'''<font color="#ff8000"> 热力学第零定律zeroth law of thermodynamics</font>'''定义了'''<font color="#ff8000"> 热平衡thermal equilibrium</font>'''，并为温度定义奠定了基础：如果两个系统都与第三个系统处于热平衡，则它们彼此也处于热平衡。<br />
<br />
<br />
<br />
The [[first law of thermodynamics]]: When energy passes, as [[Work (thermodynamics)|work]], as [[heat]], or with matter, into or out of a system, the system's [[internal energy]] changes in accord with the law of [[conservation of energy]]. Equivalently, [[perpetual motion machine of the first kind|perpetual motion machines of the first kind]] (machines that produce work with no energy input) are impossible.<br />
<br />
The first law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out of a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind (machines that produce work with no energy input) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第一定律first law of thermodynamics</font>''':当能量以'''<font color="#ff8000"> 功work</font>'''、'''<font color="#ff8000"> 热heat</font>'''或物质的形式进入或离开一个系统时，系统的'''<font color="#ff8000"> 内能 internal energy</font>'''根据能量守恒定律发生变化。同样地，第一类永动机机器(不需要能量输入就能工作的机器)是不可能造成的。<br />
<br />
<br />
<br />
The [[second law of thermodynamics]]: In a natural [[thermodynamic process]], the sum of the [[entropy|entropies]] of the interacting [[thermodynamic system]]s increases. Equivalently, [[perpetual motion machine of the second kind|perpetual motion machines of the second kind]] (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
The second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第二定律second law of thermodynamics</font>''':在自然热力学过程中，相互作用的热力学系统的熵的总和增加。同样地，第二类永动机(自发地把热能转化为机械功的机器)是不可能制造出的。<br />
<br />
<br />
<br />
The [[third law of thermodynamics]]: The [[entropy]] of a system approaches a constant value as the temperature approaches [[absolute zero]].<ref name="Kittel and Kroemer 1980"/> With the exception of non-crystalline solids ([[glass]]es) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
The third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
'''<font color="#ff8000"> 热力学第三定律third law of thermodynamics</font>''':当温度趋于'''<font color="#ff8000"> 绝对零度absolute zero</font>'''时，系统的熵趋于一个定值。除非晶固体(玻璃)外，系统在绝对零度时的熵通常接近于零。<br />
<br />
<br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<ref name="Guggenheim 1985"/><ref name="Kittel and Kroemer 1980"/><ref name="Adkins 1968"/><ref name="LJCV 2008"/><ref name="DGM 1962">De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North Holland, Amsterdam.</ref><ref name="Glansdorff and Prigogine 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London, {{ISBN|0-471-30280-5}}.</ref><br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<br />
<br />
有人提出了其他的定律，但没有一个达到公认的四个定律的普遍性，也没有在标准教科书中被讨论。<br />
<br />
<br />
==Zeroth law==<br />
<br />
热力学零定律<br />
<br />
The [[zeroth law of thermodynamics]] may be stated in the following form:<br />
<br />
The zeroth law of thermodynamics may be stated in the following form:<br />
<br />
热力学第零定律可以用以下形式表示：<br />
<br />
<br />
<br />
{{quote|If two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other.<ref>Guggenheim (1985), p.&nbsp;8.</ref>}}<br><br />
如果两个系统都与第三个系统处于热平衡状态，则它们彼此处于热平衡状态.<br />
<br />
<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a [[mass]] of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a mass of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
该定律旨在允许一个经验参数存在，即温度，作为热力学系统的一种性质，即相互处于热平衡的系统具有相同的温度。这里所述的定律适用于特定的物质(例如一定量的气体物质）来匹配其他物质的温度，但不能证明温度是一个可以用实数来衡量的量。<br />
<br />
<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter.<ref>Sommerfeld, A. (1951/1955). ''Thermodynamics and Statistical Mechanics'', vol. 5 of ''Lectures on Theoretical Physics'', edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York, p. 1.</ref><ref>[[James Serrin|Serrin, J.]] (1978). The concepts of thermodynamics, in ''Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977'', edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, {{ISBN|0-444-85166-6}}, pp. 411–51.</ref><ref>[[James Serrin|Serrin, J.]] (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pp. 3–32, in ''New Perspectives in Thermodynamics'', edited by J. Serrin, Springer, Berlin, {{ISBN|3-540-15931-2}}.</ref> Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter. Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
虽然这个版本的定律是最常见的陈述版本之一，但它只是被称为“第零定律”的众多陈述之一。有些陈述更进一步，提供了一个重要的物理事实，即温度是一维的，并且从概念上把物体按实数顺序由冷到热排列。也许对于“第零定律”并没有唯一的“最佳的表述”，因为在文献中有一系列的热力学原理的表述，每一种都要求对热力学定律作出各自适当的说明。<br />
<br />
<br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its [[Conjugate variables (thermodynamics)|conjugate variable]]. Such a temperature definition is said to be 'empirical'.<ref>Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (first edition 1968), third edition 1983, Cambridge University Press, {{ISBN|0-521-25445-0}}, pp. 18–20.</ref><ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}, p. 26.</ref><ref>Buchdahl, H.A. (1966), ''The Concepts of Classical Thermodynamics'', Cambridge University Press, London, pp. 30, 34ff, 46f, 83.</ref><ref>*Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, {{ISBN|0-471-62430-6}}, p. 22.</ref><ref>[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge, p. 10.</ref><ref>[[Harold A. Wilson (physicist)|Wilson, H.A.]] (1966). ''Thermodynamics and Statistical Mechanics'', Cambridge University Press, London, pp. 4, 8, 68, 86, 97, 311.</ref><br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable. Such a temperature definition is said to be 'empirical'.<br />
<br />
虽然这些关于温度和热平衡的概念是热力学的基础，并在19世纪得到了清楚的阐述，但是直到20世纪30年代福勒和古根海姆这样做的时候，人们才普遍感觉到需要对上述定律进行明确编号，而这时第一定律、第二定律和第三定律已经得到广泛的理解和认可。因此，它被称为第零定律。该定律作为早期定律基础的重要性在于，它允许以非循环的方式定义温度，而无需参考熵及其共轭变量。这样的温度定义被称为“经验主义”。<br />
<br />
<br />
<br />
==First law==<br />
第一定律<br />
<br />
The '''first law of thermodynamics''' is a version of the law of [[conservation of energy]], adapted for [[thermodynamic system]]s.<br />
<br />
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems.<br />
<br />
热力学第一定律是'''<font color="#ff8000"> 能量守恒conservation of energy</font>'''定律的一个版本，适用于热力学系统。<br />
<br />
<br />
The law of conservation of energy states that the total [[energy]] of an [[isolated system]] is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
能量守恒定律指出，一个孤立系统的总能量是恒定的;能量可以从一种形式转化为另一种形式，但能量既不会凭空产生也不会凭空消失。<br />
<br />
<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
对于一个没有物质转移的热力学过程，第一定律通常用公式表示为：<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
系统 q-w / math,<br />
<br />
<br />
<br />
where {{math|Δ''U''<sub>system</sub>}} denotes the change in the [[internal energy]] of a [[Thermodynamic system#Closed system|closed system]], {{math|''Q''}} denotes the quantity of energy supplied ''to'' the system as [[heat]], and {{math|''W''}} denotes the amount of [[Work (thermodynamics)|thermodynamic work]] (expressed here with a negative sign) done ''by'' the system on its surroundings. (An [[First law of thermodynamics#Sign conventions|alternate sign convention]] not used in this article is to define {{math|''W''}} as the work done ''on'' the system.) <br />
<br />
where denotes the change in the internal energy of a closed system, denotes the quantity of energy supplied to the system as heat, and denotes the amount of thermodynamic work (expressed here with a negative sign) done by the system on its surroundings. (An alternate sign convention not used in this article is to define as the work done on the system.) <br />
<br />
其中{{math|Δ''U''<sub>system</sub>}}表示一个封闭系统内部能量的变化，{{math|''Q''}} 表示外界对系统传递的热量，{{math|''W''}}表示该系统对周围环境所做的热力学功(在这里用负号表示)。(本文中没有使用的另一个符号约定是定义对系统所做的功。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）注意到前面的heat 译为了“热” {{math|''Q''}} 表？示外界对系统传递的热量 热量是否为“热”？<br />
<br />
<br />
<br />
In the case of a two-stage [[thermodynamic cycle]] of a closed system, which returns to its original state, the heat {{math|''Q<sub>in</sub>''}} supplied to the system in one stage of the cycle, minus the heat {{math|''Q<sub>out</sub>''}} removed from it in the other stage, plus the [[Work (thermodynamics)|thermodynamic work]] added to the system, {{math|''W<sub>in</sub>''}}, equals the thermodynamic work that leaves the system {{math|''W<sub>out</sub>''}}.<br />
<br />
In the case of a two-stage thermodynamic cycle of a closed system, which returns to its original state, the heat supplied to the system in one stage of the cycle, minus the heat removed from it in the other stage, plus the thermodynamic work added to the system, , equals the thermodynamic work that leaves the system .<br />
<br />
在封闭系统的两级'''<font color="#ff8000"> 热力循环thermodynamic cycle</font>'''中，该循环回到其原始状态，在循环的一个阶段向系统提供的热量{{math|''Q<sub>in</sub>''}}，减去另一个阶段从系统中去除的热量{{math|''Q<sub>out</sub>''}}，加上对系统做的的热力学功{{math|''W<sub>in</sub>''}}，等于离开系统的做的热力学功{{math|''W<sub>out</sub>''}}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
0 / math<br />
<br />
<br />
<br />
hence, for a full cycle,<br />
<br />
hence, for a full cycle,<br />
<br />
因此，一个完整的循环,<br />
<br />
<br />
<br />
::Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: {{math|''Q'' {{=}} 0}}.<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: 0}}.<br />
<br />
对于绝热系统（绝热隔离）的特殊情况，绝热隔离系统内能的变化只能是系统做功的结果，因为绝热假设是: 0}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
对于包括物质转移的过程，还需要进一步的说明: ‘在充分考虑了各个系统的基准参考状态后，当两个系统---- '''<font color="#32CD32">它们可能由不同的化学成分组成，最初只是被防渗墙隔开，或者是被隔离---- 通过移除墙体的热力学操作结合成一个新系统</font>'''，那么<br />
<br />
<br />
<br />
::<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
数学 u + u 2 / math,<br />
<br />
<br />
<br />
where {{math|''U''<sub>system</sub>}} denotes the internal energy of the combined system, and {{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} denote the internal energies of the respective separated systems.'<br />
<br />
where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.'<br />
<br />
其中{{math|''U''<sub>system</sub>}}表示组合系统的内能，{{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} 表示各自分离系统的内能<br />
<br />
<br />
<br />
The First Law encompasses several principles:<br />
<br />
The First Law encompasses several principles:<br />
<br />
第一定律包括以下几个原则:<br />
<br />
* The [[Conservation of energy|law of conservation of energy]].<br />
<br />
::This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
能量既不能被创造也不能被消灭。但是，能量可以改变形式，能量可以从一个地方流动到另一个地方。能量守恒定律的一个特殊结果是，孤立系统的总能量不变。<br />
<br />
* The concept of [[internal energy]] and its relationship to temperature.<br><br />
内能的概念及其与温度关系。<br />
<br />
::If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has [[kinetic energy]]. If the system as a whole is in an externally imposed force field (e.g. gravity), it has [[potential energy]] relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has kinetic energy. If the system as a whole is in an externally imposed force field (e.g. gravity), it has potential energy relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
如果系统具有确定的温度，则其总能量具有三个可区分的成分，分别称为动能（由与系统整体运动产生的能量），势能（由外部施加的立场产生的能量，比如重力）和内能（热热力学的基本量）。内能概念的确立将热力学第一定律与一般的能量守恒定律区分开来。<br />
——Solitude(讨论)<br />
<br />
<br />
::<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<br />
<br />
::The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, {{math|''U''}}, and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, , and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
物质的内能可以解释为其组成原子的不规则微观运动的不同动能和它们之间相互作用的势能的总和。这些微观能量统称为物质的内能，并由宏观热力学性质来解释。组成原子的微观运动的总和随着系统温度的升高而增加; 这假设在系统的微观层次上没有其他的相互作用，例如化学反应、组成原子相互间的势能。<br />
<br />
* [[Work (physics)|Work]] is a process of transferring energy to or from a system in ways that can be described by macroscopic mechanical forces exerted by factors in the surroundings, outside the system. Examples are an externally driven shaft agitating a stirrer within the system, or an externally imposed electric field that polarizes the material of the system, or a piston that compresses the system. Unless otherwise stated, it is customary to treat work as occurring without its [[dissipation]] to the surroundings. Practically speaking, in all natural process, some of the work is dissipated by internal friction or viscosity. The work done by the system can come from its overall kinetic energy, from its overall potential energy, or from its internal energy.<br />
<br />
做功是一种以某种方式向系统传递能量或从系统传递能量的过程，其方式可以用作用在系统外部及其周围环境之间的宏观机械力来描述。'''<font color="#32CD32">例如，外部驱动的轴在系统内搅动，或外部施加的电场使系统材料极化，或活塞压缩系统。</font>'''除非另有说明，习惯上把做功看作是在不影响周围环境的情况下发生的。实际上，在一切自然过程中，有些功是因内摩擦或粘黏而消失的。系统所做的功，可以来自于它的总动能，总势能或者它的内能。<br />
<br />
<br />
::For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's [[gravitational potential energy]]. Work added to the system increases the Potential Energy of the system:<br />
<br />
For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's gravitational potential energy. Work added to the system increases the Potential Energy of the system:<br />
<br />
例如，当一台机器(不是系统的一部分)将系统向上提升时，一些能量就会从机器转移到系统。系统的能量随着系统所做功的增加而增加，在这种特殊的情况下，系统的能量增加表现为系统的重力势能的增加。对系统做的增加了系统的势能:<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“对系统做的增加了系统的势能” 需要对全文进行通读 这里少词<br />
<br />
<br />
:::<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<br />
<br />
::Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
或者一般来说，以功的形式加入系统的能量可以分为动能、势能或内能:<br />
<br />
<br />
<br />
:::<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
* When matter is transferred into a system, that masses' associated internal energy and potential energy are transferred with it.<br><br />
当物质转移到一个系统中时，物质相关的内能和势能也随之转移。<br />
<br />
<br />
<br />
:::<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
在 Delta u { system } / math 中的 math left (u，Delta m right)<br />
<br />
<br />
<br />
::where {{math|''u''}} denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and {{math|Δ''M''}} denotes the amount of transferred mass.<br />
<br />
where denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and denotes the amount of transferred mass.<br />
<br />
其中{{math|''u''}}表示在周围环境中测量的转移物质的单位质量的内能; {{math|Δ''M''}}表示被转移物质的数量。<br />
<br />
* The flow of [[heat]] is a form of energy transfer.<br><br />
热的流动是能量传递的一种形式。<br />
<br />
::Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
加热是一个将能量转移到系统中或从系统中转移出的自然过程，而不是通过做功或物质的转移。热量只能从较热的系统直接传递到较冷的系统。<br />
<br />
<br />
<br />
:::If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
如果系统具有不渗透物质的刚性壁，那么能量不能通过做功传入或传出系统，而且没有外部的远程力场影响系统以改变其内能，那么内能只能通过以热的形式进行传递来改变:<br />
<br />
<br />
<br />
:::<math>\Delta U_{\rm system}=Q</math><br />
<br />
<math>\Delta U_{\rm system}=Q</math><br />
<br />
系统的 q / math<br />
<br />
<br />
<br />
where {{math|''Q''}} denotes the amount of energy transferred into the system as heat.<br />
<br />
where denotes the amount of energy transferred into the system as heat.<br />
<br />
其中 {{math|''Q''}}表示以热量形式传递到系统中的能量。<br />
<br />
<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
结合这些原理，就可以得出传统的热力学第一定律的表述: 不可能制造一台在没有等量能量输入的情况下不断做功的机器。或者更简单地说，第一类永动机是不可能造成的。<br />
<br />
==Second law==<br />
第二定律<br />
<br />
The [[second law of thermodynamics]] indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
The second law of thermodynamics indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
热力学第二定律表明了自然过程的不可逆性，并且在许多情况下，自然过程的趋向于物质很能量的空间均匀性，特别是温度。它可以用各种有趣而重要的方式来表达。<br />
<br />
<br />
<br />
It implies the existence of a quantity called the [[entropy]] of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
这意味着热力学系统中存在一个叫做熵的量。了一个叫做热力学系统熵的量的存在。就这个数量而言，它意味着<br />
<br />
{{quote|When two initially isolated systems in separate but nearby regions of space, each in [[thermodynamic equilibrium]] with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the [[entropy|entropies]] of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values.}}<br><br />
当两个最初隔离的系统分别位于彼此独立但不一定彼此处于热力学平衡的空间区域中，然后彼此相互作用时，它们最终将达到相互的热力学平衡。最初隔离的系统的熵之和小于或等于最终组合的总熵。当两个初始系统各自的强变量(温度、压力)相等时，才发生平等。那么最终的系统也有相同的值。<br />
<br />
<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
第二定律适用于可逆和不可逆的多种过程。所有的自然过程都是不可逆的。可逆过程是一个有用的和方便的理论假设，但不发生在自然界。<br />
<br />
<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
这种不可逆性的一个主要例子是通过传导或辐射进行的热传递。早在熵的概念被发现之前，人们就已经知道，当两个最初温度不同的物体直接进行热连接时，热量总是自发地从较热的物体流向较冷的物体。<br />
<br />
<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
第二定律也告诉我们除了热传递之外的不可逆性，例如摩擦力和粘度，以及化学反应。'''<font color="#32CD32">需要熵的概念给该定律提供更广泛的范围。</font>'''<br />
<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, ''δQ'', is the product of the temperature (''T''), both of the system and of the sources or destination of the heat, with the increment (''dS'') of the system's conjugate variable, its [[entropy]] (''S'')<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S)<br />
<br />
根据热力学第二定律，在理论上和假设的可逆传热中，传热元素δQ是系统和热源或热目的地的温度(t)与系统共轭变量熵（S）的增量(dS)的乘积<br />
<br />
<br />
<br />
:<math>\delta Q = T\,dS\, .</math><ref name="Guggenheim 1985"/><br />
<br />
<math>\delta Q = T\,dS\, .</math><br />
<br />
数学 delta q t ，dS ，. / math<br />
<br />
<br />
<br />
[[Entropy]] may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as ''disorder'' on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<ref>Ben-Naim, A. (2008). ''A Farewell to Entropy: Statistical Thermodynamics Based on Information'', World Scientific, New Jersey, {{ISBN|978-981-270-706-2}}.</ref><br />
<br />
Entropy may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as disorder on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<br />
<br />
当只知道宏观状态时，熵也可以被看作是对系统运动和构型的微观细节有关的物理度量。这种细节通常在微观或分子尺度上被称为无序。该定律声称，对于一个系统的两个给定的宏观指定状态，它们之间存在一个被称为熵差的量。'''<font color="#32CD32">这种熵的差异定义了需要多少额外的微观物理信息来指定一个宏观指定状态，给定另一个宏观指定状态-通常是一个方便选择的参考状态，这可能是假定存在的，而不是明确陈述的。自然过程的最终条件始终包含着微观上特定的影响，而这些影响，从过程初始条件的宏观规定来看是无法被完全准确预测的。这就是为什么熵在自然过程中会增加——熵的增加告诉我们需要多少额外的微观信息来区分最终的宏观指定状态和最初的宏观指定状态。</font>'''<br />
<br />
<br />
==Third law==<br />
第三定律<br />
<br />
The [[third law of thermodynamics]] is sometimes stated as follows:<br />
<br />
The third law of thermodynamics is sometimes stated as follows:<br />
<br />
热力学第三定律可以表示为：<br />
<br />
:''The [[entropy]] of a perfect [[crystal]] of any pure substance approaches zero as the temperature approaches [[absolute zero]].''<br />
<br />
The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero.<br />
<br />
当温度接近绝对零度时，任何纯物质的完整晶体的熵接近零。<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one [[microstate (statistical mechanics)|state with minimum energy]]. Entropy is related to the number of possible microstates according to:<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy. Entropy is related to the number of possible microstates according to:<br />
<br />
在零温时，系统必须处于热能最小的状态。如果完美晶体只有一种能量最小的状态，则该说法成立。熵与可能的微状态数有关:<br />
<br />
<br />
<br />
::<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
数学知识，数学知识，欧米茄 / 数学<br />
<br />
<br />
<br />
Where ''S'' is the entropy of the system, ''k''<sub>B</sub> [[Boltzmann constant|Boltzmann's constant]], and ''Ω'' the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (''Ω''=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
Where S is the entropy of the system, k<sub>B</sub> Boltzmann's constant, and Ω the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (Ω=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
其中 s 是系统的熵，k<sub>B</sub>是玻尔兹曼常数，以及Ω是微状态数(例如:可能的原子结构)。在绝对零度下只有一种微状态(Ω=1，因为纯物质的所有原子都是相同的，所以所有阶数都是相同的，因为只有一个组合)和 ln (1)=0。<br />
<br />
<br />
<br />
A more general form of the third law that applies to a system such as a [[glass]] that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
A more general form of the third law that applies to a system such as a glass that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
第三定律的一个更普遍的形式，适用于像玻璃这样的系统，'''<font color="#32CD32">可能有一个以上的微观上截然不同的能量状态，或可能有一个微观上截然不同的“冻结状态”，虽然不是一个严格意义上的的最低能量状态，也不是严格意义上的热力学平衡，</font>'''在绝对零度:<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]） “在绝对零度:” “在绝对零度下”？<br />
<br />
:''The entropy of a system approaches a constant value as the temperature approaches zero.''<br />
<br />
The entropy of a system approaches a constant value as the temperature approaches zero.<br />
<br />
系统的熵随着温度接近绝对零度而接近一个恒定值。<br />
<br />
<br />
<br />
The constant value (not necessarily zero) is called the [[residual entropy]] of the system.<br />
<br />
The constant value (not necessarily zero) is called the residual entropy of the system.<br />
<br />
这个常数(不一定是零)被称为系统的余熵。<br />
<br />
==History==<br />
历史<br />
<br />
{{see also|Philosophy of thermal and statistical physics}}<br><br />
热学和统计物理学的哲学<br />
<br />
[[Mechanical equivalent of heat|Circa 1797, Count Rumford (born Benjamin Thompson)]] showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] in 1824. By 1860, as formalized in the works of those such as [[Rudolf Clausius]] and [[William Thomson, 1st Baron Kelvin|William Thomson]], two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist [[Josiah Willard Gibbs]], in his memoir ''Graphical Methods in the Thermodynamics of Fluids'', clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
Circa 1797, Count Rumford (born Benjamin Thompson) showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824. By 1860, as formalized in the works of those such as Rudolf Clausius and William Thomson, two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist Josiah Willard Gibbs, in his memoir Graphical Methods in the Thermodynamics of Fluids, clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
大约在1797年，拉姆福德(出生于本杰明·汤普森)表明，无休止的机械作用可以从固定数量的工作物质中产生无限量的热量，从而挑战了热量理论。该理论认为在固定数量的工作物质中会有有限的热量 / 能量。1824年，萨迪·卡诺建立了第一个热力学原理，也就是后来的热力学第二定律。到1860年，正如鲁道夫 · 克劳修斯和威廉 · 汤姆森等人的著作所正式规定的那样，已经确立的两个热力学原理得到了发展，第一个原理和第二个原理，后来被重新定义为热力学定律。例如，1873年，热力学学家乔赛亚·威拉德·吉布斯在他的回忆录《流体热力学的图解法》中明确阐述了热力学的前两个绝对定律。整个20世纪的一些教科书对这些定律进行了不同的编号。在一些与化学无关的领域，第二定律被认为仅仅处理热机的效率问题，而所谓的第三定律则处理熵的增加问题。'''<font color="#32CD32">直接定义熵计算的零律不被认为是一条定律。</font>'''这种分离逐渐形成了第二定律，现代第三定律被广泛采用。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“熵的增加问题” 更加简明一点？“熵增问题”<br />
<br />
==See also==<br />
<br />
*化学热力学 [[Chemical thermodynamics]]<br />
<br />
*守恒定律 [[Conservation law (physics)|Conservation law]]<br />
<br />
*熵增 [[Entropy production]]<br />
<br />
*金斯伯格定理 [[Ginsberg's theorem]]<br />
<br />
*宇宙热寂 [[Heat death of the universe]]<br />
<br />
*H定理 [[H-theorem]]<br />
<br />
*科学规律 [[Laws of science]]<br />
<br />
*昂萨格倒易关系（有时被描述为热力学第四定律） [[Onsager reciprocal relations]] (sometimes described as a fourth law of thermodynamics)<br />
<br />
*统计力学 [[Statistical mechanics]]<br />
<br />
*热力学方程表 [[Table of thermodynamic equations]]<br />
<br />
<br />
<br />
==References==<br><br />
参考文献<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
==Further reading==<br />
<br />
* [[Peter Atkins|Atkins, Peter]] (2007). ''Four Laws That Drive the Universe''. OUP Oxford. {{ISBN|978-0199232369}}<br />
<br />
* Goldstein, Martin & Inge F. (1993). ''The Refrigerator and the Universe''. Harvard Univ. Press. {{ISBN|978-0674753259}}<br />
<br />
<br />
<br />
==External links==<br />
<br />
* [http://www.bbc.co.uk/programmes/b06c06nd In Our Time: Perpetual Motion], BBC discussion about the Laws, with Ruth Gregory, Frank Close and Steven Bramwell, hosted by Melvyn Bragg, first broadcast 24 September 2015.<br />
<br />
<br />
<br />
[[Category:Laws of thermodynamics| ]]<br />
<br />
[[Category:Scientific laws]]<br />
<br />
Category:Scientific laws<br />
<br />
类别: 科学定律<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Laws of thermodynamics]]. Its edit history can be viewed at [[热力学定律/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6%E5%AE%9A%E5%BE%8B_Laws_of_thermodynamics&diff=14685热力学定律 Laws of thermodynamics2020-10-01T15:40:49Z<p>趣木木：/* Third law */</p>
<hr />
<div>本词条由Solitude初步翻译<br />
<br />
{{Thermodynamics|cTopic=Laws}}<br><br />
模板：热力学<br />
<br />
The '''laws of thermodynamics''' define physical quantities, such as [[temperature]], [[energy]], and [[entropy]], that characterize [[thermodynamic system]]s at [[thermodynamic equilibrium]]. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as [[perpetual motion]]. In addition to their use in [[thermodynamics]], they are important fundamental [[Physical law|laws]] of [[physics]] in general, and are applicable in other natural [[sciences]].<br />
<br />
The laws of thermodynamics define physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems at thermodynamic equilibrium. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.<br />
<br />
'''<font color="#ff8000"> 热力学定律The laws of thermodynamics</font>'''定义了许多物理量，如'''<font color="#ff8000"> 温度temperature</font>'''、'''<font color="#ff8000"> 能量energy</font>'''和'''<font color="#ff8000">熵 entropy</font>'''，这些物理量表征处于热力学平衡的热力学系统。这些定律描述了这些物理量之间的关系，并构成了排除某些现象的可能性的基础，例如永动机。除了在热力学中的应用之外，它们也是一般物理学中的重要基本定律，也适用于其他自然科学。<br />
<br />
<br />
<br />
<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.<ref name="Guggenheim 1985">Guggenheim, E.A. (1985). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', seventh edition, North Holland, Amsterdam, {{ISBN|0-444-86951-4}}.</ref><ref name="Kittel and Kroemer 1980">Kittel, C. Kroemer, H. (1980). ''Thermal Physics'', second edition, W.H. Freeman, San Francisco, {{ISBN|0-7167-1088-9}}.</ref><ref name="Adkins 1968">Adkins, C.J. (1968). ''Equilibrium Thermodynamics'', McGraw-Hill, London, {{ISBN|0-07-084057-1}}.</ref><ref name="LJCV 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers'', Springer, Berlin, {{ISBN|978-3-540-74252-4}}.</ref><ref>{{cite book |author1=Chris Vuille |author2=Serway, Raymond A. |author3=Faughn, Jerry S. |title=College physics |publisher=Brooks/Cole, Cengage Learning |location=Belmont, CA |year=2009 |isbn=978-0-495-38693-3 |oclc= |doi= |accessdate= | page = 355 |url=https://books.google.com/books?id=CX0u0mIOZ44C&pg=PT355}}</ref>. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
传统上，'''<font color="#ff8000"> 热力学Thermodynamics</font>'''描述了三个基本定律：（简单的按顺序命名为）第一定律、第二定律和第三定律。此外，在前三个定律确立之后，人们认识到可以提出另一个对这三个定律更为基本的定律，即第零定律。<br />
<br />
<br />
<br />
The [[zeroth law of thermodynamics]] defines [[thermal equilibrium]] and forms a basis for the definition of [[temperature]]: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
'''<font color="#ff8000"> 热力学第零定律zeroth law of thermodynamics</font>'''定义了'''<font color="#ff8000"> 热平衡thermal equilibrium</font>'''，并为温度定义奠定了基础：如果两个系统都与第三个系统处于热平衡，则它们彼此也处于热平衡。<br />
<br />
<br />
<br />
The [[first law of thermodynamics]]: When energy passes, as [[Work (thermodynamics)|work]], as [[heat]], or with matter, into or out of a system, the system's [[internal energy]] changes in accord with the law of [[conservation of energy]]. Equivalently, [[perpetual motion machine of the first kind|perpetual motion machines of the first kind]] (machines that produce work with no energy input) are impossible.<br />
<br />
The first law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out of a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind (machines that produce work with no energy input) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第一定律first law of thermodynamics</font>''':当能量以'''<font color="#ff8000"> 功work</font>'''、'''<font color="#ff8000"> 热heat</font>'''或物质的形式进入或离开一个系统时，系统的'''<font color="#ff8000"> 内能 internal energy</font>'''根据能量守恒定律发生变化。同样地，第一类永动机机器(不需要能量输入就能工作的机器)是不可能造成的。<br />
<br />
<br />
<br />
The [[second law of thermodynamics]]: In a natural [[thermodynamic process]], the sum of the [[entropy|entropies]] of the interacting [[thermodynamic system]]s increases. Equivalently, [[perpetual motion machine of the second kind|perpetual motion machines of the second kind]] (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
The second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第二定律second law of thermodynamics</font>''':在自然热力学过程中，相互作用的热力学系统的熵的总和增加。同样地，第二类永动机(自发地把热能转化为机械功的机器)是不可能制造出的。<br />
<br />
<br />
<br />
The [[third law of thermodynamics]]: The [[entropy]] of a system approaches a constant value as the temperature approaches [[absolute zero]].<ref name="Kittel and Kroemer 1980"/> With the exception of non-crystalline solids ([[glass]]es) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
The third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
'''<font color="#ff8000"> 热力学第三定律third law of thermodynamics</font>''':当温度趋于'''<font color="#ff8000"> 绝对零度absolute zero</font>'''时，系统的熵趋于一个定值。除非晶固体(玻璃)外，系统在绝对零度时的熵通常接近于零。<br />
<br />
<br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<ref name="Guggenheim 1985"/><ref name="Kittel and Kroemer 1980"/><ref name="Adkins 1968"/><ref name="LJCV 2008"/><ref name="DGM 1962">De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North Holland, Amsterdam.</ref><ref name="Glansdorff and Prigogine 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London, {{ISBN|0-471-30280-5}}.</ref><br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<br />
<br />
有人提出了其他的定律，但没有一个达到公认的四个定律的普遍性，也没有在标准教科书中被讨论。<br />
<br />
<br />
==Zeroth law==<br />
<br />
热力学零定律<br />
<br />
The [[zeroth law of thermodynamics]] may be stated in the following form:<br />
<br />
The zeroth law of thermodynamics may be stated in the following form:<br />
<br />
热力学第零定律可以用以下形式表示：<br />
<br />
<br />
<br />
{{quote|If two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other.<ref>Guggenheim (1985), p.&nbsp;8.</ref>}}<br><br />
如果两个系统都与第三个系统处于热平衡状态，则它们彼此处于热平衡状态.<br />
<br />
<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a [[mass]] of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a mass of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
该定律旨在允许一个经验参数存在，即温度，作为热力学系统的一种性质，即相互处于热平衡的系统具有相同的温度。这里所述的定律适用于特定的物质(例如一定量的气体物质）来匹配其他物质的温度，但不能证明温度是一个可以用实数来衡量的量。<br />
<br />
<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter.<ref>Sommerfeld, A. (1951/1955). ''Thermodynamics and Statistical Mechanics'', vol. 5 of ''Lectures on Theoretical Physics'', edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York, p. 1.</ref><ref>[[James Serrin|Serrin, J.]] (1978). The concepts of thermodynamics, in ''Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977'', edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, {{ISBN|0-444-85166-6}}, pp. 411–51.</ref><ref>[[James Serrin|Serrin, J.]] (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pp. 3–32, in ''New Perspectives in Thermodynamics'', edited by J. Serrin, Springer, Berlin, {{ISBN|3-540-15931-2}}.</ref> Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter. Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
虽然这个版本的定律是最常见的陈述版本之一，但它只是被称为“第零定律”的众多陈述之一。有些陈述更进一步，提供了一个重要的物理事实，即温度是一维的，并且从概念上把物体按实数顺序由冷到热排列。也许对于“第零定律”并没有唯一的“最佳的表述”，因为在文献中有一系列的热力学原理的表述，每一种都要求对热力学定律作出各自适当的说明。<br />
<br />
<br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its [[Conjugate variables (thermodynamics)|conjugate variable]]. Such a temperature definition is said to be 'empirical'.<ref>Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (first edition 1968), third edition 1983, Cambridge University Press, {{ISBN|0-521-25445-0}}, pp. 18–20.</ref><ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}, p. 26.</ref><ref>Buchdahl, H.A. (1966), ''The Concepts of Classical Thermodynamics'', Cambridge University Press, London, pp. 30, 34ff, 46f, 83.</ref><ref>*Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, {{ISBN|0-471-62430-6}}, p. 22.</ref><ref>[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge, p. 10.</ref><ref>[[Harold A. Wilson (physicist)|Wilson, H.A.]] (1966). ''Thermodynamics and Statistical Mechanics'', Cambridge University Press, London, pp. 4, 8, 68, 86, 97, 311.</ref><br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable. Such a temperature definition is said to be 'empirical'.<br />
<br />
虽然这些关于温度和热平衡的概念是热力学的基础，并在19世纪得到了清楚的阐述，但是直到20世纪30年代福勒和古根海姆这样做的时候，人们才普遍感觉到需要对上述定律进行明确编号，而这时第一定律、第二定律和第三定律已经得到广泛的理解和认可。因此，它被称为第零定律。该定律作为早期定律基础的重要性在于，它允许以非循环的方式定义温度，而无需参考熵及其共轭变量。这样的温度定义被称为“经验主义”。<br />
<br />
<br />
<br />
==First law==<br />
第一定律<br />
<br />
The '''first law of thermodynamics''' is a version of the law of [[conservation of energy]], adapted for [[thermodynamic system]]s.<br />
<br />
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems.<br />
<br />
热力学第一定律是'''<font color="#ff8000"> 能量守恒conservation of energy</font>'''定律的一个版本，适用于热力学系统。<br />
<br />
<br />
The law of conservation of energy states that the total [[energy]] of an [[isolated system]] is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
能量守恒定律指出，一个孤立系统的总能量是恒定的;能量可以从一种形式转化为另一种形式，但能量既不会凭空产生也不会凭空消失。<br />
<br />
<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
对于一个没有物质转移的热力学过程，第一定律通常用公式表示为：<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
系统 q-w / math,<br />
<br />
<br />
<br />
where {{math|Δ''U''<sub>system</sub>}} denotes the change in the [[internal energy]] of a [[Thermodynamic system#Closed system|closed system]], {{math|''Q''}} denotes the quantity of energy supplied ''to'' the system as [[heat]], and {{math|''W''}} denotes the amount of [[Work (thermodynamics)|thermodynamic work]] (expressed here with a negative sign) done ''by'' the system on its surroundings. (An [[First law of thermodynamics#Sign conventions|alternate sign convention]] not used in this article is to define {{math|''W''}} as the work done ''on'' the system.) <br />
<br />
where denotes the change in the internal energy of a closed system, denotes the quantity of energy supplied to the system as heat, and denotes the amount of thermodynamic work (expressed here with a negative sign) done by the system on its surroundings. (An alternate sign convention not used in this article is to define as the work done on the system.) <br />
<br />
其中{{math|Δ''U''<sub>system</sub>}}表示一个封闭系统内部能量的变化，{{math|''Q''}} 表示外界对系统传递的热量，{{math|''W''}}表示该系统对周围环境所做的热力学功(在这里用负号表示)。(本文中没有使用的另一个符号约定是定义对系统所做的功。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）注意到前面的heat 译为了“热” {{math|''Q''}} 表？示外界对系统传递的热量 热量是否为“热”？<br />
<br />
<br />
<br />
In the case of a two-stage [[thermodynamic cycle]] of a closed system, which returns to its original state, the heat {{math|''Q<sub>in</sub>''}} supplied to the system in one stage of the cycle, minus the heat {{math|''Q<sub>out</sub>''}} removed from it in the other stage, plus the [[Work (thermodynamics)|thermodynamic work]] added to the system, {{math|''W<sub>in</sub>''}}, equals the thermodynamic work that leaves the system {{math|''W<sub>out</sub>''}}.<br />
<br />
In the case of a two-stage thermodynamic cycle of a closed system, which returns to its original state, the heat supplied to the system in one stage of the cycle, minus the heat removed from it in the other stage, plus the thermodynamic work added to the system, , equals the thermodynamic work that leaves the system .<br />
<br />
在封闭系统的两级'''<font color="#ff8000"> 热力循环thermodynamic cycle</font>'''中，该循环回到其原始状态，在循环的一个阶段向系统提供的热量{{math|''Q<sub>in</sub>''}}，减去另一个阶段从系统中去除的热量{{math|''Q<sub>out</sub>''}}，加上对系统做的的热力学功{{math|''W<sub>in</sub>''}}，等于离开系统的做的热力学功{{math|''W<sub>out</sub>''}}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
0 / math<br />
<br />
<br />
<br />
hence, for a full cycle,<br />
<br />
hence, for a full cycle,<br />
<br />
因此，一个完整的循环,<br />
<br />
<br />
<br />
::Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: {{math|''Q'' {{=}} 0}}.<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: 0}}.<br />
<br />
对于绝热系统（绝热隔离）的特殊情况，绝热隔离系统内能的变化只能是系统做功的结果，因为绝热假设是: 0}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
对于包括物质转移的过程，还需要进一步的说明: ‘在充分考虑了各个系统的基准参考状态后，当两个系统---- '''<font color="#32CD32">它们可能由不同的化学成分组成，最初只是被防渗墙隔开，或者是被隔离---- 通过移除墙体的热力学操作结合成一个新系统</font>'''，那么<br />
<br />
<br />
<br />
::<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
数学 u + u 2 / math,<br />
<br />
<br />
<br />
where {{math|''U''<sub>system</sub>}} denotes the internal energy of the combined system, and {{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} denote the internal energies of the respective separated systems.'<br />
<br />
where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.'<br />
<br />
其中{{math|''U''<sub>system</sub>}}表示组合系统的内能，{{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} 表示各自分离系统的内能<br />
<br />
<br />
<br />
The First Law encompasses several principles:<br />
<br />
The First Law encompasses several principles:<br />
<br />
第一定律包括以下几个原则:<br />
<br />
* The [[Conservation of energy|law of conservation of energy]].<br />
<br />
::This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
能量既不能被创造也不能被消灭。但是，能量可以改变形式，能量可以从一个地方流动到另一个地方。能量守恒定律的一个特殊结果是，孤立系统的总能量不变。<br />
<br />
* The concept of [[internal energy]] and its relationship to temperature.<br><br />
内能的概念及其与温度关系。<br />
<br />
::If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has [[kinetic energy]]. If the system as a whole is in an externally imposed force field (e.g. gravity), it has [[potential energy]] relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has kinetic energy. If the system as a whole is in an externally imposed force field (e.g. gravity), it has potential energy relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
如果系统具有确定的温度，则其总能量具有三个可区分的成分，分别称为动能（由与系统整体运动产生的能量），势能（由外部施加的立场产生的能量，比如重力）和内能（热热力学的基本量）。内能概念的确立将热力学第一定律与一般的能量守恒定律区分开来。<br />
——Solitude(讨论)<br />
<br />
<br />
::<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<br />
<br />
::The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, {{math|''U''}}, and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, , and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
物质的内能可以解释为其组成原子的不规则微观运动的不同动能和它们之间相互作用的势能的总和。这些微观能量统称为物质的内能，并由宏观热力学性质来解释。组成原子的微观运动的总和随着系统温度的升高而增加; 这假设在系统的微观层次上没有其他的相互作用，例如化学反应、组成原子相互间的势能。<br />
<br />
* [[Work (physics)|Work]] is a process of transferring energy to or from a system in ways that can be described by macroscopic mechanical forces exerted by factors in the surroundings, outside the system. Examples are an externally driven shaft agitating a stirrer within the system, or an externally imposed electric field that polarizes the material of the system, or a piston that compresses the system. Unless otherwise stated, it is customary to treat work as occurring without its [[dissipation]] to the surroundings. Practically speaking, in all natural process, some of the work is dissipated by internal friction or viscosity. The work done by the system can come from its overall kinetic energy, from its overall potential energy, or from its internal energy.<br />
<br />
做功是一种以某种方式向系统传递能量或从系统传递能量的过程，其方式可以用作用在系统外部及其周围环境之间的宏观机械力来描述。'''<font color="#32CD32">例如，外部驱动的轴在系统内搅动，或外部施加的电场使系统材料极化，或活塞压缩系统。</font>'''除非另有说明，习惯上把做功看作是在不影响周围环境的情况下发生的。实际上，在一切自然过程中，有些功是因内摩擦或粘黏而消失的。系统所做的功，可以来自于它的总动能，总势能或者它的内能。<br />
<br />
<br />
::For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's [[gravitational potential energy]]. Work added to the system increases the Potential Energy of the system:<br />
<br />
For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's gravitational potential energy. Work added to the system increases the Potential Energy of the system:<br />
<br />
例如，当一台机器(不是系统的一部分)将系统向上提升时，一些能量就会从机器转移到系统。系统的能量随着系统所做功的增加而增加，在这种特殊的情况下，系统的能量增加表现为系统的重力势能的增加。对系统做的增加了系统的势能:<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“对系统做的增加了系统的势能” 需要对全文进行通读 这里少词<br />
<br />
<br />
:::<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<br />
<br />
::Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
或者一般来说，以功的形式加入系统的能量可以分为动能、势能或内能:<br />
<br />
<br />
<br />
:::<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
* When matter is transferred into a system, that masses' associated internal energy and potential energy are transferred with it.<br><br />
当物质转移到一个系统中时，物质相关的内能和势能也随之转移。<br />
<br />
<br />
<br />
:::<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
在 Delta u { system } / math 中的 math left (u，Delta m right)<br />
<br />
<br />
<br />
::where {{math|''u''}} denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and {{math|Δ''M''}} denotes the amount of transferred mass.<br />
<br />
where denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and denotes the amount of transferred mass.<br />
<br />
其中{{math|''u''}}表示在周围环境中测量的转移物质的单位质量的内能; {{math|Δ''M''}}表示被转移物质的数量。<br />
<br />
* The flow of [[heat]] is a form of energy transfer.<br><br />
热的流动是能量传递的一种形式。<br />
<br />
::Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
加热是一个将能量转移到系统中或从系统中转移出的自然过程，而不是通过做功或物质的转移。热量只能从较热的系统直接传递到较冷的系统。<br />
<br />
<br />
<br />
:::If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
如果系统具有不渗透物质的刚性壁，那么能量不能通过做功传入或传出系统，而且没有外部的远程力场影响系统以改变其内能，那么内能只能通过以热的形式进行传递来改变:<br />
<br />
<br />
<br />
:::<math>\Delta U_{\rm system}=Q</math><br />
<br />
<math>\Delta U_{\rm system}=Q</math><br />
<br />
系统的 q / math<br />
<br />
<br />
<br />
where {{math|''Q''}} denotes the amount of energy transferred into the system as heat.<br />
<br />
where denotes the amount of energy transferred into the system as heat.<br />
<br />
其中 {{math|''Q''}}表示以热量形式传递到系统中的能量。<br />
<br />
<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
结合这些原理，就可以得出传统的热力学第一定律的表述: 不可能制造一台在没有等量能量输入的情况下不断做功的机器。或者更简单地说，第一类永动机是不可能造成的。<br />
<br />
==Second law==<br />
第二定律<br />
<br />
The [[second law of thermodynamics]] indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
The second law of thermodynamics indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
热力学第二定律表明了自然过程的不可逆性，并且在许多情况下，自然过程的趋向于物质很能量的空间均匀性，特别是温度。它可以用各种有趣而重要的方式来表达。<br />
<br />
<br />
<br />
It implies the existence of a quantity called the [[entropy]] of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
这意味着热力学系统中存在一个叫做熵的量。了一个叫做热力学系统熵的量的存在。就这个数量而言，它意味着<br />
<br />
{{quote|When two initially isolated systems in separate but nearby regions of space, each in [[thermodynamic equilibrium]] with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the [[entropy|entropies]] of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values.}}<br><br />
当两个最初隔离的系统分别位于彼此独立但不一定彼此处于热力学平衡的空间区域中，然后彼此相互作用时，它们最终将达到相互的热力学平衡。最初隔离的系统的熵之和小于或等于最终组合的总熵。当两个初始系统各自的强变量(温度、压力)相等时，才发生平等。那么最终的系统也有相同的值。<br />
<br />
<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
第二定律适用于可逆和不可逆的多种过程。所有的自然过程都是不可逆的。可逆过程是一个有用的和方便的理论假设，但不发生在自然界。<br />
<br />
<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
这种不可逆性的一个主要例子是通过传导或辐射进行的热传递。早在熵的概念被发现之前，人们就已经知道，当两个最初温度不同的物体直接进行热连接时，热量总是自发地从较热的物体流向较冷的物体。<br />
<br />
<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
第二定律也告诉我们除了热传递之外的不可逆性，例如摩擦力和粘度，以及化学反应。'''<font color="#32CD32">需要熵的概念给该定律提供更广泛的范围。</font>'''<br />
<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, ''δQ'', is the product of the temperature (''T''), both of the system and of the sources or destination of the heat, with the increment (''dS'') of the system's conjugate variable, its [[entropy]] (''S'')<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S)<br />
<br />
根据热力学第二定律，在理论上和假设的可逆传热中，传热元素δQ是系统和热源或热目的地的温度(t)与系统共轭变量熵（S）的增量(dS)的乘积<br />
<br />
<br />
<br />
:<math>\delta Q = T\,dS\, .</math><ref name="Guggenheim 1985"/><br />
<br />
<math>\delta Q = T\,dS\, .</math><br />
<br />
数学 delta q t ，dS ，. / math<br />
<br />
<br />
<br />
[[Entropy]] may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as ''disorder'' on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<ref>Ben-Naim, A. (2008). ''A Farewell to Entropy: Statistical Thermodynamics Based on Information'', World Scientific, New Jersey, {{ISBN|978-981-270-706-2}}.</ref><br />
<br />
Entropy may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as disorder on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<br />
<br />
当只知道宏观状态时，熵也可以被看作是对系统运动和构型的微观细节有关的物理度量。这种细节通常在微观或分子尺度上被称为无序。该定律声称，对于一个系统的两个给定的宏观指定状态，它们之间存在一个被称为熵差的量。'''<font color="#32CD32">这种熵的差异定义了需要多少额外的微观物理信息来指定一个宏观指定状态，给定另一个宏观指定状态-通常是一个方便选择的参考状态，这可能是假定存在的，而不是明确陈述的。自然过程的最终条件始终包含着微观上特定的影响，而这些影响，从过程初始条件的宏观规定来看是无法被完全准确预测的。这就是为什么熵在自然过程中会增加——熵的增加告诉我们需要多少额外的微观信息来区分最终的宏观指定状态和最初的宏观指定状态。</font>'''<br />
<br />
<br />
==Third law==<br />
第三定律<br />
<br />
The [[third law of thermodynamics]] is sometimes stated as follows:<br />
<br />
The third law of thermodynamics is sometimes stated as follows:<br />
<br />
热力学第三定律可以表示为：<br />
<br />
:''The [[entropy]] of a perfect [[crystal]] of any pure substance approaches zero as the temperature approaches [[absolute zero]].''<br />
<br />
The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero.<br />
<br />
当温度接近绝对零度时，任何纯物质的完整晶体的熵接近零。<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one [[microstate (statistical mechanics)|state with minimum energy]]. Entropy is related to the number of possible microstates according to:<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy. Entropy is related to the number of possible microstates according to:<br />
<br />
在零温时，系统必须处于热能最小的状态。如果完美晶体只有一种能量最小的状态，则该说法成立。熵与可能的微状态数有关:<br />
<br />
<br />
<br />
::<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
数学知识，数学知识，欧米茄 / 数学<br />
<br />
<br />
<br />
Where ''S'' is the entropy of the system, ''k''<sub>B</sub> [[Boltzmann constant|Boltzmann's constant]], and ''Ω'' the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (''Ω''=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
Where S is the entropy of the system, k<sub>B</sub> Boltzmann's constant, and Ω the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (Ω=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
其中 s 是系统的熵，k<sub>B</sub>是玻尔兹曼常数，以及Ω是微状态数(例如:可能的原子结构)。在绝对零度下只有一种微状态(Ω=1，因为纯物质的所有原子都是相同的，所以所有阶数都是相同的，因为只有一个组合)和 ln (1)=0。<br />
<br />
<br />
<br />
A more general form of the third law that applies to a system such as a [[glass]] that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
A more general form of the third law that applies to a system such as a glass that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
第三定律的一个更普遍的形式，适用于像玻璃这样的系统，'''<font color="#32CD32">可能有一个以上的微观上截然不同的能量状态，或可能有一个微观上截然不同的“冻结状态”，虽然不是一个严格意义上的的最低能量状态，也不是严格意义上的热力学平衡，</font>'''在绝对零度:<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]） “在绝对零度:” “在绝对零度下”？<br />
<br />
:''The entropy of a system approaches a constant value as the temperature approaches zero.''<br />
<br />
The entropy of a system approaches a constant value as the temperature approaches zero.<br />
<br />
系统的熵随着温度接近绝对零度而接近一个恒定值。<br />
<br />
<br />
<br />
The constant value (not necessarily zero) is called the [[residual entropy]] of the system.<br />
<br />
The constant value (not necessarily zero) is called the residual entropy of the system.<br />
<br />
这个常数(不一定是零)被称为系统的余熵。<br />
<br />
==History==<br />
历史<br />
<br />
{{see also|Philosophy of thermal and statistical physics}}<br><br />
热学和统计物理学的哲学<br />
<br />
[[Mechanical equivalent of heat|Circa 1797, Count Rumford (born Benjamin Thompson)]] showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] in 1824. By 1860, as formalized in the works of those such as [[Rudolf Clausius]] and [[William Thomson, 1st Baron Kelvin|William Thomson]], two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist [[Josiah Willard Gibbs]], in his memoir ''Graphical Methods in the Thermodynamics of Fluids'', clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
Circa 1797, Count Rumford (born Benjamin Thompson) showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824. By 1860, as formalized in the works of those such as Rudolf Clausius and William Thomson, two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist Josiah Willard Gibbs, in his memoir Graphical Methods in the Thermodynamics of Fluids, clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
大约在1797年，拉姆福德(出生于本杰明·汤普森)表明，无休止的机械作用可以从固定数量的工作物质中产生无限量的热量，从而挑战了热量理论。该理论认为在固定数量的工作物质中会有有限的热量 / 能量。1824年，萨迪·卡诺建立了第一个热力学原理，也就是后来的热力学第二定律。到1860年，正如鲁道夫 · 克劳修斯和威廉 · 汤姆森等人的著作所正式规定的那样，已经确立的两个热力学原理得到了发展，第一个原理和第二个原理，后来被重新定义为热力学定律。例如，1873年，热力学学家乔赛亚·威拉德·吉布斯在他的回忆录《流体热力学的图解法》中明确阐述了热力学的前两个绝对定律。整个20世纪的一些教科书对这些定律进行了不同的编号。在一些与化学无关的领域，第二定律被认为仅仅处理热机的效率问题，而所谓的第三定律则处理熵的增加问题。'''<font color="#32CD32">直接定义熵计算的零律不被认为是一条定律。</font>'''这种分离逐渐形成了第二定律，现代第三定律被广泛采用。<br />
<br />
<br />
<br />
==See also==<br />
<br />
*化学热力学 [[Chemical thermodynamics]]<br />
<br />
*守恒定律 [[Conservation law (physics)|Conservation law]]<br />
<br />
*熵增 [[Entropy production]]<br />
<br />
*金斯伯格定理 [[Ginsberg's theorem]]<br />
<br />
*宇宙热寂 [[Heat death of the universe]]<br />
<br />
*H定理 [[H-theorem]]<br />
<br />
*科学规律 [[Laws of science]]<br />
<br />
*昂萨格倒易关系（有时被描述为热力学第四定律） [[Onsager reciprocal relations]] (sometimes described as a fourth law of thermodynamics)<br />
<br />
*统计力学 [[Statistical mechanics]]<br />
<br />
*热力学方程表 [[Table of thermodynamic equations]]<br />
<br />
<br />
<br />
==References==<br><br />
参考文献<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
==Further reading==<br />
<br />
* [[Peter Atkins|Atkins, Peter]] (2007). ''Four Laws That Drive the Universe''. OUP Oxford. {{ISBN|978-0199232369}}<br />
<br />
* Goldstein, Martin & Inge F. (1993). ''The Refrigerator and the Universe''. Harvard Univ. Press. {{ISBN|978-0674753259}}<br />
<br />
<br />
<br />
==External links==<br />
<br />
* [http://www.bbc.co.uk/programmes/b06c06nd In Our Time: Perpetual Motion], BBC discussion about the Laws, with Ruth Gregory, Frank Close and Steven Bramwell, hosted by Melvyn Bragg, first broadcast 24 September 2015.<br />
<br />
<br />
<br />
[[Category:Laws of thermodynamics| ]]<br />
<br />
[[Category:Scientific laws]]<br />
<br />
Category:Scientific laws<br />
<br />
类别: 科学定律<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Laws of thermodynamics]]. Its edit history can be viewed at [[热力学定律/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6%E5%AE%9A%E5%BE%8B_Laws_of_thermodynamics&diff=14684热力学定律 Laws of thermodynamics2020-10-01T15:40:26Z<p>趣木木：/* Third law */</p>
<hr />
<div>本词条由Solitude初步翻译<br />
<br />
{{Thermodynamics|cTopic=Laws}}<br><br />
模板：热力学<br />
<br />
The '''laws of thermodynamics''' define physical quantities, such as [[temperature]], [[energy]], and [[entropy]], that characterize [[thermodynamic system]]s at [[thermodynamic equilibrium]]. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as [[perpetual motion]]. In addition to their use in [[thermodynamics]], they are important fundamental [[Physical law|laws]] of [[physics]] in general, and are applicable in other natural [[sciences]].<br />
<br />
The laws of thermodynamics define physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems at thermodynamic equilibrium. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.<br />
<br />
'''<font color="#ff8000"> 热力学定律The laws of thermodynamics</font>'''定义了许多物理量，如'''<font color="#ff8000"> 温度temperature</font>'''、'''<font color="#ff8000"> 能量energy</font>'''和'''<font color="#ff8000">熵 entropy</font>'''，这些物理量表征处于热力学平衡的热力学系统。这些定律描述了这些物理量之间的关系，并构成了排除某些现象的可能性的基础，例如永动机。除了在热力学中的应用之外，它们也是一般物理学中的重要基本定律，也适用于其他自然科学。<br />
<br />
<br />
<br />
<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.<ref name="Guggenheim 1985">Guggenheim, E.A. (1985). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', seventh edition, North Holland, Amsterdam, {{ISBN|0-444-86951-4}}.</ref><ref name="Kittel and Kroemer 1980">Kittel, C. Kroemer, H. (1980). ''Thermal Physics'', second edition, W.H. Freeman, San Francisco, {{ISBN|0-7167-1088-9}}.</ref><ref name="Adkins 1968">Adkins, C.J. (1968). ''Equilibrium Thermodynamics'', McGraw-Hill, London, {{ISBN|0-07-084057-1}}.</ref><ref name="LJCV 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers'', Springer, Berlin, {{ISBN|978-3-540-74252-4}}.</ref><ref>{{cite book |author1=Chris Vuille |author2=Serway, Raymond A. |author3=Faughn, Jerry S. |title=College physics |publisher=Brooks/Cole, Cengage Learning |location=Belmont, CA |year=2009 |isbn=978-0-495-38693-3 |oclc= |doi= |accessdate= | page = 355 |url=https://books.google.com/books?id=CX0u0mIOZ44C&pg=PT355}}</ref>. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
传统上，'''<font color="#ff8000"> 热力学Thermodynamics</font>'''描述了三个基本定律：（简单的按顺序命名为）第一定律、第二定律和第三定律。此外，在前三个定律确立之后，人们认识到可以提出另一个对这三个定律更为基本的定律，即第零定律。<br />
<br />
<br />
<br />
The [[zeroth law of thermodynamics]] defines [[thermal equilibrium]] and forms a basis for the definition of [[temperature]]: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
'''<font color="#ff8000"> 热力学第零定律zeroth law of thermodynamics</font>'''定义了'''<font color="#ff8000"> 热平衡thermal equilibrium</font>'''，并为温度定义奠定了基础：如果两个系统都与第三个系统处于热平衡，则它们彼此也处于热平衡。<br />
<br />
<br />
<br />
The [[first law of thermodynamics]]: When energy passes, as [[Work (thermodynamics)|work]], as [[heat]], or with matter, into or out of a system, the system's [[internal energy]] changes in accord with the law of [[conservation of energy]]. Equivalently, [[perpetual motion machine of the first kind|perpetual motion machines of the first kind]] (machines that produce work with no energy input) are impossible.<br />
<br />
The first law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out of a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind (machines that produce work with no energy input) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第一定律first law of thermodynamics</font>''':当能量以'''<font color="#ff8000"> 功work</font>'''、'''<font color="#ff8000"> 热heat</font>'''或物质的形式进入或离开一个系统时，系统的'''<font color="#ff8000"> 内能 internal energy</font>'''根据能量守恒定律发生变化。同样地，第一类永动机机器(不需要能量输入就能工作的机器)是不可能造成的。<br />
<br />
<br />
<br />
The [[second law of thermodynamics]]: In a natural [[thermodynamic process]], the sum of the [[entropy|entropies]] of the interacting [[thermodynamic system]]s increases. Equivalently, [[perpetual motion machine of the second kind|perpetual motion machines of the second kind]] (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
The second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第二定律second law of thermodynamics</font>''':在自然热力学过程中，相互作用的热力学系统的熵的总和增加。同样地，第二类永动机(自发地把热能转化为机械功的机器)是不可能制造出的。<br />
<br />
<br />
<br />
The [[third law of thermodynamics]]: The [[entropy]] of a system approaches a constant value as the temperature approaches [[absolute zero]].<ref name="Kittel and Kroemer 1980"/> With the exception of non-crystalline solids ([[glass]]es) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
The third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
'''<font color="#ff8000"> 热力学第三定律third law of thermodynamics</font>''':当温度趋于'''<font color="#ff8000"> 绝对零度absolute zero</font>'''时，系统的熵趋于一个定值。除非晶固体(玻璃)外，系统在绝对零度时的熵通常接近于零。<br />
<br />
<br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<ref name="Guggenheim 1985"/><ref name="Kittel and Kroemer 1980"/><ref name="Adkins 1968"/><ref name="LJCV 2008"/><ref name="DGM 1962">De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North Holland, Amsterdam.</ref><ref name="Glansdorff and Prigogine 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London, {{ISBN|0-471-30280-5}}.</ref><br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<br />
<br />
有人提出了其他的定律，但没有一个达到公认的四个定律的普遍性，也没有在标准教科书中被讨论。<br />
<br />
<br />
==Zeroth law==<br />
<br />
热力学零定律<br />
<br />
The [[zeroth law of thermodynamics]] may be stated in the following form:<br />
<br />
The zeroth law of thermodynamics may be stated in the following form:<br />
<br />
热力学第零定律可以用以下形式表示：<br />
<br />
<br />
<br />
{{quote|If two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other.<ref>Guggenheim (1985), p.&nbsp;8.</ref>}}<br><br />
如果两个系统都与第三个系统处于热平衡状态，则它们彼此处于热平衡状态.<br />
<br />
<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a [[mass]] of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a mass of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
该定律旨在允许一个经验参数存在，即温度，作为热力学系统的一种性质，即相互处于热平衡的系统具有相同的温度。这里所述的定律适用于特定的物质(例如一定量的气体物质）来匹配其他物质的温度，但不能证明温度是一个可以用实数来衡量的量。<br />
<br />
<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter.<ref>Sommerfeld, A. (1951/1955). ''Thermodynamics and Statistical Mechanics'', vol. 5 of ''Lectures on Theoretical Physics'', edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York, p. 1.</ref><ref>[[James Serrin|Serrin, J.]] (1978). The concepts of thermodynamics, in ''Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977'', edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, {{ISBN|0-444-85166-6}}, pp. 411–51.</ref><ref>[[James Serrin|Serrin, J.]] (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pp. 3–32, in ''New Perspectives in Thermodynamics'', edited by J. Serrin, Springer, Berlin, {{ISBN|3-540-15931-2}}.</ref> Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter. Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
虽然这个版本的定律是最常见的陈述版本之一，但它只是被称为“第零定律”的众多陈述之一。有些陈述更进一步，提供了一个重要的物理事实，即温度是一维的，并且从概念上把物体按实数顺序由冷到热排列。也许对于“第零定律”并没有唯一的“最佳的表述”，因为在文献中有一系列的热力学原理的表述，每一种都要求对热力学定律作出各自适当的说明。<br />
<br />
<br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its [[Conjugate variables (thermodynamics)|conjugate variable]]. Such a temperature definition is said to be 'empirical'.<ref>Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (first edition 1968), third edition 1983, Cambridge University Press, {{ISBN|0-521-25445-0}}, pp. 18–20.</ref><ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}, p. 26.</ref><ref>Buchdahl, H.A. (1966), ''The Concepts of Classical Thermodynamics'', Cambridge University Press, London, pp. 30, 34ff, 46f, 83.</ref><ref>*Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, {{ISBN|0-471-62430-6}}, p. 22.</ref><ref>[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge, p. 10.</ref><ref>[[Harold A. Wilson (physicist)|Wilson, H.A.]] (1966). ''Thermodynamics and Statistical Mechanics'', Cambridge University Press, London, pp. 4, 8, 68, 86, 97, 311.</ref><br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable. Such a temperature definition is said to be 'empirical'.<br />
<br />
虽然这些关于温度和热平衡的概念是热力学的基础，并在19世纪得到了清楚的阐述，但是直到20世纪30年代福勒和古根海姆这样做的时候，人们才普遍感觉到需要对上述定律进行明确编号，而这时第一定律、第二定律和第三定律已经得到广泛的理解和认可。因此，它被称为第零定律。该定律作为早期定律基础的重要性在于，它允许以非循环的方式定义温度，而无需参考熵及其共轭变量。这样的温度定义被称为“经验主义”。<br />
<br />
<br />
<br />
==First law==<br />
第一定律<br />
<br />
The '''first law of thermodynamics''' is a version of the law of [[conservation of energy]], adapted for [[thermodynamic system]]s.<br />
<br />
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems.<br />
<br />
热力学第一定律是'''<font color="#ff8000"> 能量守恒conservation of energy</font>'''定律的一个版本，适用于热力学系统。<br />
<br />
<br />
The law of conservation of energy states that the total [[energy]] of an [[isolated system]] is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
能量守恒定律指出，一个孤立系统的总能量是恒定的;能量可以从一种形式转化为另一种形式，但能量既不会凭空产生也不会凭空消失。<br />
<br />
<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
对于一个没有物质转移的热力学过程，第一定律通常用公式表示为：<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
系统 q-w / math,<br />
<br />
<br />
<br />
where {{math|Δ''U''<sub>system</sub>}} denotes the change in the [[internal energy]] of a [[Thermodynamic system#Closed system|closed system]], {{math|''Q''}} denotes the quantity of energy supplied ''to'' the system as [[heat]], and {{math|''W''}} denotes the amount of [[Work (thermodynamics)|thermodynamic work]] (expressed here with a negative sign) done ''by'' the system on its surroundings. (An [[First law of thermodynamics#Sign conventions|alternate sign convention]] not used in this article is to define {{math|''W''}} as the work done ''on'' the system.) <br />
<br />
where denotes the change in the internal energy of a closed system, denotes the quantity of energy supplied to the system as heat, and denotes the amount of thermodynamic work (expressed here with a negative sign) done by the system on its surroundings. (An alternate sign convention not used in this article is to define as the work done on the system.) <br />
<br />
其中{{math|Δ''U''<sub>system</sub>}}表示一个封闭系统内部能量的变化，{{math|''Q''}} 表示外界对系统传递的热量，{{math|''W''}}表示该系统对周围环境所做的热力学功(在这里用负号表示)。(本文中没有使用的另一个符号约定是定义对系统所做的功。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）注意到前面的heat 译为了“热” {{math|''Q''}} 表？示外界对系统传递的热量 热量是否为“热”？<br />
<br />
<br />
<br />
In the case of a two-stage [[thermodynamic cycle]] of a closed system, which returns to its original state, the heat {{math|''Q<sub>in</sub>''}} supplied to the system in one stage of the cycle, minus the heat {{math|''Q<sub>out</sub>''}} removed from it in the other stage, plus the [[Work (thermodynamics)|thermodynamic work]] added to the system, {{math|''W<sub>in</sub>''}}, equals the thermodynamic work that leaves the system {{math|''W<sub>out</sub>''}}.<br />
<br />
In the case of a two-stage thermodynamic cycle of a closed system, which returns to its original state, the heat supplied to the system in one stage of the cycle, minus the heat removed from it in the other stage, plus the thermodynamic work added to the system, , equals the thermodynamic work that leaves the system .<br />
<br />
在封闭系统的两级'''<font color="#ff8000"> 热力循环thermodynamic cycle</font>'''中，该循环回到其原始状态，在循环的一个阶段向系统提供的热量{{math|''Q<sub>in</sub>''}}，减去另一个阶段从系统中去除的热量{{math|''Q<sub>out</sub>''}}，加上对系统做的的热力学功{{math|''W<sub>in</sub>''}}，等于离开系统的做的热力学功{{math|''W<sub>out</sub>''}}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
0 / math<br />
<br />
<br />
<br />
hence, for a full cycle,<br />
<br />
hence, for a full cycle,<br />
<br />
因此，一个完整的循环,<br />
<br />
<br />
<br />
::Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: {{math|''Q'' {{=}} 0}}.<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: 0}}.<br />
<br />
对于绝热系统（绝热隔离）的特殊情况，绝热隔离系统内能的变化只能是系统做功的结果，因为绝热假设是: 0}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
对于包括物质转移的过程，还需要进一步的说明: ‘在充分考虑了各个系统的基准参考状态后，当两个系统---- '''<font color="#32CD32">它们可能由不同的化学成分组成，最初只是被防渗墙隔开，或者是被隔离---- 通过移除墙体的热力学操作结合成一个新系统</font>'''，那么<br />
<br />
<br />
<br />
::<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
数学 u + u 2 / math,<br />
<br />
<br />
<br />
where {{math|''U''<sub>system</sub>}} denotes the internal energy of the combined system, and {{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} denote the internal energies of the respective separated systems.'<br />
<br />
where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.'<br />
<br />
其中{{math|''U''<sub>system</sub>}}表示组合系统的内能，{{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} 表示各自分离系统的内能<br />
<br />
<br />
<br />
The First Law encompasses several principles:<br />
<br />
The First Law encompasses several principles:<br />
<br />
第一定律包括以下几个原则:<br />
<br />
* The [[Conservation of energy|law of conservation of energy]].<br />
<br />
::This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
能量既不能被创造也不能被消灭。但是，能量可以改变形式，能量可以从一个地方流动到另一个地方。能量守恒定律的一个特殊结果是，孤立系统的总能量不变。<br />
<br />
* The concept of [[internal energy]] and its relationship to temperature.<br><br />
内能的概念及其与温度关系。<br />
<br />
::If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has [[kinetic energy]]. If the system as a whole is in an externally imposed force field (e.g. gravity), it has [[potential energy]] relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has kinetic energy. If the system as a whole is in an externally imposed force field (e.g. gravity), it has potential energy relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
如果系统具有确定的温度，则其总能量具有三个可区分的成分，分别称为动能（由与系统整体运动产生的能量），势能（由外部施加的立场产生的能量，比如重力）和内能（热热力学的基本量）。内能概念的确立将热力学第一定律与一般的能量守恒定律区分开来。<br />
——Solitude(讨论)<br />
<br />
<br />
::<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<br />
<br />
::The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, {{math|''U''}}, and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, , and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
物质的内能可以解释为其组成原子的不规则微观运动的不同动能和它们之间相互作用的势能的总和。这些微观能量统称为物质的内能，并由宏观热力学性质来解释。组成原子的微观运动的总和随着系统温度的升高而增加; 这假设在系统的微观层次上没有其他的相互作用，例如化学反应、组成原子相互间的势能。<br />
<br />
* [[Work (physics)|Work]] is a process of transferring energy to or from a system in ways that can be described by macroscopic mechanical forces exerted by factors in the surroundings, outside the system. Examples are an externally driven shaft agitating a stirrer within the system, or an externally imposed electric field that polarizes the material of the system, or a piston that compresses the system. Unless otherwise stated, it is customary to treat work as occurring without its [[dissipation]] to the surroundings. Practically speaking, in all natural process, some of the work is dissipated by internal friction or viscosity. The work done by the system can come from its overall kinetic energy, from its overall potential energy, or from its internal energy.<br />
<br />
做功是一种以某种方式向系统传递能量或从系统传递能量的过程，其方式可以用作用在系统外部及其周围环境之间的宏观机械力来描述。'''<font color="#32CD32">例如，外部驱动的轴在系统内搅动，或外部施加的电场使系统材料极化，或活塞压缩系统。</font>'''除非另有说明，习惯上把做功看作是在不影响周围环境的情况下发生的。实际上，在一切自然过程中，有些功是因内摩擦或粘黏而消失的。系统所做的功，可以来自于它的总动能，总势能或者它的内能。<br />
<br />
<br />
::For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's [[gravitational potential energy]]. Work added to the system increases the Potential Energy of the system:<br />
<br />
For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's gravitational potential energy. Work added to the system increases the Potential Energy of the system:<br />
<br />
例如，当一台机器(不是系统的一部分)将系统向上提升时，一些能量就会从机器转移到系统。系统的能量随着系统所做功的增加而增加，在这种特殊的情况下，系统的能量增加表现为系统的重力势能的增加。对系统做的增加了系统的势能:<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“对系统做的增加了系统的势能” 需要对全文进行通读 这里少词<br />
<br />
<br />
:::<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<br />
<br />
::Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
或者一般来说，以功的形式加入系统的能量可以分为动能、势能或内能:<br />
<br />
<br />
<br />
:::<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
* When matter is transferred into a system, that masses' associated internal energy and potential energy are transferred with it.<br><br />
当物质转移到一个系统中时，物质相关的内能和势能也随之转移。<br />
<br />
<br />
<br />
:::<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
在 Delta u { system } / math 中的 math left (u，Delta m right)<br />
<br />
<br />
<br />
::where {{math|''u''}} denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and {{math|Δ''M''}} denotes the amount of transferred mass.<br />
<br />
where denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and denotes the amount of transferred mass.<br />
<br />
其中{{math|''u''}}表示在周围环境中测量的转移物质的单位质量的内能; {{math|Δ''M''}}表示被转移物质的数量。<br />
<br />
* The flow of [[heat]] is a form of energy transfer.<br><br />
热的流动是能量传递的一种形式。<br />
<br />
::Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
加热是一个将能量转移到系统中或从系统中转移出的自然过程，而不是通过做功或物质的转移。热量只能从较热的系统直接传递到较冷的系统。<br />
<br />
<br />
<br />
:::If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
如果系统具有不渗透物质的刚性壁，那么能量不能通过做功传入或传出系统，而且没有外部的远程力场影响系统以改变其内能，那么内能只能通过以热的形式进行传递来改变:<br />
<br />
<br />
<br />
:::<math>\Delta U_{\rm system}=Q</math><br />
<br />
<math>\Delta U_{\rm system}=Q</math><br />
<br />
系统的 q / math<br />
<br />
<br />
<br />
where {{math|''Q''}} denotes the amount of energy transferred into the system as heat.<br />
<br />
where denotes the amount of energy transferred into the system as heat.<br />
<br />
其中 {{math|''Q''}}表示以热量形式传递到系统中的能量。<br />
<br />
<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
结合这些原理，就可以得出传统的热力学第一定律的表述: 不可能制造一台在没有等量能量输入的情况下不断做功的机器。或者更简单地说，第一类永动机是不可能造成的。<br />
<br />
==Second law==<br />
第二定律<br />
<br />
The [[second law of thermodynamics]] indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
The second law of thermodynamics indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
热力学第二定律表明了自然过程的不可逆性，并且在许多情况下，自然过程的趋向于物质很能量的空间均匀性，特别是温度。它可以用各种有趣而重要的方式来表达。<br />
<br />
<br />
<br />
It implies the existence of a quantity called the [[entropy]] of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
这意味着热力学系统中存在一个叫做熵的量。了一个叫做热力学系统熵的量的存在。就这个数量而言，它意味着<br />
<br />
{{quote|When two initially isolated systems in separate but nearby regions of space, each in [[thermodynamic equilibrium]] with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the [[entropy|entropies]] of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values.}}<br><br />
当两个最初隔离的系统分别位于彼此独立但不一定彼此处于热力学平衡的空间区域中，然后彼此相互作用时，它们最终将达到相互的热力学平衡。最初隔离的系统的熵之和小于或等于最终组合的总熵。当两个初始系统各自的强变量(温度、压力)相等时，才发生平等。那么最终的系统也有相同的值。<br />
<br />
<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
第二定律适用于可逆和不可逆的多种过程。所有的自然过程都是不可逆的。可逆过程是一个有用的和方便的理论假设，但不发生在自然界。<br />
<br />
<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
这种不可逆性的一个主要例子是通过传导或辐射进行的热传递。早在熵的概念被发现之前，人们就已经知道，当两个最初温度不同的物体直接进行热连接时，热量总是自发地从较热的物体流向较冷的物体。<br />
<br />
<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
第二定律也告诉我们除了热传递之外的不可逆性，例如摩擦力和粘度，以及化学反应。'''<font color="#32CD32">需要熵的概念给该定律提供更广泛的范围。</font>'''<br />
<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, ''δQ'', is the product of the temperature (''T''), both of the system and of the sources or destination of the heat, with the increment (''dS'') of the system's conjugate variable, its [[entropy]] (''S'')<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S)<br />
<br />
根据热力学第二定律，在理论上和假设的可逆传热中，传热元素δQ是系统和热源或热目的地的温度(t)与系统共轭变量熵（S）的增量(dS)的乘积<br />
<br />
<br />
<br />
:<math>\delta Q = T\,dS\, .</math><ref name="Guggenheim 1985"/><br />
<br />
<math>\delta Q = T\,dS\, .</math><br />
<br />
数学 delta q t ，dS ，. / math<br />
<br />
<br />
<br />
[[Entropy]] may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as ''disorder'' on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<ref>Ben-Naim, A. (2008). ''A Farewell to Entropy: Statistical Thermodynamics Based on Information'', World Scientific, New Jersey, {{ISBN|978-981-270-706-2}}.</ref><br />
<br />
Entropy may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as disorder on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<br />
<br />
当只知道宏观状态时，熵也可以被看作是对系统运动和构型的微观细节有关的物理度量。这种细节通常在微观或分子尺度上被称为无序。该定律声称，对于一个系统的两个给定的宏观指定状态，它们之间存在一个被称为熵差的量。'''<font color="#32CD32">这种熵的差异定义了需要多少额外的微观物理信息来指定一个宏观指定状态，给定另一个宏观指定状态-通常是一个方便选择的参考状态，这可能是假定存在的，而不是明确陈述的。自然过程的最终条件始终包含着微观上特定的影响，而这些影响，从过程初始条件的宏观规定来看是无法被完全准确预测的。这就是为什么熵在自然过程中会增加——熵的增加告诉我们需要多少额外的微观信息来区分最终的宏观指定状态和最初的宏观指定状态。</font>'''<br />
<br />
<br />
==Third law==<br />
第三定律<br />
<br />
The [[third law of thermodynamics]] is sometimes stated as follows:<br />
<br />
The third law of thermodynamics is sometimes stated as follows:<br />
<br />
热力学第三定律可以表示为：<br />
<br />
:''The [[entropy]] of a perfect [[crystal]] of any pure substance approaches zero as the temperature approaches [[absolute zero]].''<br />
<br />
The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero.<br />
<br />
当温度接近绝对零度时，任何纯物质的完整晶体的熵接近零。<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one [[microstate (statistical mechanics)|state with minimum energy]]. Entropy is related to the number of possible microstates according to:<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy. Entropy is related to the number of possible microstates according to:<br />
<br />
在零温时，系统必须处于热能最小的状态。如果完美晶体只有一种能量最小的状态，则该说法成立。熵与可能的微状态数有关:<br />
<br />
<br />
<br />
::<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
数学知识，数学知识，欧米茄 / 数学<br />
<br />
<br />
<br />
Where ''S'' is the entropy of the system, ''k''<sub>B</sub> [[Boltzmann constant|Boltzmann's constant]], and ''Ω'' the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (''Ω''=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
Where S is the entropy of the system, k<sub>B</sub> Boltzmann's constant, and Ω the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (Ω=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
其中 s 是系统的熵，k<sub>B</sub>是玻尔兹曼常数，以及Ω是微状态数(例如:可能的原子结构)。在绝对零度下只有一种微状态(Ω=1，因为纯物质的所有原子都是相同的，所以所有阶数都是相同的，因为只有一个组合)和 ln (1)=0。<br />
<br />
<br />
<br />
A more general form of the third law that applies to a system such as a [[glass]] that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
A more general form of the third law that applies to a system such as a glass that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
第三定律的一个更普遍的形式，适用于像玻璃这样的系统，'''<font color="#32CD32">可能有一个以上的微观上截然不同的能量状态，或可能有一个微观上截然不同的“冻结状态”，虽然不是一个严格意义上的的最低能量状态，也不是严格意义上的热力学平衡，</font>'''在绝对零度:<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]） “在绝对零度:<br />
” “在绝对零度下”？<br />
<br />
:''The entropy of a system approaches a constant value as the temperature approaches zero.''<br />
<br />
The entropy of a system approaches a constant value as the temperature approaches zero.<br />
<br />
系统的熵随着温度接近绝对零度而接近一个恒定值。<br />
<br />
<br />
<br />
The constant value (not necessarily zero) is called the [[residual entropy]] of the system.<br />
<br />
The constant value (not necessarily zero) is called the residual entropy of the system.<br />
<br />
这个常数(不一定是零)被称为系统的余熵。<br />
<br />
==History==<br />
历史<br />
<br />
{{see also|Philosophy of thermal and statistical physics}}<br><br />
热学和统计物理学的哲学<br />
<br />
[[Mechanical equivalent of heat|Circa 1797, Count Rumford (born Benjamin Thompson)]] showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] in 1824. By 1860, as formalized in the works of those such as [[Rudolf Clausius]] and [[William Thomson, 1st Baron Kelvin|William Thomson]], two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist [[Josiah Willard Gibbs]], in his memoir ''Graphical Methods in the Thermodynamics of Fluids'', clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
Circa 1797, Count Rumford (born Benjamin Thompson) showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824. By 1860, as formalized in the works of those such as Rudolf Clausius and William Thomson, two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist Josiah Willard Gibbs, in his memoir Graphical Methods in the Thermodynamics of Fluids, clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
大约在1797年，拉姆福德(出生于本杰明·汤普森)表明，无休止的机械作用可以从固定数量的工作物质中产生无限量的热量，从而挑战了热量理论。该理论认为在固定数量的工作物质中会有有限的热量 / 能量。1824年，萨迪·卡诺建立了第一个热力学原理，也就是后来的热力学第二定律。到1860年，正如鲁道夫 · 克劳修斯和威廉 · 汤姆森等人的著作所正式规定的那样，已经确立的两个热力学原理得到了发展，第一个原理和第二个原理，后来被重新定义为热力学定律。例如，1873年，热力学学家乔赛亚·威拉德·吉布斯在他的回忆录《流体热力学的图解法》中明确阐述了热力学的前两个绝对定律。整个20世纪的一些教科书对这些定律进行了不同的编号。在一些与化学无关的领域，第二定律被认为仅仅处理热机的效率问题，而所谓的第三定律则处理熵的增加问题。'''<font color="#32CD32">直接定义熵计算的零律不被认为是一条定律。</font>'''这种分离逐渐形成了第二定律，现代第三定律被广泛采用。<br />
<br />
<br />
<br />
==See also==<br />
<br />
*化学热力学 [[Chemical thermodynamics]]<br />
<br />
*守恒定律 [[Conservation law (physics)|Conservation law]]<br />
<br />
*熵增 [[Entropy production]]<br />
<br />
*金斯伯格定理 [[Ginsberg's theorem]]<br />
<br />
*宇宙热寂 [[Heat death of the universe]]<br />
<br />
*H定理 [[H-theorem]]<br />
<br />
*科学规律 [[Laws of science]]<br />
<br />
*昂萨格倒易关系（有时被描述为热力学第四定律） [[Onsager reciprocal relations]] (sometimes described as a fourth law of thermodynamics)<br />
<br />
*统计力学 [[Statistical mechanics]]<br />
<br />
*热力学方程表 [[Table of thermodynamic equations]]<br />
<br />
<br />
<br />
==References==<br><br />
参考文献<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
==Further reading==<br />
<br />
* [[Peter Atkins|Atkins, Peter]] (2007). ''Four Laws That Drive the Universe''. OUP Oxford. {{ISBN|978-0199232369}}<br />
<br />
* Goldstein, Martin & Inge F. (1993). ''The Refrigerator and the Universe''. Harvard Univ. Press. {{ISBN|978-0674753259}}<br />
<br />
<br />
<br />
==External links==<br />
<br />
* [http://www.bbc.co.uk/programmes/b06c06nd In Our Time: Perpetual Motion], BBC discussion about the Laws, with Ruth Gregory, Frank Close and Steven Bramwell, hosted by Melvyn Bragg, first broadcast 24 September 2015.<br />
<br />
<br />
<br />
[[Category:Laws of thermodynamics| ]]<br />
<br />
[[Category:Scientific laws]]<br />
<br />
Category:Scientific laws<br />
<br />
类别: 科学定律<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Laws of thermodynamics]]. Its edit history can be viewed at [[热力学定律/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6%E5%AE%9A%E5%BE%8B_Laws_of_thermodynamics&diff=14683热力学定律 Laws of thermodynamics2020-10-01T15:38:22Z<p>趣木木：/* First law */</p>
<hr />
<div>本词条由Solitude初步翻译<br />
<br />
{{Thermodynamics|cTopic=Laws}}<br><br />
模板：热力学<br />
<br />
The '''laws of thermodynamics''' define physical quantities, such as [[temperature]], [[energy]], and [[entropy]], that characterize [[thermodynamic system]]s at [[thermodynamic equilibrium]]. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as [[perpetual motion]]. In addition to their use in [[thermodynamics]], they are important fundamental [[Physical law|laws]] of [[physics]] in general, and are applicable in other natural [[sciences]].<br />
<br />
The laws of thermodynamics define physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems at thermodynamic equilibrium. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.<br />
<br />
'''<font color="#ff8000"> 热力学定律The laws of thermodynamics</font>'''定义了许多物理量，如'''<font color="#ff8000"> 温度temperature</font>'''、'''<font color="#ff8000"> 能量energy</font>'''和'''<font color="#ff8000">熵 entropy</font>'''，这些物理量表征处于热力学平衡的热力学系统。这些定律描述了这些物理量之间的关系，并构成了排除某些现象的可能性的基础，例如永动机。除了在热力学中的应用之外，它们也是一般物理学中的重要基本定律，也适用于其他自然科学。<br />
<br />
<br />
<br />
<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.<ref name="Guggenheim 1985">Guggenheim, E.A. (1985). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', seventh edition, North Holland, Amsterdam, {{ISBN|0-444-86951-4}}.</ref><ref name="Kittel and Kroemer 1980">Kittel, C. Kroemer, H. (1980). ''Thermal Physics'', second edition, W.H. Freeman, San Francisco, {{ISBN|0-7167-1088-9}}.</ref><ref name="Adkins 1968">Adkins, C.J. (1968). ''Equilibrium Thermodynamics'', McGraw-Hill, London, {{ISBN|0-07-084057-1}}.</ref><ref name="LJCV 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers'', Springer, Berlin, {{ISBN|978-3-540-74252-4}}.</ref><ref>{{cite book |author1=Chris Vuille |author2=Serway, Raymond A. |author3=Faughn, Jerry S. |title=College physics |publisher=Brooks/Cole, Cengage Learning |location=Belmont, CA |year=2009 |isbn=978-0-495-38693-3 |oclc= |doi= |accessdate= | page = 355 |url=https://books.google.com/books?id=CX0u0mIOZ44C&pg=PT355}}</ref>. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
传统上，'''<font color="#ff8000"> 热力学Thermodynamics</font>'''描述了三个基本定律：（简单的按顺序命名为）第一定律、第二定律和第三定律。此外，在前三个定律确立之后，人们认识到可以提出另一个对这三个定律更为基本的定律，即第零定律。<br />
<br />
<br />
<br />
The [[zeroth law of thermodynamics]] defines [[thermal equilibrium]] and forms a basis for the definition of [[temperature]]: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
'''<font color="#ff8000"> 热力学第零定律zeroth law of thermodynamics</font>'''定义了'''<font color="#ff8000"> 热平衡thermal equilibrium</font>'''，并为温度定义奠定了基础：如果两个系统都与第三个系统处于热平衡，则它们彼此也处于热平衡。<br />
<br />
<br />
<br />
The [[first law of thermodynamics]]: When energy passes, as [[Work (thermodynamics)|work]], as [[heat]], or with matter, into or out of a system, the system's [[internal energy]] changes in accord with the law of [[conservation of energy]]. Equivalently, [[perpetual motion machine of the first kind|perpetual motion machines of the first kind]] (machines that produce work with no energy input) are impossible.<br />
<br />
The first law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out of a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind (machines that produce work with no energy input) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第一定律first law of thermodynamics</font>''':当能量以'''<font color="#ff8000"> 功work</font>'''、'''<font color="#ff8000"> 热heat</font>'''或物质的形式进入或离开一个系统时，系统的'''<font color="#ff8000"> 内能 internal energy</font>'''根据能量守恒定律发生变化。同样地，第一类永动机机器(不需要能量输入就能工作的机器)是不可能造成的。<br />
<br />
<br />
<br />
The [[second law of thermodynamics]]: In a natural [[thermodynamic process]], the sum of the [[entropy|entropies]] of the interacting [[thermodynamic system]]s increases. Equivalently, [[perpetual motion machine of the second kind|perpetual motion machines of the second kind]] (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
The second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第二定律second law of thermodynamics</font>''':在自然热力学过程中，相互作用的热力学系统的熵的总和增加。同样地，第二类永动机(自发地把热能转化为机械功的机器)是不可能制造出的。<br />
<br />
<br />
<br />
The [[third law of thermodynamics]]: The [[entropy]] of a system approaches a constant value as the temperature approaches [[absolute zero]].<ref name="Kittel and Kroemer 1980"/> With the exception of non-crystalline solids ([[glass]]es) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
The third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
'''<font color="#ff8000"> 热力学第三定律third law of thermodynamics</font>''':当温度趋于'''<font color="#ff8000"> 绝对零度absolute zero</font>'''时，系统的熵趋于一个定值。除非晶固体(玻璃)外，系统在绝对零度时的熵通常接近于零。<br />
<br />
<br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<ref name="Guggenheim 1985"/><ref name="Kittel and Kroemer 1980"/><ref name="Adkins 1968"/><ref name="LJCV 2008"/><ref name="DGM 1962">De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North Holland, Amsterdam.</ref><ref name="Glansdorff and Prigogine 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London, {{ISBN|0-471-30280-5}}.</ref><br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<br />
<br />
有人提出了其他的定律，但没有一个达到公认的四个定律的普遍性，也没有在标准教科书中被讨论。<br />
<br />
<br />
==Zeroth law==<br />
<br />
热力学零定律<br />
<br />
The [[zeroth law of thermodynamics]] may be stated in the following form:<br />
<br />
The zeroth law of thermodynamics may be stated in the following form:<br />
<br />
热力学第零定律可以用以下形式表示：<br />
<br />
<br />
<br />
{{quote|If two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other.<ref>Guggenheim (1985), p.&nbsp;8.</ref>}}<br><br />
如果两个系统都与第三个系统处于热平衡状态，则它们彼此处于热平衡状态.<br />
<br />
<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a [[mass]] of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a mass of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
该定律旨在允许一个经验参数存在，即温度，作为热力学系统的一种性质，即相互处于热平衡的系统具有相同的温度。这里所述的定律适用于特定的物质(例如一定量的气体物质）来匹配其他物质的温度，但不能证明温度是一个可以用实数来衡量的量。<br />
<br />
<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter.<ref>Sommerfeld, A. (1951/1955). ''Thermodynamics and Statistical Mechanics'', vol. 5 of ''Lectures on Theoretical Physics'', edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York, p. 1.</ref><ref>[[James Serrin|Serrin, J.]] (1978). The concepts of thermodynamics, in ''Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977'', edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, {{ISBN|0-444-85166-6}}, pp. 411–51.</ref><ref>[[James Serrin|Serrin, J.]] (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pp. 3–32, in ''New Perspectives in Thermodynamics'', edited by J. Serrin, Springer, Berlin, {{ISBN|3-540-15931-2}}.</ref> Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter. Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
虽然这个版本的定律是最常见的陈述版本之一，但它只是被称为“第零定律”的众多陈述之一。有些陈述更进一步，提供了一个重要的物理事实，即温度是一维的，并且从概念上把物体按实数顺序由冷到热排列。也许对于“第零定律”并没有唯一的“最佳的表述”，因为在文献中有一系列的热力学原理的表述，每一种都要求对热力学定律作出各自适当的说明。<br />
<br />
<br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its [[Conjugate variables (thermodynamics)|conjugate variable]]. Such a temperature definition is said to be 'empirical'.<ref>Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (first edition 1968), third edition 1983, Cambridge University Press, {{ISBN|0-521-25445-0}}, pp. 18–20.</ref><ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}, p. 26.</ref><ref>Buchdahl, H.A. (1966), ''The Concepts of Classical Thermodynamics'', Cambridge University Press, London, pp. 30, 34ff, 46f, 83.</ref><ref>*Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, {{ISBN|0-471-62430-6}}, p. 22.</ref><ref>[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge, p. 10.</ref><ref>[[Harold A. Wilson (physicist)|Wilson, H.A.]] (1966). ''Thermodynamics and Statistical Mechanics'', Cambridge University Press, London, pp. 4, 8, 68, 86, 97, 311.</ref><br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable. Such a temperature definition is said to be 'empirical'.<br />
<br />
虽然这些关于温度和热平衡的概念是热力学的基础，并在19世纪得到了清楚的阐述，但是直到20世纪30年代福勒和古根海姆这样做的时候，人们才普遍感觉到需要对上述定律进行明确编号，而这时第一定律、第二定律和第三定律已经得到广泛的理解和认可。因此，它被称为第零定律。该定律作为早期定律基础的重要性在于，它允许以非循环的方式定义温度，而无需参考熵及其共轭变量。这样的温度定义被称为“经验主义”。<br />
<br />
<br />
<br />
==First law==<br />
第一定律<br />
<br />
The '''first law of thermodynamics''' is a version of the law of [[conservation of energy]], adapted for [[thermodynamic system]]s.<br />
<br />
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems.<br />
<br />
热力学第一定律是'''<font color="#ff8000"> 能量守恒conservation of energy</font>'''定律的一个版本，适用于热力学系统。<br />
<br />
<br />
The law of conservation of energy states that the total [[energy]] of an [[isolated system]] is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
能量守恒定律指出，一个孤立系统的总能量是恒定的;能量可以从一种形式转化为另一种形式，但能量既不会凭空产生也不会凭空消失。<br />
<br />
<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
对于一个没有物质转移的热力学过程，第一定律通常用公式表示为：<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
系统 q-w / math,<br />
<br />
<br />
<br />
where {{math|Δ''U''<sub>system</sub>}} denotes the change in the [[internal energy]] of a [[Thermodynamic system#Closed system|closed system]], {{math|''Q''}} denotes the quantity of energy supplied ''to'' the system as [[heat]], and {{math|''W''}} denotes the amount of [[Work (thermodynamics)|thermodynamic work]] (expressed here with a negative sign) done ''by'' the system on its surroundings. (An [[First law of thermodynamics#Sign conventions|alternate sign convention]] not used in this article is to define {{math|''W''}} as the work done ''on'' the system.) <br />
<br />
where denotes the change in the internal energy of a closed system, denotes the quantity of energy supplied to the system as heat, and denotes the amount of thermodynamic work (expressed here with a negative sign) done by the system on its surroundings. (An alternate sign convention not used in this article is to define as the work done on the system.) <br />
<br />
其中{{math|Δ''U''<sub>system</sub>}}表示一个封闭系统内部能量的变化，{{math|''Q''}} 表示外界对系统传递的热量，{{math|''W''}}表示该系统对周围环境所做的热力学功(在这里用负号表示)。(本文中没有使用的另一个符号约定是定义对系统所做的功。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）注意到前面的heat 译为了“热” {{math|''Q''}} 表？示外界对系统传递的热量 热量是否为“热”？<br />
<br />
<br />
<br />
In the case of a two-stage [[thermodynamic cycle]] of a closed system, which returns to its original state, the heat {{math|''Q<sub>in</sub>''}} supplied to the system in one stage of the cycle, minus the heat {{math|''Q<sub>out</sub>''}} removed from it in the other stage, plus the [[Work (thermodynamics)|thermodynamic work]] added to the system, {{math|''W<sub>in</sub>''}}, equals the thermodynamic work that leaves the system {{math|''W<sub>out</sub>''}}.<br />
<br />
In the case of a two-stage thermodynamic cycle of a closed system, which returns to its original state, the heat supplied to the system in one stage of the cycle, minus the heat removed from it in the other stage, plus the thermodynamic work added to the system, , equals the thermodynamic work that leaves the system .<br />
<br />
在封闭系统的两级'''<font color="#ff8000"> 热力循环thermodynamic cycle</font>'''中，该循环回到其原始状态，在循环的一个阶段向系统提供的热量{{math|''Q<sub>in</sub>''}}，减去另一个阶段从系统中去除的热量{{math|''Q<sub>out</sub>''}}，加上对系统做的的热力学功{{math|''W<sub>in</sub>''}}，等于离开系统的做的热力学功{{math|''W<sub>out</sub>''}}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
0 / math<br />
<br />
<br />
<br />
hence, for a full cycle,<br />
<br />
hence, for a full cycle,<br />
<br />
因此，一个完整的循环,<br />
<br />
<br />
<br />
::Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: {{math|''Q'' {{=}} 0}}.<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: 0}}.<br />
<br />
对于绝热系统（绝热隔离）的特殊情况，绝热隔离系统内能的变化只能是系统做功的结果，因为绝热假设是: 0}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
对于包括物质转移的过程，还需要进一步的说明: ‘在充分考虑了各个系统的基准参考状态后，当两个系统---- '''<font color="#32CD32">它们可能由不同的化学成分组成，最初只是被防渗墙隔开，或者是被隔离---- 通过移除墙体的热力学操作结合成一个新系统</font>'''，那么<br />
<br />
<br />
<br />
::<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
数学 u + u 2 / math,<br />
<br />
<br />
<br />
where {{math|''U''<sub>system</sub>}} denotes the internal energy of the combined system, and {{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} denote the internal energies of the respective separated systems.'<br />
<br />
where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.'<br />
<br />
其中{{math|''U''<sub>system</sub>}}表示组合系统的内能，{{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} 表示各自分离系统的内能<br />
<br />
<br />
<br />
The First Law encompasses several principles:<br />
<br />
The First Law encompasses several principles:<br />
<br />
第一定律包括以下几个原则:<br />
<br />
* The [[Conservation of energy|law of conservation of energy]].<br />
<br />
::This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
能量既不能被创造也不能被消灭。但是，能量可以改变形式，能量可以从一个地方流动到另一个地方。能量守恒定律的一个特殊结果是，孤立系统的总能量不变。<br />
<br />
* The concept of [[internal energy]] and its relationship to temperature.<br><br />
内能的概念及其与温度关系。<br />
<br />
::If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has [[kinetic energy]]. If the system as a whole is in an externally imposed force field (e.g. gravity), it has [[potential energy]] relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has kinetic energy. If the system as a whole is in an externally imposed force field (e.g. gravity), it has potential energy relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
如果系统具有确定的温度，则其总能量具有三个可区分的成分，分别称为动能（由与系统整体运动产生的能量），势能（由外部施加的立场产生的能量，比如重力）和内能（热热力学的基本量）。内能概念的确立将热力学第一定律与一般的能量守恒定律区分开来。<br />
——Solitude(讨论)<br />
<br />
<br />
::<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<br />
<br />
::The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, {{math|''U''}}, and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, , and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
物质的内能可以解释为其组成原子的不规则微观运动的不同动能和它们之间相互作用的势能的总和。这些微观能量统称为物质的内能，并由宏观热力学性质来解释。组成原子的微观运动的总和随着系统温度的升高而增加; 这假设在系统的微观层次上没有其他的相互作用，例如化学反应、组成原子相互间的势能。<br />
<br />
* [[Work (physics)|Work]] is a process of transferring energy to or from a system in ways that can be described by macroscopic mechanical forces exerted by factors in the surroundings, outside the system. Examples are an externally driven shaft agitating a stirrer within the system, or an externally imposed electric field that polarizes the material of the system, or a piston that compresses the system. Unless otherwise stated, it is customary to treat work as occurring without its [[dissipation]] to the surroundings. Practically speaking, in all natural process, some of the work is dissipated by internal friction or viscosity. The work done by the system can come from its overall kinetic energy, from its overall potential energy, or from its internal energy.<br />
<br />
做功是一种以某种方式向系统传递能量或从系统传递能量的过程，其方式可以用作用在系统外部及其周围环境之间的宏观机械力来描述。'''<font color="#32CD32">例如，外部驱动的轴在系统内搅动，或外部施加的电场使系统材料极化，或活塞压缩系统。</font>'''除非另有说明，习惯上把做功看作是在不影响周围环境的情况下发生的。实际上，在一切自然过程中，有些功是因内摩擦或粘黏而消失的。系统所做的功，可以来自于它的总动能，总势能或者它的内能。<br />
<br />
<br />
::For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's [[gravitational potential energy]]. Work added to the system increases the Potential Energy of the system:<br />
<br />
For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's gravitational potential energy. Work added to the system increases the Potential Energy of the system:<br />
<br />
例如，当一台机器(不是系统的一部分)将系统向上提升时，一些能量就会从机器转移到系统。系统的能量随着系统所做功的增加而增加，在这种特殊的情况下，系统的能量增加表现为系统的重力势能的增加。对系统做的增加了系统的势能:<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“对系统做的增加了系统的势能” 需要对全文进行通读 这里少词<br />
<br />
<br />
:::<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<br />
<br />
::Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
或者一般来说，以功的形式加入系统的能量可以分为动能、势能或内能:<br />
<br />
<br />
<br />
:::<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
* When matter is transferred into a system, that masses' associated internal energy and potential energy are transferred with it.<br><br />
当物质转移到一个系统中时，物质相关的内能和势能也随之转移。<br />
<br />
<br />
<br />
:::<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
在 Delta u { system } / math 中的 math left (u，Delta m right)<br />
<br />
<br />
<br />
::where {{math|''u''}} denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and {{math|Δ''M''}} denotes the amount of transferred mass.<br />
<br />
where denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and denotes the amount of transferred mass.<br />
<br />
其中{{math|''u''}}表示在周围环境中测量的转移物质的单位质量的内能; {{math|Δ''M''}}表示被转移物质的数量。<br />
<br />
* The flow of [[heat]] is a form of energy transfer.<br><br />
热的流动是能量传递的一种形式。<br />
<br />
::Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
加热是一个将能量转移到系统中或从系统中转移出的自然过程，而不是通过做功或物质的转移。热量只能从较热的系统直接传递到较冷的系统。<br />
<br />
<br />
<br />
:::If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
如果系统具有不渗透物质的刚性壁，那么能量不能通过做功传入或传出系统，而且没有外部的远程力场影响系统以改变其内能，那么内能只能通过以热的形式进行传递来改变:<br />
<br />
<br />
<br />
:::<math>\Delta U_{\rm system}=Q</math><br />
<br />
<math>\Delta U_{\rm system}=Q</math><br />
<br />
系统的 q / math<br />
<br />
<br />
<br />
where {{math|''Q''}} denotes the amount of energy transferred into the system as heat.<br />
<br />
where denotes the amount of energy transferred into the system as heat.<br />
<br />
其中 {{math|''Q''}}表示以热量形式传递到系统中的能量。<br />
<br />
<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
结合这些原理，就可以得出传统的热力学第一定律的表述: 不可能制造一台在没有等量能量输入的情况下不断做功的机器。或者更简单地说，第一类永动机是不可能造成的。<br />
<br />
==Second law==<br />
第二定律<br />
<br />
The [[second law of thermodynamics]] indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
The second law of thermodynamics indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
热力学第二定律表明了自然过程的不可逆性，并且在许多情况下，自然过程的趋向于物质很能量的空间均匀性，特别是温度。它可以用各种有趣而重要的方式来表达。<br />
<br />
<br />
<br />
It implies the existence of a quantity called the [[entropy]] of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
这意味着热力学系统中存在一个叫做熵的量。了一个叫做热力学系统熵的量的存在。就这个数量而言，它意味着<br />
<br />
{{quote|When two initially isolated systems in separate but nearby regions of space, each in [[thermodynamic equilibrium]] with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the [[entropy|entropies]] of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values.}}<br><br />
当两个最初隔离的系统分别位于彼此独立但不一定彼此处于热力学平衡的空间区域中，然后彼此相互作用时，它们最终将达到相互的热力学平衡。最初隔离的系统的熵之和小于或等于最终组合的总熵。当两个初始系统各自的强变量(温度、压力)相等时，才发生平等。那么最终的系统也有相同的值。<br />
<br />
<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
第二定律适用于可逆和不可逆的多种过程。所有的自然过程都是不可逆的。可逆过程是一个有用的和方便的理论假设，但不发生在自然界。<br />
<br />
<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
这种不可逆性的一个主要例子是通过传导或辐射进行的热传递。早在熵的概念被发现之前，人们就已经知道，当两个最初温度不同的物体直接进行热连接时，热量总是自发地从较热的物体流向较冷的物体。<br />
<br />
<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
第二定律也告诉我们除了热传递之外的不可逆性，例如摩擦力和粘度，以及化学反应。'''<font color="#32CD32">需要熵的概念给该定律提供更广泛的范围。</font>'''<br />
<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, ''δQ'', is the product of the temperature (''T''), both of the system and of the sources or destination of the heat, with the increment (''dS'') of the system's conjugate variable, its [[entropy]] (''S'')<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S)<br />
<br />
根据热力学第二定律，在理论上和假设的可逆传热中，传热元素δQ是系统和热源或热目的地的温度(t)与系统共轭变量熵（S）的增量(dS)的乘积<br />
<br />
<br />
<br />
:<math>\delta Q = T\,dS\, .</math><ref name="Guggenheim 1985"/><br />
<br />
<math>\delta Q = T\,dS\, .</math><br />
<br />
数学 delta q t ，dS ，. / math<br />
<br />
<br />
<br />
[[Entropy]] may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as ''disorder'' on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<ref>Ben-Naim, A. (2008). ''A Farewell to Entropy: Statistical Thermodynamics Based on Information'', World Scientific, New Jersey, {{ISBN|978-981-270-706-2}}.</ref><br />
<br />
Entropy may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as disorder on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<br />
<br />
当只知道宏观状态时，熵也可以被看作是对系统运动和构型的微观细节有关的物理度量。这种细节通常在微观或分子尺度上被称为无序。该定律声称，对于一个系统的两个给定的宏观指定状态，它们之间存在一个被称为熵差的量。'''<font color="#32CD32">这种熵的差异定义了需要多少额外的微观物理信息来指定一个宏观指定状态，给定另一个宏观指定状态-通常是一个方便选择的参考状态，这可能是假定存在的，而不是明确陈述的。自然过程的最终条件始终包含着微观上特定的影响，而这些影响，从过程初始条件的宏观规定来看是无法被完全准确预测的。这就是为什么熵在自然过程中会增加——熵的增加告诉我们需要多少额外的微观信息来区分最终的宏观指定状态和最初的宏观指定状态。</font>'''<br />
<br />
<br />
==Third law==<br />
第三定律<br />
<br />
The [[third law of thermodynamics]] is sometimes stated as follows:<br />
<br />
The third law of thermodynamics is sometimes stated as follows:<br />
<br />
热力学第三定律可以表示为：<br />
<br />
:''The [[entropy]] of a perfect [[crystal]] of any pure substance approaches zero as the temperature approaches [[absolute zero]].''<br />
<br />
The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero.<br />
<br />
当温度接近绝对零度时，任何纯物质的完整晶体的熵接近零。<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one [[microstate (statistical mechanics)|state with minimum energy]]. Entropy is related to the number of possible microstates according to:<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy. Entropy is related to the number of possible microstates according to:<br />
<br />
在零温时，系统必须处于热能最小的状态。如果完美晶体只有一种能量最小的状态，则该说法成立。熵与可能的微状态数有关:<br />
<br />
<br />
<br />
::<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
数学知识，数学知识，欧米茄 / 数学<br />
<br />
<br />
<br />
Where ''S'' is the entropy of the system, ''k''<sub>B</sub> [[Boltzmann constant|Boltzmann's constant]], and ''Ω'' the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (''Ω''=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
Where S is the entropy of the system, k<sub>B</sub> Boltzmann's constant, and Ω the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (Ω=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
其中 s 是系统的熵，k<sub>B</sub>是玻尔兹曼常数，以及Ω是微状态数(例如:可能的原子结构)。在绝对零度下只有一种微状态(Ω=1，因为纯物质的所有原子都是相同的，所以所有阶数都是相同的，因为只有一个组合)和 ln (1)=0。<br />
<br />
<br />
<br />
A more general form of the third law that applies to a system such as a [[glass]] that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
A more general form of the third law that applies to a system such as a glass that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
第三定律的一个更普遍的形式，适用于像玻璃这样的系统，'''<font color="#32CD32">可能有一个以上的微观上截然不同的能量状态，或可能有一个微观上截然不同的“冻结状态”，虽然不是一个严格意义上的的最低能量状态，也不是严格意义上的热力学平衡，</font>'''在绝对零度:<br />
<br />
:''The entropy of a system approaches a constant value as the temperature approaches zero.''<br />
<br />
The entropy of a system approaches a constant value as the temperature approaches zero.<br />
<br />
系统的熵随着温度接近绝对零度而接近一个恒定值。<br />
<br />
<br />
<br />
The constant value (not necessarily zero) is called the [[residual entropy]] of the system.<br />
<br />
The constant value (not necessarily zero) is called the residual entropy of the system.<br />
<br />
这个常数(不一定是零)被称为系统的余熵。<br />
<br />
<br />
<br />
==History==<br />
历史<br />
<br />
{{see also|Philosophy of thermal and statistical physics}}<br><br />
热学和统计物理学的哲学<br />
<br />
[[Mechanical equivalent of heat|Circa 1797, Count Rumford (born Benjamin Thompson)]] showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] in 1824. By 1860, as formalized in the works of those such as [[Rudolf Clausius]] and [[William Thomson, 1st Baron Kelvin|William Thomson]], two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist [[Josiah Willard Gibbs]], in his memoir ''Graphical Methods in the Thermodynamics of Fluids'', clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
Circa 1797, Count Rumford (born Benjamin Thompson) showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824. By 1860, as formalized in the works of those such as Rudolf Clausius and William Thomson, two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist Josiah Willard Gibbs, in his memoir Graphical Methods in the Thermodynamics of Fluids, clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
大约在1797年，拉姆福德(出生于本杰明·汤普森)表明，无休止的机械作用可以从固定数量的工作物质中产生无限量的热量，从而挑战了热量理论。该理论认为在固定数量的工作物质中会有有限的热量 / 能量。1824年，萨迪·卡诺建立了第一个热力学原理，也就是后来的热力学第二定律。到1860年，正如鲁道夫 · 克劳修斯和威廉 · 汤姆森等人的著作所正式规定的那样，已经确立的两个热力学原理得到了发展，第一个原理和第二个原理，后来被重新定义为热力学定律。例如，1873年，热力学学家乔赛亚·威拉德·吉布斯在他的回忆录《流体热力学的图解法》中明确阐述了热力学的前两个绝对定律。整个20世纪的一些教科书对这些定律进行了不同的编号。在一些与化学无关的领域，第二定律被认为仅仅处理热机的效率问题，而所谓的第三定律则处理熵的增加问题。'''<font color="#32CD32">直接定义熵计算的零律不被认为是一条定律。</font>'''这种分离逐渐形成了第二定律，现代第三定律被广泛采用。<br />
<br />
<br />
<br />
==See also==<br />
<br />
*化学热力学 [[Chemical thermodynamics]]<br />
<br />
*守恒定律 [[Conservation law (physics)|Conservation law]]<br />
<br />
*熵增 [[Entropy production]]<br />
<br />
*金斯伯格定理 [[Ginsberg's theorem]]<br />
<br />
*宇宙热寂 [[Heat death of the universe]]<br />
<br />
*H定理 [[H-theorem]]<br />
<br />
*科学规律 [[Laws of science]]<br />
<br />
*昂萨格倒易关系（有时被描述为热力学第四定律） [[Onsager reciprocal relations]] (sometimes described as a fourth law of thermodynamics)<br />
<br />
*统计力学 [[Statistical mechanics]]<br />
<br />
*热力学方程表 [[Table of thermodynamic equations]]<br />
<br />
<br />
<br />
==References==<br><br />
参考文献<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
==Further reading==<br />
<br />
* [[Peter Atkins|Atkins, Peter]] (2007). ''Four Laws That Drive the Universe''. OUP Oxford. {{ISBN|978-0199232369}}<br />
<br />
* Goldstein, Martin & Inge F. (1993). ''The Refrigerator and the Universe''. Harvard Univ. Press. {{ISBN|978-0674753259}}<br />
<br />
<br />
<br />
==External links==<br />
<br />
* [http://www.bbc.co.uk/programmes/b06c06nd In Our Time: Perpetual Motion], BBC discussion about the Laws, with Ruth Gregory, Frank Close and Steven Bramwell, hosted by Melvyn Bragg, first broadcast 24 September 2015.<br />
<br />
<br />
<br />
[[Category:Laws of thermodynamics| ]]<br />
<br />
[[Category:Scientific laws]]<br />
<br />
Category:Scientific laws<br />
<br />
类别: 科学定律<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Laws of thermodynamics]]. Its edit history can be viewed at [[热力学定律/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6%E5%AE%9A%E5%BE%8B_Laws_of_thermodynamics&diff=14682热力学定律 Laws of thermodynamics2020-10-01T15:32:40Z<p>趣木木：/* First law */</p>
<hr />
<div>本词条由Solitude初步翻译<br />
<br />
{{Thermodynamics|cTopic=Laws}}<br><br />
模板：热力学<br />
<br />
The '''laws of thermodynamics''' define physical quantities, such as [[temperature]], [[energy]], and [[entropy]], that characterize [[thermodynamic system]]s at [[thermodynamic equilibrium]]. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as [[perpetual motion]]. In addition to their use in [[thermodynamics]], they are important fundamental [[Physical law|laws]] of [[physics]] in general, and are applicable in other natural [[sciences]].<br />
<br />
The laws of thermodynamics define physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems at thermodynamic equilibrium. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.<br />
<br />
'''<font color="#ff8000"> 热力学定律The laws of thermodynamics</font>'''定义了许多物理量，如'''<font color="#ff8000"> 温度temperature</font>'''、'''<font color="#ff8000"> 能量energy</font>'''和'''<font color="#ff8000">熵 entropy</font>'''，这些物理量表征处于热力学平衡的热力学系统。这些定律描述了这些物理量之间的关系，并构成了排除某些现象的可能性的基础，例如永动机。除了在热力学中的应用之外，它们也是一般物理学中的重要基本定律，也适用于其他自然科学。<br />
<br />
<br />
<br />
<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.<ref name="Guggenheim 1985">Guggenheim, E.A. (1985). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', seventh edition, North Holland, Amsterdam, {{ISBN|0-444-86951-4}}.</ref><ref name="Kittel and Kroemer 1980">Kittel, C. Kroemer, H. (1980). ''Thermal Physics'', second edition, W.H. Freeman, San Francisco, {{ISBN|0-7167-1088-9}}.</ref><ref name="Adkins 1968">Adkins, C.J. (1968). ''Equilibrium Thermodynamics'', McGraw-Hill, London, {{ISBN|0-07-084057-1}}.</ref><ref name="LJCV 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers'', Springer, Berlin, {{ISBN|978-3-540-74252-4}}.</ref><ref>{{cite book |author1=Chris Vuille |author2=Serway, Raymond A. |author3=Faughn, Jerry S. |title=College physics |publisher=Brooks/Cole, Cengage Learning |location=Belmont, CA |year=2009 |isbn=978-0-495-38693-3 |oclc= |doi= |accessdate= | page = 355 |url=https://books.google.com/books?id=CX0u0mIOZ44C&pg=PT355}}</ref>. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
传统上，'''<font color="#ff8000"> 热力学Thermodynamics</font>'''描述了三个基本定律：（简单的按顺序命名为）第一定律、第二定律和第三定律。此外，在前三个定律确立之后，人们认识到可以提出另一个对这三个定律更为基本的定律，即第零定律。<br />
<br />
<br />
<br />
The [[zeroth law of thermodynamics]] defines [[thermal equilibrium]] and forms a basis for the definition of [[temperature]]: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
'''<font color="#ff8000"> 热力学第零定律zeroth law of thermodynamics</font>'''定义了'''<font color="#ff8000"> 热平衡thermal equilibrium</font>'''，并为温度定义奠定了基础：如果两个系统都与第三个系统处于热平衡，则它们彼此也处于热平衡。<br />
<br />
<br />
<br />
The [[first law of thermodynamics]]: When energy passes, as [[Work (thermodynamics)|work]], as [[heat]], or with matter, into or out of a system, the system's [[internal energy]] changes in accord with the law of [[conservation of energy]]. Equivalently, [[perpetual motion machine of the first kind|perpetual motion machines of the first kind]] (machines that produce work with no energy input) are impossible.<br />
<br />
The first law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out of a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind (machines that produce work with no energy input) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第一定律first law of thermodynamics</font>''':当能量以'''<font color="#ff8000"> 功work</font>'''、'''<font color="#ff8000"> 热heat</font>'''或物质的形式进入或离开一个系统时，系统的'''<font color="#ff8000"> 内能 internal energy</font>'''根据能量守恒定律发生变化。同样地，第一类永动机机器(不需要能量输入就能工作的机器)是不可能造成的。<br />
<br />
<br />
<br />
The [[second law of thermodynamics]]: In a natural [[thermodynamic process]], the sum of the [[entropy|entropies]] of the interacting [[thermodynamic system]]s increases. Equivalently, [[perpetual motion machine of the second kind|perpetual motion machines of the second kind]] (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
The second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第二定律second law of thermodynamics</font>''':在自然热力学过程中，相互作用的热力学系统的熵的总和增加。同样地，第二类永动机(自发地把热能转化为机械功的机器)是不可能制造出的。<br />
<br />
<br />
<br />
The [[third law of thermodynamics]]: The [[entropy]] of a system approaches a constant value as the temperature approaches [[absolute zero]].<ref name="Kittel and Kroemer 1980"/> With the exception of non-crystalline solids ([[glass]]es) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
The third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
'''<font color="#ff8000"> 热力学第三定律third law of thermodynamics</font>''':当温度趋于'''<font color="#ff8000"> 绝对零度absolute zero</font>'''时，系统的熵趋于一个定值。除非晶固体(玻璃)外，系统在绝对零度时的熵通常接近于零。<br />
<br />
<br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<ref name="Guggenheim 1985"/><ref name="Kittel and Kroemer 1980"/><ref name="Adkins 1968"/><ref name="LJCV 2008"/><ref name="DGM 1962">De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North Holland, Amsterdam.</ref><ref name="Glansdorff and Prigogine 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London, {{ISBN|0-471-30280-5}}.</ref><br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<br />
<br />
有人提出了其他的定律，但没有一个达到公认的四个定律的普遍性，也没有在标准教科书中被讨论。<br />
<br />
<br />
==Zeroth law==<br />
<br />
热力学零定律<br />
<br />
The [[zeroth law of thermodynamics]] may be stated in the following form:<br />
<br />
The zeroth law of thermodynamics may be stated in the following form:<br />
<br />
热力学第零定律可以用以下形式表示：<br />
<br />
<br />
<br />
{{quote|If two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other.<ref>Guggenheim (1985), p.&nbsp;8.</ref>}}<br><br />
如果两个系统都与第三个系统处于热平衡状态，则它们彼此处于热平衡状态.<br />
<br />
<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a [[mass]] of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a mass of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
该定律旨在允许一个经验参数存在，即温度，作为热力学系统的一种性质，即相互处于热平衡的系统具有相同的温度。这里所述的定律适用于特定的物质(例如一定量的气体物质）来匹配其他物质的温度，但不能证明温度是一个可以用实数来衡量的量。<br />
<br />
<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter.<ref>Sommerfeld, A. (1951/1955). ''Thermodynamics and Statistical Mechanics'', vol. 5 of ''Lectures on Theoretical Physics'', edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York, p. 1.</ref><ref>[[James Serrin|Serrin, J.]] (1978). The concepts of thermodynamics, in ''Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977'', edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, {{ISBN|0-444-85166-6}}, pp. 411–51.</ref><ref>[[James Serrin|Serrin, J.]] (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pp. 3–32, in ''New Perspectives in Thermodynamics'', edited by J. Serrin, Springer, Berlin, {{ISBN|3-540-15931-2}}.</ref> Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter. Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
虽然这个版本的定律是最常见的陈述版本之一，但它只是被称为“第零定律”的众多陈述之一。有些陈述更进一步，提供了一个重要的物理事实，即温度是一维的，并且从概念上把物体按实数顺序由冷到热排列。也许对于“第零定律”并没有唯一的“最佳的表述”，因为在文献中有一系列的热力学原理的表述，每一种都要求对热力学定律作出各自适当的说明。<br />
<br />
<br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its [[Conjugate variables (thermodynamics)|conjugate variable]]. Such a temperature definition is said to be 'empirical'.<ref>Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (first edition 1968), third edition 1983, Cambridge University Press, {{ISBN|0-521-25445-0}}, pp. 18–20.</ref><ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}, p. 26.</ref><ref>Buchdahl, H.A. (1966), ''The Concepts of Classical Thermodynamics'', Cambridge University Press, London, pp. 30, 34ff, 46f, 83.</ref><ref>*Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, {{ISBN|0-471-62430-6}}, p. 22.</ref><ref>[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge, p. 10.</ref><ref>[[Harold A. Wilson (physicist)|Wilson, H.A.]] (1966). ''Thermodynamics and Statistical Mechanics'', Cambridge University Press, London, pp. 4, 8, 68, 86, 97, 311.</ref><br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable. Such a temperature definition is said to be 'empirical'.<br />
<br />
虽然这些关于温度和热平衡的概念是热力学的基础，并在19世纪得到了清楚的阐述，但是直到20世纪30年代福勒和古根海姆这样做的时候，人们才普遍感觉到需要对上述定律进行明确编号，而这时第一定律、第二定律和第三定律已经得到广泛的理解和认可。因此，它被称为第零定律。该定律作为早期定律基础的重要性在于，它允许以非循环的方式定义温度，而无需参考熵及其共轭变量。这样的温度定义被称为“经验主义”。<br />
<br />
<br />
<br />
==First law==<br />
第一定律<br />
<br />
The '''first law of thermodynamics''' is a version of the law of [[conservation of energy]], adapted for [[thermodynamic system]]s.<br />
<br />
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems.<br />
<br />
热力学第一定律是'''<font color="#ff8000"> 能量守恒conservation of energy</font>'''定律的一个版本，适用于热力学系统。<br />
<br />
<br />
The law of conservation of energy states that the total [[energy]] of an [[isolated system]] is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
能量守恒定律指出，一个孤立系统的总能量是恒定的;能量可以从一种形式转化为另一种形式，但能量既不会凭空产生也不会凭空消失。<br />
<br />
<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
对于一个没有物质转移的热力学过程，第一定律通常用公式表示为：<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
系统 q-w / math,<br />
<br />
<br />
<br />
where {{math|Δ''U''<sub>system</sub>}} denotes the change in the [[internal energy]] of a [[Thermodynamic system#Closed system|closed system]], {{math|''Q''}} denotes the quantity of energy supplied ''to'' the system as [[heat]], and {{math|''W''}} denotes the amount of [[Work (thermodynamics)|thermodynamic work]] (expressed here with a negative sign) done ''by'' the system on its surroundings. (An [[First law of thermodynamics#Sign conventions|alternate sign convention]] not used in this article is to define {{math|''W''}} as the work done ''on'' the system.) <br />
<br />
where denotes the change in the internal energy of a closed system, denotes the quantity of energy supplied to the system as heat, and denotes the amount of thermodynamic work (expressed here with a negative sign) done by the system on its surroundings. (An alternate sign convention not used in this article is to define as the work done on the system.) <br />
<br />
其中{{math|Δ''U''<sub>system</sub>}}表示一个封闭系统内部能量的变化，{{math|''Q''}} 表示外界对系统传递的热量，{{math|''W''}}表示该系统对周围环境所做的热力学功(在这里用负号表示)。(本文中没有使用的另一个符号约定是定义对系统所做的功。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）注意到前面的heat 译为了“热” {{math|''Q''}} 表？示外界对系统传递的热量 热量是否为“热”？<br />
<br />
<br />
<br />
In the case of a two-stage [[thermodynamic cycle]] of a closed system, which returns to its original state, the heat {{math|''Q<sub>in</sub>''}} supplied to the system in one stage of the cycle, minus the heat {{math|''Q<sub>out</sub>''}} removed from it in the other stage, plus the [[Work (thermodynamics)|thermodynamic work]] added to the system, {{math|''W<sub>in</sub>''}}, equals the thermodynamic work that leaves the system {{math|''W<sub>out</sub>''}}.<br />
<br />
In the case of a two-stage thermodynamic cycle of a closed system, which returns to its original state, the heat supplied to the system in one stage of the cycle, minus the heat removed from it in the other stage, plus the thermodynamic work added to the system, , equals the thermodynamic work that leaves the system .<br />
<br />
在封闭系统的两级'''<font color="#ff8000"> 热力循环thermodynamic cycle</font>'''中，该循环回到其原始状态，在循环的一个阶段向系统提供的热量{{math|''Q<sub>in</sub>''}}，减去另一个阶段从系统中去除的热量{{math|''Q<sub>out</sub>''}}，加上对系统做的的热力学功{{math|''W<sub>in</sub>''}}，等于离开系统的做的热力学功{{math|''W<sub>out</sub>''}}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
0 / math<br />
<br />
<br />
<br />
hence, for a full cycle,<br />
<br />
hence, for a full cycle,<br />
<br />
因此，一个完整的循环,<br />
<br />
<br />
<br />
::Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: {{math|''Q'' {{=}} 0}}.<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: 0}}.<br />
<br />
对于绝热系统（绝热隔离）的特殊情况，绝热隔离系统内能的变化只能是系统做功的结果，因为绝热假设是: 0}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
对于包括物质转移的过程，还需要进一步的说明: ‘在充分考虑了各个系统的基准参考状态后，当两个系统---- '''<font color="#32CD32">它们可能由不同的化学成分组成，最初只是被防渗墙隔开，或者是被隔离---- 通过移除墙体的热力学操作结合成一个新系统</font>'''，那么<br />
<br />
<br />
<br />
::<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
数学 u + u 2 / math,<br />
<br />
<br />
<br />
where {{math|''U''<sub>system</sub>}} denotes the internal energy of the combined system, and {{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} denote the internal energies of the respective separated systems.'<br />
<br />
where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.'<br />
<br />
其中{{math|''U''<sub>system</sub>}}表示组合系统的内能，{{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} 表示各自分离系统的内能<br />
<br />
<br />
<br />
The First Law encompasses several principles:<br />
<br />
The First Law encompasses several principles:<br />
<br />
第一定律包括以下几个原则:<br />
<br />
* The [[Conservation of energy|law of conservation of energy]].<br />
<br />
::This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
能量既不能被创造也不能被消灭。但是，能量可以改变形式，能量可以从一个地方流动到另一个地方。能量守恒定律的一个特殊结果是，孤立系统的总能量不变。<br />
<br />
* The concept of [[internal energy]] and its relationship to temperature.<br><br />
内能的概念及其与温度关系。<br />
<br />
::If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has [[kinetic energy]]. If the system as a whole is in an externally imposed force field (e.g. gravity), it has [[potential energy]] relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has kinetic energy. If the system as a whole is in an externally imposed force field (e.g. gravity), it has potential energy relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
如果系统具有确定的温度，则其总能量具有三个可区分的成分，分别称为动能（由与系统整体运动产生的能量），势能（由外部施加的立场产生的能量，比如重力）和内能（热热力学的基本量）。内能概念的确立将热力学第一定律与一般的能量守恒定律区分开来。<br />
——Solitude(讨论)<br />
<br />
<br />
::<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<br />
<br />
::The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, {{math|''U''}}, and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, , and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
物质的内能可以解释为其组成原子的不规则微观运动的不同动能和它们之间相互作用的势能的总和。这些微观能量统称为物质的内能，并由宏观热力学性质来解释。组成原子的微观运动的总和随着系统温度的升高而增加; 这假设在系统的微观层次上没有其他的相互作用，例如化学反应、组成原子相互间的势能。<br />
<br />
* [[Work (physics)|Work]] is a process of transferring energy to or from a system in ways that can be described by macroscopic mechanical forces exerted by factors in the surroundings, outside the system. Examples are an externally driven shaft agitating a stirrer within the system, or an externally imposed electric field that polarizes the material of the system, or a piston that compresses the system. Unless otherwise stated, it is customary to treat work as occurring without its [[dissipation]] to the surroundings. Practically speaking, in all natural process, some of the work is dissipated by internal friction or viscosity. The work done by the system can come from its overall kinetic energy, from its overall potential energy, or from its internal energy.<br />
<br />
做功是一种以某种方式向系统传递能量或从系统传递能量的过程，其方式可以用作用在系统外部及其周围环境之间的宏观机械力来描述。'''<font color="#32CD32">例如，外部驱动的轴在系统内搅动，或外部施加的电场使系统材料极化，或活塞压缩系统。</font>'''除非另有说明，习惯上把做功看作是在不影响周围环境的情况下发生的。实际上，在一切自然过程中，有些功是因内摩擦或粘黏而消失的。系统所做的功，可以来自于它的总动能，总势能或者它的内能。<br />
<br />
<br />
::For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's [[gravitational potential energy]]. Work added to the system increases the Potential Energy of the system:<br />
<br />
For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's gravitational potential energy. Work added to the system increases the Potential Energy of the system:<br />
<br />
例如，当一台机器(不是系统的一部分)将系统向上提升时，一些能量就会从机器转移到系统。系统的能量随着系统所做功的增加而增加，在这种特殊的情况下，系统的能量增加表现为系统的重力势能的增加。对系统做的增加了系统的势能:<br />
<br />
<br />
<br />
:::<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<br />
<br />
::Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
或者一般来说，以功的形式加入系统的能量可以分为动能、势能或内能:<br />
<br />
<br />
<br />
:::<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
* When matter is transferred into a system, that masses' associated internal energy and potential energy are transferred with it.<br><br />
当物质转移到一个系统中时，物质相关的内能和势能也随之转移。<br />
<br />
<br />
<br />
:::<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
在 Delta u { system } / math 中的 math left (u，Delta m right)<br />
<br />
<br />
<br />
::where {{math|''u''}} denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and {{math|Δ''M''}} denotes the amount of transferred mass.<br />
<br />
where denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and denotes the amount of transferred mass.<br />
<br />
其中{{math|''u''}}表示在周围环境中测量的转移物质的单位质量的内能; {{math|Δ''M''}}表示被转移物质的数量。<br />
<br />
* The flow of [[heat]] is a form of energy transfer.<br><br />
热的流动是能量传递的一种形式。<br />
<br />
::Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
加热是一个将能量转移到系统中或从系统中转移出的自然过程，而不是通过做功或物质的转移。热量只能从较热的系统直接传递到较冷的系统。<br />
<br />
<br />
<br />
:::If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
如果系统具有不渗透物质的刚性壁，那么能量不能通过做功传入或传出系统，而且没有外部的远程力场影响系统以改变其内能，那么内能只能通过以热的形式进行传递来改变:<br />
<br />
<br />
<br />
:::<math>\Delta U_{\rm system}=Q</math><br />
<br />
<math>\Delta U_{\rm system}=Q</math><br />
<br />
系统的 q / math<br />
<br />
<br />
<br />
where {{math|''Q''}} denotes the amount of energy transferred into the system as heat.<br />
<br />
where denotes the amount of energy transferred into the system as heat.<br />
<br />
其中 {{math|''Q''}}表示以热量形式传递到系统中的能量。<br />
<br />
<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
结合这些原理，就可以得出传统的热力学第一定律的表述: 不可能制造一台在没有等量能量输入的情况下不断做功的机器。或者更简单地说，第一类永动机是不可能造成的。<br />
<br />
==Second law==<br />
第二定律<br />
<br />
The [[second law of thermodynamics]] indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
The second law of thermodynamics indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
热力学第二定律表明了自然过程的不可逆性，并且在许多情况下，自然过程的趋向于物质很能量的空间均匀性，特别是温度。它可以用各种有趣而重要的方式来表达。<br />
<br />
<br />
<br />
It implies the existence of a quantity called the [[entropy]] of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
这意味着热力学系统中存在一个叫做熵的量。了一个叫做热力学系统熵的量的存在。就这个数量而言，它意味着<br />
<br />
{{quote|When two initially isolated systems in separate but nearby regions of space, each in [[thermodynamic equilibrium]] with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the [[entropy|entropies]] of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values.}}<br><br />
当两个最初隔离的系统分别位于彼此独立但不一定彼此处于热力学平衡的空间区域中，然后彼此相互作用时，它们最终将达到相互的热力学平衡。最初隔离的系统的熵之和小于或等于最终组合的总熵。当两个初始系统各自的强变量(温度、压力)相等时，才发生平等。那么最终的系统也有相同的值。<br />
<br />
<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
第二定律适用于可逆和不可逆的多种过程。所有的自然过程都是不可逆的。可逆过程是一个有用的和方便的理论假设，但不发生在自然界。<br />
<br />
<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
这种不可逆性的一个主要例子是通过传导或辐射进行的热传递。早在熵的概念被发现之前，人们就已经知道，当两个最初温度不同的物体直接进行热连接时，热量总是自发地从较热的物体流向较冷的物体。<br />
<br />
<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
第二定律也告诉我们除了热传递之外的不可逆性，例如摩擦力和粘度，以及化学反应。'''<font color="#32CD32">需要熵的概念给该定律提供更广泛的范围。</font>'''<br />
<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, ''δQ'', is the product of the temperature (''T''), both of the system and of the sources or destination of the heat, with the increment (''dS'') of the system's conjugate variable, its [[entropy]] (''S'')<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S)<br />
<br />
根据热力学第二定律，在理论上和假设的可逆传热中，传热元素δQ是系统和热源或热目的地的温度(t)与系统共轭变量熵（S）的增量(dS)的乘积<br />
<br />
<br />
<br />
:<math>\delta Q = T\,dS\, .</math><ref name="Guggenheim 1985"/><br />
<br />
<math>\delta Q = T\,dS\, .</math><br />
<br />
数学 delta q t ，dS ，. / math<br />
<br />
<br />
<br />
[[Entropy]] may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as ''disorder'' on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<ref>Ben-Naim, A. (2008). ''A Farewell to Entropy: Statistical Thermodynamics Based on Information'', World Scientific, New Jersey, {{ISBN|978-981-270-706-2}}.</ref><br />
<br />
Entropy may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as disorder on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<br />
<br />
当只知道宏观状态时，熵也可以被看作是对系统运动和构型的微观细节有关的物理度量。这种细节通常在微观或分子尺度上被称为无序。该定律声称，对于一个系统的两个给定的宏观指定状态，它们之间存在一个被称为熵差的量。'''<font color="#32CD32">这种熵的差异定义了需要多少额外的微观物理信息来指定一个宏观指定状态，给定另一个宏观指定状态-通常是一个方便选择的参考状态，这可能是假定存在的，而不是明确陈述的。自然过程的最终条件始终包含着微观上特定的影响，而这些影响，从过程初始条件的宏观规定来看是无法被完全准确预测的。这就是为什么熵在自然过程中会增加——熵的增加告诉我们需要多少额外的微观信息来区分最终的宏观指定状态和最初的宏观指定状态。</font>'''<br />
<br />
<br />
==Third law==<br />
第三定律<br />
<br />
The [[third law of thermodynamics]] is sometimes stated as follows:<br />
<br />
The third law of thermodynamics is sometimes stated as follows:<br />
<br />
热力学第三定律可以表示为：<br />
<br />
:''The [[entropy]] of a perfect [[crystal]] of any pure substance approaches zero as the temperature approaches [[absolute zero]].''<br />
<br />
The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero.<br />
<br />
当温度接近绝对零度时，任何纯物质的完整晶体的熵接近零。<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one [[microstate (statistical mechanics)|state with minimum energy]]. Entropy is related to the number of possible microstates according to:<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy. Entropy is related to the number of possible microstates according to:<br />
<br />
在零温时，系统必须处于热能最小的状态。如果完美晶体只有一种能量最小的状态，则该说法成立。熵与可能的微状态数有关:<br />
<br />
<br />
<br />
::<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
数学知识，数学知识，欧米茄 / 数学<br />
<br />
<br />
<br />
Where ''S'' is the entropy of the system, ''k''<sub>B</sub> [[Boltzmann constant|Boltzmann's constant]], and ''Ω'' the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (''Ω''=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
Where S is the entropy of the system, k<sub>B</sub> Boltzmann's constant, and Ω the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (Ω=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
其中 s 是系统的熵，k<sub>B</sub>是玻尔兹曼常数，以及Ω是微状态数(例如:可能的原子结构)。在绝对零度下只有一种微状态(Ω=1，因为纯物质的所有原子都是相同的，所以所有阶数都是相同的，因为只有一个组合)和 ln (1)=0。<br />
<br />
<br />
<br />
A more general form of the third law that applies to a system such as a [[glass]] that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
A more general form of the third law that applies to a system such as a glass that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
第三定律的一个更普遍的形式，适用于像玻璃这样的系统，'''<font color="#32CD32">可能有一个以上的微观上截然不同的能量状态，或可能有一个微观上截然不同的“冻结状态”，虽然不是一个严格意义上的的最低能量状态，也不是严格意义上的热力学平衡，</font>'''在绝对零度:<br />
<br />
:''The entropy of a system approaches a constant value as the temperature approaches zero.''<br />
<br />
The entropy of a system approaches a constant value as the temperature approaches zero.<br />
<br />
系统的熵随着温度接近绝对零度而接近一个恒定值。<br />
<br />
<br />
<br />
The constant value (not necessarily zero) is called the [[residual entropy]] of the system.<br />
<br />
The constant value (not necessarily zero) is called the residual entropy of the system.<br />
<br />
这个常数(不一定是零)被称为系统的余熵。<br />
<br />
<br />
<br />
==History==<br />
历史<br />
<br />
{{see also|Philosophy of thermal and statistical physics}}<br><br />
热学和统计物理学的哲学<br />
<br />
[[Mechanical equivalent of heat|Circa 1797, Count Rumford (born Benjamin Thompson)]] showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] in 1824. By 1860, as formalized in the works of those such as [[Rudolf Clausius]] and [[William Thomson, 1st Baron Kelvin|William Thomson]], two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist [[Josiah Willard Gibbs]], in his memoir ''Graphical Methods in the Thermodynamics of Fluids'', clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
Circa 1797, Count Rumford (born Benjamin Thompson) showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824. By 1860, as formalized in the works of those such as Rudolf Clausius and William Thomson, two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist Josiah Willard Gibbs, in his memoir Graphical Methods in the Thermodynamics of Fluids, clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
大约在1797年，拉姆福德(出生于本杰明·汤普森)表明，无休止的机械作用可以从固定数量的工作物质中产生无限量的热量，从而挑战了热量理论。该理论认为在固定数量的工作物质中会有有限的热量 / 能量。1824年，萨迪·卡诺建立了第一个热力学原理，也就是后来的热力学第二定律。到1860年，正如鲁道夫 · 克劳修斯和威廉 · 汤姆森等人的著作所正式规定的那样，已经确立的两个热力学原理得到了发展，第一个原理和第二个原理，后来被重新定义为热力学定律。例如，1873年，热力学学家乔赛亚·威拉德·吉布斯在他的回忆录《流体热力学的图解法》中明确阐述了热力学的前两个绝对定律。整个20世纪的一些教科书对这些定律进行了不同的编号。在一些与化学无关的领域，第二定律被认为仅仅处理热机的效率问题，而所谓的第三定律则处理熵的增加问题。'''<font color="#32CD32">直接定义熵计算的零律不被认为是一条定律。</font>'''这种分离逐渐形成了第二定律，现代第三定律被广泛采用。<br />
<br />
<br />
<br />
==See also==<br />
<br />
*化学热力学 [[Chemical thermodynamics]]<br />
<br />
*守恒定律 [[Conservation law (physics)|Conservation law]]<br />
<br />
*熵增 [[Entropy production]]<br />
<br />
*金斯伯格定理 [[Ginsberg's theorem]]<br />
<br />
*宇宙热寂 [[Heat death of the universe]]<br />
<br />
*H定理 [[H-theorem]]<br />
<br />
*科学规律 [[Laws of science]]<br />
<br />
*昂萨格倒易关系（有时被描述为热力学第四定律） [[Onsager reciprocal relations]] (sometimes described as a fourth law of thermodynamics)<br />
<br />
*统计力学 [[Statistical mechanics]]<br />
<br />
*热力学方程表 [[Table of thermodynamic equations]]<br />
<br />
<br />
<br />
==References==<br><br />
参考文献<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
==Further reading==<br />
<br />
* [[Peter Atkins|Atkins, Peter]] (2007). ''Four Laws That Drive the Universe''. OUP Oxford. {{ISBN|978-0199232369}}<br />
<br />
* Goldstein, Martin & Inge F. (1993). ''The Refrigerator and the Universe''. Harvard Univ. Press. {{ISBN|978-0674753259}}<br />
<br />
<br />
<br />
==External links==<br />
<br />
* [http://www.bbc.co.uk/programmes/b06c06nd In Our Time: Perpetual Motion], BBC discussion about the Laws, with Ruth Gregory, Frank Close and Steven Bramwell, hosted by Melvyn Bragg, first broadcast 24 September 2015.<br />
<br />
<br />
<br />
[[Category:Laws of thermodynamics| ]]<br />
<br />
[[Category:Scientific laws]]<br />
<br />
Category:Scientific laws<br />
<br />
类别: 科学定律<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Laws of thermodynamics]]. Its edit history can be viewed at [[热力学定律/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E7%83%AD%E5%8A%9B%E5%AD%A6%E5%AE%9A%E5%BE%8B_Laws_of_thermodynamics&diff=14681热力学定律 Laws of thermodynamics2020-10-01T15:29:06Z<p>趣木木：</p>
<hr />
<div>本词条由Solitude初步翻译<br />
<br />
{{Thermodynamics|cTopic=Laws}}<br><br />
模板：热力学<br />
<br />
The '''laws of thermodynamics''' define physical quantities, such as [[temperature]], [[energy]], and [[entropy]], that characterize [[thermodynamic system]]s at [[thermodynamic equilibrium]]. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as [[perpetual motion]]. In addition to their use in [[thermodynamics]], they are important fundamental [[Physical law|laws]] of [[physics]] in general, and are applicable in other natural [[sciences]].<br />
<br />
The laws of thermodynamics define physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems at thermodynamic equilibrium. The laws describe the relationships between these quantities, and form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.<br />
<br />
'''<font color="#ff8000"> 热力学定律The laws of thermodynamics</font>'''定义了许多物理量，如'''<font color="#ff8000"> 温度temperature</font>'''、'''<font color="#ff8000"> 能量energy</font>'''和'''<font color="#ff8000">熵 entropy</font>'''，这些物理量表征处于热力学平衡的热力学系统。这些定律描述了这些物理量之间的关系，并构成了排除某些现象的可能性的基础，例如永动机。除了在热力学中的应用之外，它们也是一般物理学中的重要基本定律，也适用于其他自然科学。<br />
<br />
<br />
<br />
<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.<ref name="Guggenheim 1985">Guggenheim, E.A. (1985). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', seventh edition, North Holland, Amsterdam, {{ISBN|0-444-86951-4}}.</ref><ref name="Kittel and Kroemer 1980">Kittel, C. Kroemer, H. (1980). ''Thermal Physics'', second edition, W.H. Freeman, San Francisco, {{ISBN|0-7167-1088-9}}.</ref><ref name="Adkins 1968">Adkins, C.J. (1968). ''Equilibrium Thermodynamics'', McGraw-Hill, London, {{ISBN|0-07-084057-1}}.</ref><ref name="LJCV 2008">Lebon, G., Jou, D., Casas-Vázquez, J. (2008). ''Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers'', Springer, Berlin, {{ISBN|978-3-540-74252-4}}.</ref><ref>{{cite book |author1=Chris Vuille |author2=Serway, Raymond A. |author3=Faughn, Jerry S. |title=College physics |publisher=Brooks/Cole, Cengage Learning |location=Belmont, CA |year=2009 |isbn=978-0-495-38693-3 |oclc= |doi= |accessdate= | page = 355 |url=https://books.google.com/books?id=CX0u0mIOZ44C&pg=PT355}}</ref>. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
Thermodynamics has traditionally recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law.. In addition, after the first three laws were established, it was recognized that another law, more fundamental to all three, could be stated, which was named the zeroth law.<br />
<br />
传统上，'''<font color="#ff8000"> 热力学Thermodynamics</font>'''描述了三个基本定律：（简单的按顺序命名为）第一定律、第二定律和第三定律。此外，在前三个定律确立之后，人们认识到可以提出另一个对这三个定律更为基本的定律，即第零定律。<br />
<br />
<br />
<br />
The [[zeroth law of thermodynamics]] defines [[thermal equilibrium]] and forms a basis for the definition of [[temperature]]: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.<br />
<br />
'''<font color="#ff8000"> 热力学第零定律zeroth law of thermodynamics</font>'''定义了'''<font color="#ff8000"> 热平衡thermal equilibrium</font>'''，并为温度定义奠定了基础：如果两个系统都与第三个系统处于热平衡，则它们彼此也处于热平衡。<br />
<br />
<br />
<br />
The [[first law of thermodynamics]]: When energy passes, as [[Work (thermodynamics)|work]], as [[heat]], or with matter, into or out of a system, the system's [[internal energy]] changes in accord with the law of [[conservation of energy]]. Equivalently, [[perpetual motion machine of the first kind|perpetual motion machines of the first kind]] (machines that produce work with no energy input) are impossible.<br />
<br />
The first law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out of a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind (machines that produce work with no energy input) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第一定律first law of thermodynamics</font>''':当能量以'''<font color="#ff8000"> 功work</font>'''、'''<font color="#ff8000"> 热heat</font>'''或物质的形式进入或离开一个系统时，系统的'''<font color="#ff8000"> 内能 internal energy</font>'''根据能量守恒定律发生变化。同样地，第一类永动机机器(不需要能量输入就能工作的机器)是不可能造成的。<br />
<br />
<br />
<br />
The [[second law of thermodynamics]]: In a natural [[thermodynamic process]], the sum of the [[entropy|entropies]] of the interacting [[thermodynamic system]]s increases. Equivalently, [[perpetual motion machine of the second kind|perpetual motion machines of the second kind]] (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
The second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.<br />
<br />
'''<font color="#ff8000"> 热力学第二定律second law of thermodynamics</font>''':在自然热力学过程中，相互作用的热力学系统的熵的总和增加。同样地，第二类永动机(自发地把热能转化为机械功的机器)是不可能制造出的。<br />
<br />
<br />
<br />
The [[third law of thermodynamics]]: The [[entropy]] of a system approaches a constant value as the temperature approaches [[absolute zero]].<ref name="Kittel and Kroemer 1980"/> With the exception of non-crystalline solids ([[glass]]es) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
The third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero.<br />
<br />
'''<font color="#ff8000"> 热力学第三定律third law of thermodynamics</font>''':当温度趋于'''<font color="#ff8000"> 绝对零度absolute zero</font>'''时，系统的熵趋于一个定值。除非晶固体(玻璃)外，系统在绝对零度时的熵通常接近于零。<br />
<br />
<br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<ref name="Guggenheim 1985"/><ref name="Kittel and Kroemer 1980"/><ref name="Adkins 1968"/><ref name="LJCV 2008"/><ref name="DGM 1962">De Groot, S.R., Mazur, P. (1962). ''Non-equilibrium Thermodynamics'', North Holland, Amsterdam.</ref><ref name="Glansdorff and Prigogine 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London, {{ISBN|0-471-30280-5}}.</ref><br />
<br />
Additional laws have been suggested, but none of them achieved the generality of the four accepted laws, and are not discussed in standard textbooks.<br />
<br />
有人提出了其他的定律，但没有一个达到公认的四个定律的普遍性，也没有在标准教科书中被讨论。<br />
<br />
<br />
==Zeroth law==<br />
<br />
热力学零定律<br />
<br />
The [[zeroth law of thermodynamics]] may be stated in the following form:<br />
<br />
The zeroth law of thermodynamics may be stated in the following form:<br />
<br />
热力学第零定律可以用以下形式表示：<br />
<br />
<br />
<br />
{{quote|If two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other.<ref>Guggenheim (1985), p.&nbsp;8.</ref>}}<br><br />
如果两个系统都与第三个系统处于热平衡状态，则它们彼此处于热平衡状态.<br />
<br />
<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a [[mass]] of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a mass of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.<br />
<br />
该定律旨在允许一个经验参数存在，即温度，作为热力学系统的一种性质，即相互处于热平衡的系统具有相同的温度。这里所述的定律适用于特定的物质(例如一定量的气体物质）来匹配其他物质的温度，但不能证明温度是一个可以用实数来衡量的量。<br />
<br />
<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter.<ref>Sommerfeld, A. (1951/1955). ''Thermodynamics and Statistical Mechanics'', vol. 5 of ''Lectures on Theoretical Physics'', edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York, p. 1.</ref><ref>[[James Serrin|Serrin, J.]] (1978). The concepts of thermodynamics, in ''Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977'', edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, {{ISBN|0-444-85166-6}}, pp. 411–51.</ref><ref>[[James Serrin|Serrin, J.]] (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pp. 3–32, in ''New Perspectives in Thermodynamics'', edited by J. Serrin, Springer, Berlin, {{ISBN|3-540-15931-2}}.</ref> Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in real number sequence from colder to hotter. Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.<br />
<br />
虽然这个版本的定律是最常见的陈述版本之一，但它只是被称为“第零定律”的众多陈述之一。有些陈述更进一步，提供了一个重要的物理事实，即温度是一维的，并且从概念上把物体按实数顺序由冷到热排列。也许对于“第零定律”并没有唯一的“最佳的表述”，因为在文献中有一系列的热力学原理的表述，每一种都要求对热力学定律作出各自适当的说明。<br />
<br />
<br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its [[Conjugate variables (thermodynamics)|conjugate variable]]. Such a temperature definition is said to be 'empirical'.<ref>Adkins, C.J. (1968/1983). ''Equilibrium Thermodynamics'', (first edition 1968), third edition 1983, Cambridge University Press, {{ISBN|0-521-25445-0}}, pp. 18–20.</ref><ref>Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, {{ISBN|0-88318-797-3}}, p. 26.</ref><ref>Buchdahl, H.A. (1966), ''The Concepts of Classical Thermodynamics'', Cambridge University Press, London, pp. 30, 34ff, 46f, 83.</ref><ref>*Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, {{ISBN|0-471-62430-6}}, p. 22.</ref><ref>[[Brian Pippard|Pippard, A.B.]] (1957/1966). ''Elements of Classical Thermodynamics for Advanced Students of Physics'', original publication 1957, reprint 1966, Cambridge University Press, Cambridge, p. 10.</ref><ref>[[Harold A. Wilson (physicist)|Wilson, H.A.]] (1966). ''Thermodynamics and Statistical Mechanics'', Cambridge University Press, London, pp. 4, 8, 68, 86, 97, 311.</ref><br />
<br />
Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable. Such a temperature definition is said to be 'empirical'.<br />
<br />
虽然这些关于温度和热平衡的概念是热力学的基础，并在19世纪得到了清楚的阐述，但是直到20世纪30年代福勒和古根海姆这样做的时候，人们才普遍感觉到需要对上述定律进行明确编号，而这时第一定律、第二定律和第三定律已经得到广泛的理解和认可。因此，它被称为第零定律。该定律作为早期定律基础的重要性在于，它允许以非循环的方式定义温度，而无需参考熵及其共轭变量。这样的温度定义被称为“经验主义”。<br />
<br />
<br />
<br />
==First law==<br />
第一定律<br />
<br />
The '''first law of thermodynamics''' is a version of the law of [[conservation of energy]], adapted for [[thermodynamic system]]s.<br />
<br />
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems.<br />
<br />
热力学第一定律是'''<font color="#ff8000"> 能量守恒conservation of energy</font>'''定律的一个版本，适用于热力学系统。<br />
<br />
<br />
The law of conservation of energy states that the total [[energy]] of an [[isolated system]] is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.<br />
<br />
能量守恒定律指出，一个孤立系统的总能量是恒定的;能量可以从一种形式转化为另一种形式，但能量既不会凭空产生也不会凭空消失。<br />
<br />
<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
For a thermodynamic process without transfer of matter, the first law is often formulated<br />
<br />
对于一个没有物质转移的热力学过程，第一定律通常用公式表示为：<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
<math>\Delta U_{\rm system} = Q - W</math>,<br />
<br />
系统 q-w / math,<br />
<br />
<br />
<br />
where {{math|Δ''U''<sub>system</sub>}} denotes the change in the [[internal energy]] of a [[Thermodynamic system#Closed system|closed system]], {{math|''Q''}} denotes the quantity of energy supplied ''to'' the system as [[heat]], and {{math|''W''}} denotes the amount of [[Work (thermodynamics)|thermodynamic work]] (expressed here with a negative sign) done ''by'' the system on its surroundings. (An [[First law of thermodynamics#Sign conventions|alternate sign convention]] not used in this article is to define {{math|''W''}} as the work done ''on'' the system.) <br />
<br />
where denotes the change in the internal energy of a closed system, denotes the quantity of energy supplied to the system as heat, and denotes the amount of thermodynamic work (expressed here with a negative sign) done by the system on its surroundings. (An alternate sign convention not used in this article is to define as the work done on the system.) <br />
<br />
其中{{math|Δ''U''<sub>system</sub>}}表示一个封闭系统内部能量的变化，{{math|''Q''}} 表示外界对系统传递的热量，{{math|''W''}}表示该系统对周围环境所做的热力学功(在这里用负号表示)。(本文中没有使用的另一个符号约定是定义对系统所做的功。<br />
<br />
<br />
<br />
In the case of a two-stage [[thermodynamic cycle]] of a closed system, which returns to its original state, the heat {{math|''Q<sub>in</sub>''}} supplied to the system in one stage of the cycle, minus the heat {{math|''Q<sub>out</sub>''}} removed from it in the other stage, plus the [[Work (thermodynamics)|thermodynamic work]] added to the system, {{math|''W<sub>in</sub>''}}, equals the thermodynamic work that leaves the system {{math|''W<sub>out</sub>''}}.<br />
<br />
In the case of a two-stage thermodynamic cycle of a closed system, which returns to its original state, the heat supplied to the system in one stage of the cycle, minus the heat removed from it in the other stage, plus the thermodynamic work added to the system, , equals the thermodynamic work that leaves the system .<br />
<br />
在封闭系统的两级'''<font color="#ff8000"> 热力循环thermodynamic cycle</font>'''中，该循环回到其原始状态，在循环的一个阶段向系统提供的热量{{math|''Q<sub>in</sub>''}}，减去另一个阶段从系统中去除的热量{{math|''Q<sub>out</sub>''}}，加上对系统做的的热力学功{{math|''W<sub>in</sub>''}}，等于离开系统的做的热力学功{{math|''W<sub>out</sub>''}}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
<math>\Delta U_{\rm system\,(full\,cycle)}=0</math><br />
<br />
0 / math<br />
<br />
<br />
<br />
hence, for a full cycle,<br />
<br />
hence, for a full cycle,<br />
<br />
因此，一个完整的循环,<br />
<br />
<br />
<br />
::Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
Or <math>Q - W = Q_{\rm in} - Q_{\rm out} - (W_{\rm out} - W_{\rm in}) =0</math>.<br />
<br />
<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: {{math|''Q'' {{=}} 0}}.<br />
<br />
For the particular case of a thermally isolated system (adiabatically isolated), the change of the internal energy of an adiabatically isolated system can only be the result of the work added to the system, because the adiabatic assumption is: 0}}.<br />
<br />
对于绝热系统（绝热隔离）的特殊情况，绝热隔离系统内能的变化只能是系统做功的结果，因为绝热假设是: 0}。<br />
<br />
<br />
<br />
::<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<math>\Delta U_{\rm system} = U_{\rm final} - U_{\rm initial} = W_{\rm in} - W_{\rm out} </math><br />
<br />
<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
For processes that include transfer of matter, a further statement is needed: 'With due account of the respective fiducial reference states of the systems, when two systems, which may be of different chemical compositions, initially separated only by an impermeable wall, and otherwise isolated, are combined into a new system by the thermodynamic operation of removal of the wall, then<br />
<br />
对于包括物质转移的过程，还需要进一步的说明: ‘在充分考虑了各个系统的基准参考状态后，当两个系统---- '''<font color="#32CD32">它们可能由不同的化学成分组成，最初只是被防渗墙隔开，或者是被隔离---- 通过移除墙体的热力学操作结合成一个新系统</font>'''，那么<br />
<br />
<br />
<br />
::<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
<math>U_{\rm system} = U_1 + U_2</math>,<br />
<br />
数学 u + u 2 / math,<br />
<br />
<br />
<br />
where {{math|''U''<sub>system</sub>}} denotes the internal energy of the combined system, and {{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} denote the internal energies of the respective separated systems.'<br />
<br />
where denotes the internal energy of the combined system, and and denote the internal energies of the respective separated systems.'<br />
<br />
其中{{math|''U''<sub>system</sub>}}表示组合系统的内能，{{math|''U''<sub>1</sub>}} and {{math|''U''<sub>2</sub>}} 表示各自分离系统的内能<br />
<br />
<br />
<br />
The First Law encompasses several principles:<br />
<br />
The First Law encompasses several principles:<br />
<br />
第一定律包括以下几个原则:<br />
<br />
* The [[Conservation of energy|law of conservation of energy]].<br />
<br />
::This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. A particular consequence of the law of conservation of energy is that the total energy of an isolated system does not change.<br />
<br />
能量既不能被创造也不能被消灭。但是，能量可以改变形式，能量可以从一个地方流动到另一个地方。能量守恒定律的一个特殊结果是，孤立系统的总能量不变。<br />
<br />
* The concept of [[internal energy]] and its relationship to temperature.<br><br />
内能的概念及其与温度关系。<br />
<br />
::If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has [[kinetic energy]]. If the system as a whole is in an externally imposed force field (e.g. gravity), it has [[potential energy]] relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
If a system has a definite temperature, then its total energy has three distinguishable components. If the system is in motion as a whole, it has kinetic energy. If the system as a whole is in an externally imposed force field (e.g. gravity), it has potential energy relative to some reference point in space. Finally, it has internal energy, which is a fundamental quantity of thermodynamics. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.<br />
<br />
如果系统具有确定的温度，则其总能量具有三个可区分的成分，分别称为动能（由与系统整体运动产生的能量），势能（由外部施加的立场产生的能量，比如重力）和内能（热热力学的基本量）。内能概念的确立将热力学第一定律与一般的能量守恒定律区分开来。<br />
——Solitude(讨论)<br />
<br />
<br />
::<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<math>E_{\rm total} = \mathrm{KE}_{\rm system} + \mathrm{PE}_{\rm system} + U_{\rm system}</math><br />
<br />
<br />
<br />
::The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, {{math|''U''}}, and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
The internal energy of a substance can be explained as the sum of the diverse kinetic energies of the erratic microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Those microscopic energy terms are collectively called the substance's internal energy, , and are accounted for by macroscopic thermodynamic property. The total of the kinetic energies of microscopic motions of the constituent atoms increases as the system's temperature increases; this assumes no other interactions at the microscopic level of the system such as chemical reactions, potential energy of constituent atoms with respect to each other.<br />
<br />
物质的内能可以解释为其组成原子的不规则微观运动的不同动能和它们之间相互作用的势能的总和。这些微观能量统称为物质的内能，并由宏观热力学性质来解释。组成原子的微观运动的总和随着系统温度的升高而增加; 这假设在系统的微观层次上没有其他的相互作用，例如化学反应、组成原子相互间的势能。<br />
<br />
* [[Work (physics)|Work]] is a process of transferring energy to or from a system in ways that can be described by macroscopic mechanical forces exerted by factors in the surroundings, outside the system. Examples are an externally driven shaft agitating a stirrer within the system, or an externally imposed electric field that polarizes the material of the system, or a piston that compresses the system. Unless otherwise stated, it is customary to treat work as occurring without its [[dissipation]] to the surroundings. Practically speaking, in all natural process, some of the work is dissipated by internal friction or viscosity. The work done by the system can come from its overall kinetic energy, from its overall potential energy, or from its internal energy.<br />
<br />
做功是一种以某种方式向系统传递能量或从系统传递能量的过程，其方式可以用作用在系统外部及其周围环境之间的宏观机械力来描述。'''<font color="#32CD32">例如，外部驱动的轴在系统内搅动，或外部施加的电场使系统材料极化，或活塞压缩系统。</font>'''除非另有说明，习惯上把做功看作是在不影响周围环境的情况下发生的。实际上，在一切自然过程中，有些功是因内摩擦或粘黏而消失的。系统所做的功，可以来自于它的总动能，总势能或者它的内能。<br />
<br />
<br />
::For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's [[gravitational potential energy]]. Work added to the system increases the Potential Energy of the system:<br />
<br />
For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's gravitational potential energy. Work added to the system increases the Potential Energy of the system:<br />
<br />
例如，当一台机器(不是系统的一部分)将系统向上提升时，一些能量就会从机器转移到系统。系统的能量随着系统所做功的增加而增加，在这种特殊的情况下，系统的能量增加表现为系统的重力势能的增加。对系统做的增加了系统的势能:<br />
<br />
<br />
<br />
:::<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{PE}_{\rm system}</math><br />
<br />
<br />
<br />
::Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
Or in general, the energy added to the system in the form of work can be partitioned to kinetic, potential or internal energy forms:<br />
<br />
或者一般来说，以功的形式加入系统的能量可以分为动能、势能或内能:<br />
<br />
<br />
<br />
:::<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
<math>W = \Delta \mathrm{KE}_{\rm system}+\Delta \mathrm{PE}_{\rm system}+\Delta U_{\rm system}</math><br />
<br />
* When matter is transferred into a system, that masses' associated internal energy and potential energy are transferred with it.<br><br />
当物质转移到一个系统中时，物质相关的内能和势能也随之转移。<br />
<br />
<br />
<br />
:::<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
<math>\left( u \,\Delta M \right)_{\rm in} = \Delta U_{\rm system}</math><br />
<br />
在 Delta u { system } / math 中的 math left (u，Delta m right)<br />
<br />
<br />
<br />
::where {{math|''u''}} denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and {{math|Δ''M''}} denotes the amount of transferred mass.<br />
<br />
where denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and denotes the amount of transferred mass.<br />
<br />
其中{{math|''u''}}表示在周围环境中测量的转移物质的单位质量的内能; {{math|Δ''M''}}表示被转移物质的数量。<br />
<br />
* The flow of [[heat]] is a form of energy transfer.<br><br />
热的流动是能量传递的一种形式。<br />
<br />
::Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
Heating is a natural process of moving energy to or from a system other than by work or the transfer of matter. Direct passage of heat is only from a hotter to a colder system.<br />
<br />
加热是一个将能量转移到系统中或从系统中转移出的自然过程，而不是通过做功或物质的转移。热量只能从较热的系统直接传递到较冷的系统。<br />
<br />
<br />
<br />
:::If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
If the system has rigid walls that are impermeable to matter, and consequently energy cannot be transferred as work into or out from the system, and no external long-range force field affects it that could change its internal energy, then the internal energy can only be changed by the transfer of energy as heat:<br />
<br />
如果系统具有不渗透物质的刚性壁，那么能量不能通过做功传入或传出系统，而且没有外部的远程力场影响系统以改变其内能，那么内能只能通过以热的形式进行传递来改变:<br />
<br />
<br />
<br />
:::<math>\Delta U_{\rm system}=Q</math><br />
<br />
<math>\Delta U_{\rm system}=Q</math><br />
<br />
系统的 q / math<br />
<br />
<br />
<br />
where {{math|''Q''}} denotes the amount of energy transferred into the system as heat.<br />
<br />
where denotes the amount of energy transferred into the system as heat.<br />
<br />
其中 {{math|''Q''}}表示以热量形式传递到系统中的能量。<br />
<br />
<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible.<br />
<br />
结合这些原理，就可以得出传统的热力学第一定律的表述: 不可能制造一台在没有等量能量输入的情况下不断做功的机器。或者更简单地说，第一类永动机是不可能造成的。<br />
<br />
<br />
<br />
==Second law==<br />
第二定律<br />
<br />
The [[second law of thermodynamics]] indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
The second law of thermodynamics indicates the irreversibility of natural processes and, in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.<br />
<br />
热力学第二定律表明了自然过程的不可逆性，并且在许多情况下，自然过程的趋向于物质很能量的空间均匀性，特别是温度。它可以用各种有趣而重要的方式来表达。<br />
<br />
<br />
<br />
It implies the existence of a quantity called the [[entropy]] of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that<br />
<br />
这意味着热力学系统中存在一个叫做熵的量。了一个叫做热力学系统熵的量的存在。就这个数量而言，它意味着<br />
<br />
{{quote|When two initially isolated systems in separate but nearby regions of space, each in [[thermodynamic equilibrium]] with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the [[entropy|entropies]] of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values.}}<br><br />
当两个最初隔离的系统分别位于彼此独立但不一定彼此处于热力学平衡的空间区域中，然后彼此相互作用时，它们最终将达到相互的热力学平衡。最初隔离的系统的熵之和小于或等于最终组合的总熵。当两个初始系统各自的强变量(温度、压力)相等时，才发生平等。那么最终的系统也有相同的值。<br />
<br />
<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.<br />
<br />
第二定律适用于可逆和不可逆的多种过程。所有的自然过程都是不可逆的。可逆过程是一个有用的和方便的理论假设，但不发生在自然界。<br />
<br />
<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.<br />
<br />
这种不可逆性的一个主要例子是通过传导或辐射进行的热传递。早在熵的概念被发现之前，人们就已经知道，当两个最初温度不同的物体直接进行热连接时，热量总是自发地从较热的物体流向较冷的物体。<br />
<br />
<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.<br />
<br />
第二定律也告诉我们除了热传递之外的不可逆性，例如摩擦力和粘度，以及化学反应。'''<font color="#32CD32">需要熵的概念给该定律提供更广泛的范围。</font>'''<br />
<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, ''δQ'', is the product of the temperature (''T''), both of the system and of the sources or destination of the heat, with the increment (''dS'') of the system's conjugate variable, its [[entropy]] (''S'')<br />
<br />
According to the second law of thermodynamics, in a theoretical and fictive reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S)<br />
<br />
根据热力学第二定律，在理论上和假设的可逆传热中，传热元素δQ是系统和热源或热目的地的温度(t)与系统共轭变量熵（S）的增量(dS)的乘积<br />
<br />
<br />
<br />
:<math>\delta Q = T\,dS\, .</math><ref name="Guggenheim 1985"/><br />
<br />
<math>\delta Q = T\,dS\, .</math><br />
<br />
数学 delta q t ，dS ，. / math<br />
<br />
<br />
<br />
[[Entropy]] may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as ''disorder'' on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<ref>Ben-Naim, A. (2008). ''A Farewell to Entropy: Statistical Thermodynamics Based on Information'', World Scientific, New Jersey, {{ISBN|978-981-270-706-2}}.</ref><br />
<br />
Entropy may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. This lack of information is often described as disorder on a microscopic or molecular scale. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.<br />
<br />
当只知道宏观状态时，熵也可以被看作是对系统运动和构型的微观细节有关的物理度量。这种细节通常在微观或分子尺度上被称为无序。该定律声称，对于一个系统的两个给定的宏观指定状态，它们之间存在一个被称为熵差的量。'''<font color="#32CD32">这种熵的差异定义了需要多少额外的微观物理信息来指定一个宏观指定状态，给定另一个宏观指定状态-通常是一个方便选择的参考状态，这可能是假定存在的，而不是明确陈述的。自然过程的最终条件始终包含着微观上特定的影响，而这些影响，从过程初始条件的宏观规定来看是无法被完全准确预测的。这就是为什么熵在自然过程中会增加——熵的增加告诉我们需要多少额外的微观信息来区分最终的宏观指定状态和最初的宏观指定状态。</font>'''<br />
<br />
<br />
==Third law==<br />
第三定律<br />
<br />
The [[third law of thermodynamics]] is sometimes stated as follows:<br />
<br />
The third law of thermodynamics is sometimes stated as follows:<br />
<br />
热力学第三定律可以表示为：<br />
<br />
:''The [[entropy]] of a perfect [[crystal]] of any pure substance approaches zero as the temperature approaches [[absolute zero]].''<br />
<br />
The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero.<br />
<br />
当温度接近绝对零度时，任何纯物质的完整晶体的熵接近零。<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one [[microstate (statistical mechanics)|state with minimum energy]]. Entropy is related to the number of possible microstates according to:<br />
<br />
At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy. Entropy is related to the number of possible microstates according to:<br />
<br />
在零温时，系统必须处于热能最小的状态。如果完美晶体只有一种能量最小的状态，则该说法成立。熵与可能的微状态数有关:<br />
<br />
<br />
<br />
::<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
<math>S = k_{\mathrm B}\, \mathrm{ln}\, \Omega</math><br />
<br />
数学知识，数学知识，欧米茄 / 数学<br />
<br />
<br />
<br />
Where ''S'' is the entropy of the system, ''k''<sub>B</sub> [[Boltzmann constant|Boltzmann's constant]], and ''Ω'' the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (''Ω''=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
Where S is the entropy of the system, k<sub>B</sub> Boltzmann's constant, and Ω the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (Ω=1 as all the atoms are identical for a pure substance and as a result all orders are identical as there is only one combination) and ln(1) = 0.<br />
<br />
其中 s 是系统的熵，k<sub>B</sub>是玻尔兹曼常数，以及Ω是微状态数(例如:可能的原子结构)。在绝对零度下只有一种微状态(Ω=1，因为纯物质的所有原子都是相同的，所以所有阶数都是相同的，因为只有一个组合)和 ln (1)=0。<br />
<br />
<br />
<br />
A more general form of the third law that applies to a system such as a [[glass]] that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
A more general form of the third law that applies to a system such as a glass that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:<br />
<br />
第三定律的一个更普遍的形式，适用于像玻璃这样的系统，'''<font color="#32CD32">可能有一个以上的微观上截然不同的能量状态，或可能有一个微观上截然不同的“冻结状态”，虽然不是一个严格意义上的的最低能量状态，也不是严格意义上的热力学平衡，</font>'''在绝对零度:<br />
<br />
:''The entropy of a system approaches a constant value as the temperature approaches zero.''<br />
<br />
The entropy of a system approaches a constant value as the temperature approaches zero.<br />
<br />
系统的熵随着温度接近绝对零度而接近一个恒定值。<br />
<br />
<br />
<br />
The constant value (not necessarily zero) is called the [[residual entropy]] of the system.<br />
<br />
The constant value (not necessarily zero) is called the residual entropy of the system.<br />
<br />
这个常数(不一定是零)被称为系统的余熵。<br />
<br />
<br />
<br />
==History==<br />
历史<br />
<br />
{{see also|Philosophy of thermal and statistical physics}}<br><br />
热学和统计物理学的哲学<br />
<br />
[[Mechanical equivalent of heat|Circa 1797, Count Rumford (born Benjamin Thompson)]] showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by [[Nicolas Léonard Sadi Carnot|Sadi Carnot]] in 1824. By 1860, as formalized in the works of those such as [[Rudolf Clausius]] and [[William Thomson, 1st Baron Kelvin|William Thomson]], two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist [[Josiah Willard Gibbs]], in his memoir ''Graphical Methods in the Thermodynamics of Fluids'', clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
Circa 1797, Count Rumford (born Benjamin Thompson) showed that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance thus challenging the caloric theory of heat, which held that there would be a finite amount of caloric heat/energy in a fixed amount of working substance. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824. By 1860, as formalized in the works of those such as Rudolf Clausius and William Thomson, two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist Josiah Willard Gibbs, in his memoir Graphical Methods in the Thermodynamics of Fluids, clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.<br />
<br />
大约在1797年，拉姆福德(出生于本杰明·汤普森)表明，无休止的机械作用可以从固定数量的工作物质中产生无限量的热量，从而挑战了热量理论。该理论认为在固定数量的工作物质中会有有限的热量 / 能量。1824年，萨迪·卡诺建立了第一个热力学原理，也就是后来的热力学第二定律。到1860年，正如鲁道夫 · 克劳修斯和威廉 · 汤姆森等人的著作所正式规定的那样，已经确立的两个热力学原理得到了发展，第一个原理和第二个原理，后来被重新定义为热力学定律。例如，1873年，热力学学家乔赛亚·威拉德·吉布斯在他的回忆录《流体热力学的图解法》中明确阐述了热力学的前两个绝对定律。整个20世纪的一些教科书对这些定律进行了不同的编号。在一些与化学无关的领域，第二定律被认为仅仅处理热机的效率问题，而所谓的第三定律则处理熵的增加问题。'''<font color="#32CD32">直接定义熵计算的零律不被认为是一条定律。</font>'''这种分离逐渐形成了第二定律，现代第三定律被广泛采用。<br />
<br />
<br />
<br />
==See also==<br />
<br />
*化学热力学 [[Chemical thermodynamics]]<br />
<br />
*守恒定律 [[Conservation law (physics)|Conservation law]]<br />
<br />
*熵增 [[Entropy production]]<br />
<br />
*金斯伯格定理 [[Ginsberg's theorem]]<br />
<br />
*宇宙热寂 [[Heat death of the universe]]<br />
<br />
*H定理 [[H-theorem]]<br />
<br />
*科学规律 [[Laws of science]]<br />
<br />
*昂萨格倒易关系（有时被描述为热力学第四定律） [[Onsager reciprocal relations]] (sometimes described as a fourth law of thermodynamics)<br />
<br />
*统计力学 [[Statistical mechanics]]<br />
<br />
*热力学方程表 [[Table of thermodynamic equations]]<br />
<br />
<br />
<br />
==References==<br><br />
参考文献<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
==Further reading==<br />
<br />
* [[Peter Atkins|Atkins, Peter]] (2007). ''Four Laws That Drive the Universe''. OUP Oxford. {{ISBN|978-0199232369}}<br />
<br />
* Goldstein, Martin & Inge F. (1993). ''The Refrigerator and the Universe''. Harvard Univ. Press. {{ISBN|978-0674753259}}<br />
<br />
<br />
<br />
==External links==<br />
<br />
* [http://www.bbc.co.uk/programmes/b06c06nd In Our Time: Perpetual Motion], BBC discussion about the Laws, with Ruth Gregory, Frank Close and Steven Bramwell, hosted by Melvyn Bragg, first broadcast 24 September 2015.<br />
<br />
<br />
<br />
[[Category:Laws of thermodynamics| ]]<br />
<br />
[[Category:Scientific laws]]<br />
<br />
Category:Scientific laws<br />
<br />
类别: 科学定律<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Laws of thermodynamics]]. Its edit history can be viewed at [[热力学定律/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E5%9B%9A%E5%BE%92%E5%9B%B0%E5%A2%83&diff=14680囚徒困境2020-10-01T15:23:32Z<p>趣木木：</p>
<hr />
<div>此词条由Henry初步翻译。<br />
<br />
{{other uses}}<br />
<br />
{{short description|Canonical example of a game analyzed in game theory}}<br />
<br />
{| class="wikitable floatright"<br />
<br />
{| class="wikitable floatright"<br />
<br />
{ | class“ wikitable floatright”<br />
<br />
|+ Prisoner's dilemma payoff matrix<br />
<br />
|+ Prisoner's dilemma payoff matrix<br />
<br />
囚徒困境支付矩阵<br />
<br />
! {{diagonal split header|A|B}}<br />
<br />
! <br />
<br />
!<br />
<br />
! B stays<br />silent<br />
<br />
! B stays<br />silent<br />
<br />
!B 保持安静<br />
<br />
! B<br />betrays<br />
<br />
! B<br />betrays<br />
<br />
!背叛<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! A stays<br />silent<br />
<br />
! A stays<br />silent<br />
<br />
!A 保持安静<br />
<br />
| {{diagonal split header|-1|-1|transparent}}<br />
<br />
| <br />
<br />
|<br />
<br />
| {{diagonal split header|-3|0|transparent}}<br />
<br />
| <br />
<br />
|<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! A<br />betrays<br />
<br />
! A<br />betrays<br />
<br />
!一个叛徒<br />
<br />
| {{diagonal split header|0|-3|transparent}}<br />
<br />
| <br />
<br />
|<br />
<br />
| {{diagonal split header|-2|-2|transparent}}<br />
<br />
| <br />
<br />
|<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
The '''prisoner's dilemma''' is a standard example of a game analyzed in [[game theory]] that shows why two completely [[Rationality#Economics|rational]] individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by [[Merrill Flood]] and [[Melvin Dresher]] while working at [[RAND Corporation|RAND]] in 1950. [[Albert W. Tucker]] formalized the game with prison sentence rewards and named it "prisoner's dilemma",<ref>Poundstone, 1992</ref> presenting it as follows:<br />
<br />
The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", prensenting it as follows:<br />
<br />
囚徒困境是博弈论分析的一个代表性例子，它揭示了为什么两个完全理性的个体可能不会合作，即使这样做似乎对他们最有利。它最初是由 Merrill Flood 和 Melvin Dresher 于1950年在兰德公司工作时构建的。Albert W. Tucker将这种博弈以囚徒的方式加以阐述，并将其命名为“囚徒困境” ，具体阐述如下：<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）专有名词单独筛出来 利用语法标出来 参读自审清单中的每一项<br />
<br />
<br />
{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
<br />
{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
<br />
{{引号 | 一个犯罪团伙的两名成员被捕入狱。每个囚犯都被关在各自的禁闭室里，没有任何与其他囚犯沟通的方式。检察官缺乏足够的证据来定罪这两人的主要指控，但有足够的证据来定罪两人较轻的指控。同时，检察官向每个犯人提供了一个交易。每个囚犯都有机会出卖对方，证明对方犯下罪行，或者他们可以进行合作，保持沉默。可能的结果是:<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）检察官缺乏足够的证据来定罪这两人的主要指控，但有足够的证据来定罪两人较轻的指控 这个可以考虑一下主要指控和次要指控 以及较重指控与较轻指控的对比<br />
* If A and B each betray the other, each of them serves two years in prison<br />
如果A和B都背叛了对方，他们都会在监狱服刑两年。<br />
* If A betrays B but B remains silent, A will be set free and B will serve three years in prison<br />
如果A背叛了B但B什么都没说，A会被无罪释放而B会服刑三年。<br />
* If A remains silent but B betrays A, A will serve three years in prison and B will be set free<br />
如果A保持沉默但B背叛了A，A会服刑三年而B会无罪释放。<br />
* If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).}}<br />
如果A和B都保持沉默，他们就只用服刑一年。<br />
<br />
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other.<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref> In reality, humans display a [[systemic bias]] towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action.<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref> This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome.<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref> The prisoner's dilemma became the focus of extensive experimental research.<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
<br />
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other. In reality, humans display a systemic bias towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action. This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome. The prisoner's dilemma became the focus of extensive experimental research. <br />
<br />
这意味着，除了监禁刑罚之外，囚犯没有机会奖励或惩罚他们的同伴，他们的决定也不会影响他们未来的声誉。因为背叛一个同伴比与他们合作能得到更大的回报，所以所有纯粹理性的、自私自利的囚犯都会背叛对方，这意味着，对于两个纯粹理性的囚犯来说，唯一可能的结果就是他们相互背叛。在现实中，尽管“理性”自利行为的简单模型已经预测到了这一点，人类在这种和类似的博弈中对合作行为依然表现出一种系统性的偏见。自从在兰德公司首次进行这项测试以来，这种对合作的偏见就已经为人所知; 参与测试的秘书们相互信任，为了最佳的共同结果而共同努力。囚徒困境成为大量实验研究的焦点。<br />
<br />
<br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by [[backward induction]]) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<br />
<br />
一个扩展的“迭代”版本的博弈由此衍生出来。在这个版本中，经典博弈会在在同一组囚犯之间重复进行，他们不断有机会因为以前的决定而惩罚另一个。如果参与者知道博弈的次数，那么(通过逆向归纳法)两个经典理性的玩家就会因为和在单次博弈相同的原因反复背叛对方。在无限次或未知次数的博弈中，没有固定的最优策略，囚徒困境竞赛因而能被用来竞赛并且检验这种情况下的算法。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“他们不断有机会因为以前的决定而惩罚另一个”是否考虑 补出“另一个”的主语是什么 另一个囚犯或者其他<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）“囚徒困境竞赛” 可以再斟酌一下？<br />
<br />
The prisoner's dilemma game can be used as a model for many [[#Real-life examples|real world situations]] involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.<br />
<br />
The prisoner's dilemma game can be used as a model for many real world situations involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.<br />
<br />
囚徒困境博弈可以作为许多现实世界中涉及合作行为的模型。在非正式用法中，”囚徒困境”一词可适用于不严格符合传统或迭代博弈的正式标准的情况: 例如，两个实体可以从合作中获得巨大利益或者会因为不能合作而遭受损失，但却发现协调其活动很困难或代价昂贵（并非不可能存在这种情况）。<br />
<br />
<br />
<br />
==Strategy for the prisoner's dilemma==<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]） 注意章节名的翻译<br />
<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
两名囚犯被分开关押在各自的房间里，不能相互交流。<br />
<br />
The normal game is shown below:<br />
<br />
The normal game is shown below:<br />
<br />
正常的博弈如下:<br />
<br />
<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class“ wikitable”<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! {{diagonal split header|<br />Prisoner A|Prisoner B}} !! Prisoner B stays silent<br>(''cooperates'') !! Prisoner B betrays<br>(''defects'')<br />
<br />
! !! Prisoner B stays silent<br>(cooperates) !! Prisoner B betrays<br>(defects)<br />
<br />
!!!犯人 b 保持沉默，合作! ！犯人 b 出卖了自己的缺点<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A stays silent<br>(''cooperates'')<br />
<br />
! Prisoner A stays silent<br>(cooperates)<br />
<br />
!犯人 a 保持沉默<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
每人服刑1年囚犯 a: 3年囚犯 b: 无罪释放<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A betrays<br>(''defects'')<br />
<br />
! Prisoner A betrays<br>(defects)<br />
<br />
!犯人 a 出卖了自己的缺点<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
囚犯 a: 获释囚犯 b: 3年每人服刑2年<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by [[Dilemma#Use in logic|dilemma]]: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by dilemma: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
假设两个囚犯都了解博弈的本质，对彼此没有忠诚，且在博弈之外没有机会得到报复或奖励。那么不管对方怎么决定，每个犯人背叛对方都会得到更高的奖励(“叛变”)。推理涉及一个进退两难的论点:B 要么合作，要么叛变。如果B合作，A 应该叛变，因为得到释放总比服刑1年好。如果 B叛变，A也应该叛变，因为服刑2年总比服刑3年好。所以不管怎样，a 都应该叛变。并行推理表明B应该选择叛变。<br />
<br />
<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a [[dominant strategy]]. Mutual defection is the only strong [[Nash equilibrium]] in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a dominant strategy. Mutual defection is the only strong Nash equilibrium in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
因为不管对方的选择如何，背叛总是比合作带来更好的回报，所以这是一个占优势的策略。相互背叛是游戏中唯一的强纳什均衡点（每个参与者单方面的改变策略只能使自己的情况变糟)。因此，困境在于，虽然相互合作比相互背叛产生更好的结果，但它却不是理性的结果，因为从自我利益的角度来看，合作的选择是非理性的。<br />
<br />
<br />
<br />
==Generalized form==<br />
<br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
传统囚徒困境的结构可以从其最初的囚徒环境中概括出来。假设两个玩家用红色和蓝色表示，并且每个玩家选择“合作”或“背叛”。<br />
<br />
<br />
<br />
If both players cooperate, they both receive the reward ''R'' for cooperating. If both players defect, they both receive the punishment payoff ''P''. If Blue defects while Red cooperates, then Blue receives the temptation payoff ''T'', while Red receives the "sucker's" payoff, ''S''. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff ''S'', while Red receives the temptation payoff ''T''.<br />
<br />
If both players cooperate, they both receive the reward R for cooperating. If both players defect, they both receive the punishment payoff P. If Blue defects while Red cooperates, then Blue receives the temptation payoff T, while Red receives the "sucker's" payoff, S. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff S, while Red receives the tem punishment payoffptation payoff T.<br />
<br />
如果两个玩家合作，他们都会因为合作而获得奖励R。如果两个参与人都叛变，他们都会受到惩罚 P。 如果蓝方叛变而红方合作，那么蓝方得到诱惑回报 T，而红方受到到“上当受骗者”损失S，同样地，如果蓝方合作而红方叛变，那么蓝方得到上当受骗者的支付S，而红方得到诱惑支付 T。<br />
<br />
<br />
<br />
This can be expressed in [[Normal-form game|normal form]]:<br />
<br />
This can be expressed in normal form:<br />
<br />
这可以用标准形式来表示:<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{ | 类“ wikitable”样式“ text-align: center”<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
| + 正则 PD 支付矩阵<br />
<br />
! {{diagonal split header|{{color|#009|Blue}}|{{color|#900|Red}}}}<br />
<br />
! |}}<br />
<br />
!|}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | <br />
<br />
!范围“ col”样式“ width: 60px; ” | <br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
! scope="col" style="width:60px;" | <br />
<br />
!范围“ col”样式“ width: 60px; ” | <br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
! scope="row" style="width:60px;" | <br />
<br />
!作用域“ row”样式“ width: 60px; ” | <br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
! scope="row" | <br />
<br />
!瞄准镜<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
要成为强意义下的囚徒困境博弈，收益必须满足以下条件:<br />
<br />
<br />
<br />
:{{tmath|T > R > P > S}}<br />
<br />
<br />
<br />
The payoff relationship {{tmath|R > P}} implies that mutual cooperation is superior to mutual defection, while the payoff relationships {{tmath|T > R}} and {{tmath|P > S}} imply that defection is the [[dominant strategy]] for both agents.<br />
<br />
The payoff relationship implies that mutual cooperation is superior to mutual defection, while the payoff relationships and imply that defection is the dominant strategy for both agents.<br />
<br />
回报关系意味着相互合作优于相互背叛，然而回报关系也意味着相互背叛背叛是双方的主导策略。<br />
<br />
<br />
<br />
===Special case: donation game===<br />
<br />
The "donation game"<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref> is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit ''b'' at a personal cost ''c'' with ''b'' > ''c''. Defection means offering nothing. The payoff matrix is thus<br />
<br />
The "donation game" is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit b at a personal cost c with b > c. Defection means offering nothing. The payoff matrix is thus<br />
<br />
“捐赠博弈”是囚徒困境的一种形式，在这种博弈中，合作相当于以个人成本C为另一方提供一个收益B，而叛变意味着什么也不提供。回报矩阵是这样的<br />
C<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{ | 类“ wikitable”样式“ text-align: center”<br />
<br />
! {{diagonal split header|{{navy (color)|Blue}}|{{color|#900|Red}}}}<br />
<br />
! |}}<br />
<br />
!|}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | <br />
<br />
!范围“ col”样式“ width: 60px; ” | <br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
! scope="col" style="width:60px;" | <br />
<br />
!范围“ col”样式“ width: 60px; ” | <br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
! scope="row" style="width:60px;" | <br />
<br />
!作用域“ row”样式“ width: 60px; ” | <br />
<br />
| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
! scope="row" | <br />
<br />
!瞄准镜<br />
<br />
| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
Note that {{tmath|2R>T+S}} (i.e. {{tmath|2(b-c)>b-c}}) which qualifies the donation game to be an iterated game (see next section).<br />
<br />
Note that (i.e. ) which qualifies the donation game to be an iterated game (see next section).<br />
<br />
请注意(即)这使得捐赠博弈成为一个迭代博弈(见下一节)。<br />
<br />
<br />
The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The [[marginal utility]] of an apple to the orange-grower X is ''b'', which is higher than the marginal utility (''c'') of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is ''b'' while the marginal utility of an apple is ''c''. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of ''b''-''c''. If one "defects" and does not deliver as promised, the defector will receive a payoff of ''b'', while the cooperator will lose ''c''. If both defect, then neither one gains or loses anything.<br />
<br />
The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The marginal utility of an apple to the orange-grower X is b, which is higher than the marginal utility (c) of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is b while the marginal utility of an apple is c. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of b-c. If one "defects" and does not deliver as promised, the defector will receive a payoff of b, while the cooperator will lose c. If both defect, then neither one gains or loses anything.<br />
<br />
捐赠博弈可能适用于市场。假设 X种橘子，Y 种苹果。苹果对橙子种植者 X 的边际效用是 b，这比橙子的边际效用c高，因为 x 有橙子剩余而没有苹果。同样，对于苹果种植者 y 来说，橙子的边际效用是 b，而苹果的边际效用是 c。 如果 X 和Y签约交换一个苹果和一个橙子，并且每个人都完成了交易，那么每个人都会得到 从c到b的效用收益。如果一方违约没有按照承诺交货，那么这个违约者将得到 b 效用的收益，而合作者将失去 c的效用收益。 如果两者都违约，那么谁也不会得到或失去任何东西。<br />
<br />
<br />
<br />
==The iterated prisoner's dilemma==<br />
<br />
{{more citations needed section|date=November 2012}}<br />
<br />
If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
<br />
If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
<br />
如果两个参与者连续进行多次囚徒困境博弈，他们记住对手先前的行动并相应地改变策略，这种博弈被称为迭代囚徒困境。<br />
<br />
<br />
<br />
In addition to the general form above, the iterative version also requires that {{tmath|2R > T + S}}, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
<br />
In addition to the general form above, the iterative version also requires that , to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
<br />
除了上面的一般形式之外，迭代版本还要求，防止交替的合作和背叛能比相互合作带来更大的回报。<br />
<br />
<br />
<br />
The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "[[Peace war game|peace-war game]]".<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
<br />
The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "peace-war game".<br />
<br />
迭代囚徒困境博弈是一些人类合作与信任理论的基础。假设博弈可以为两个需要信任的人之间的交易建模，那么群体中的合作行为也可以由多个参与者迭代的博弈模型来建模。因此，这些年来，它吸引了许多学者。1975年，葛夫曼和普尔估计关于它的学术文章超过2000篇。迭代的的囚徒困境也被称为“和平-战争博弈”。<br />
<br />
<br />
<br />
If the game is played exactly ''N'' times and both players know this, then it is optimal to defect in all rounds. The only possible [[Nash equilibrium]] is to always defect. The proof is [[Mathematical induction|inductive]]: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
<br />
If the game is played exactly N times and both players know this, then it is optimal to defect in all rounds. The only possible Nash equilibrium is to always defect. The proof is inductive: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
<br />
如果这个游戏正好玩了 n 次，并且两个玩家都知道这一点，那么在所有回合中最佳的策略就是叛变。唯一可能的纳什均衡点就是永远叛变。证据是归纳的: 一个人不妨在最后一回合叛变，因为对手以后没有机会反击。因此，双方都会在最后一个回合叛变。所以玩家同样也会在倒数第二回合时变节，因为无论做什么，对手都会在倒数第三回合变节，依此类推。同样方法适用于博弈次<br />
数未知但次数有限的情况。<br />
Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The [[superrational]] strategy in the iterated prisoner's dilemma with fixed ''N'' is to cooperate against a superrational opponent, and in the limit of large ''N'', experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
<br />
Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The superrational strategy in the iterated prisoner's dilemma with fixed N is to cooperate against a superrational opponent, and in the limit of large N, experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
<br />
与标准的囚徒困境不同，在迭代的囚徒困境中，叛变策略是严重违反直觉的，以至于不能预测人类玩家的行为。然而，在标准的经济理论中，这是唯一正确的答案。具有固定次数 n 的迭代囚徒困境中的超理性策略是与超理性对手进行合作，在 n 很大的限制下，实验结果的策略与超理性结果的策略一致，而不是博弈论的理性结果。<br />
<br />
<br />
<br />
For [[cooperation]] to emerge between game theoretic rational players, the total number of rounds ''N'' must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by [[Robert Aumann]] in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
<br />
For cooperation to emerge between game theoretic rational players, the total number of rounds N must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by Robert Aumann in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
<br />
为了使博弈论理性参与者之间出现合作，参与者必须不知道 n 回合的总数。在这种情况下，“总是叛变”可能不再是一个严格占主导地位的策略，而只是一个纳什均衡点。罗伯特 · 奥曼在1959年的一篇论文中表明，理性参与者在无限多次的博弈中通过反复互动可以维持合作的结果。<br />
<br />
<br />
<br />
According to a 2019 experimental study in the ''American Economic Review'' which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, [[Tit for tat|tit-for-tat]], and [[Grim trigger]]. Which strategy the subjects chose depended on the parameters of the game.<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
<br />
According to a 2019 experimental study in the American Economic Review which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, tit-for-tat, and Grim trigger. Which strategy the subjects chose depended on the parameters of the game.<br />
<br />
《美国经济评论》(American Economic Review)2019年的一项实验研究测试了现实生活中的实验对象在完全监控的情况下在迭代的囚徒困境中使用的策略，结果显示，大多数选择的策略都是叛变、针锋相对抑或是触发策略。受试者选择的策略取决于博弈的参数。<br />
<br />
<br />
<br />
===Strategy for the iterated prisoner's dilemma===<br />
<br />
Interest in the iterated prisoner's dilemma (IPD) was kindled by [[Robert Axelrod]] in his book ''[[The Evolution of Cooperation]]'' (1984). In it he reports on a tournament he organized of the ''N'' step prisoner's dilemma (with ''N'' fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
<br />
Interest in the iterated prisoner's dilemma (IPD) was kindled by Robert Axelrod in his book The Evolution of Cooperation (1984). In it he reports on a tournament he organized of the N step prisoner's dilemma (with N fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
<br />
罗伯特 · 阿克塞尔罗德在他的著作《合作的进化》(1984)中激起了了人们对迭代的囚徒困境(IPD)的兴趣。在这篇文章中，他报道了一个关于 n 次囚徒困境的比赛，参赛者必须一次又一次地选择他们共同的策略，并且要记住他们之前的遭遇。阿克塞尔罗德邀请世界各地的学术界同仁设计计算机策略来参加此次比赛。输入的程序在算法复杂性、最初敌意、宽恕能力等方面差异很大。<br />
<br />
<br />
<br />
Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more [[altruism|altruistic]] strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by [[natural selection]].<br />
<br />
Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selection.<br />
<br />
阿克塞尔罗德发现，当这些遭遇在很长一段时间内在许多玩家身上重复发生时，每个玩家都有不同的策略，从长远来看，贪婪策略往往表现得非常糟糕，而更加利他的策略表现得更好，这完全是根据自身利益来判断的。他利用这一结果，揭示了通过自然选择，从最初纯粹自私行为向利他行为进化的可能机制。<br />
<br />
<br />
<br />
The winning [[deterministic algorithm|deterministic]] strategy was tit for tat, which [[Anatol Rapoport]] developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of [[BASIC]], and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
<br />
The winning deterministic strategy was tit for tat, which Anatol Rapoport developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
<br />
最终获胜的决定性策略是以牙还牙，这是阿纳托尔 · 拉波波特开发并参加比赛的策略。这是所有参赛程序中最简单的一个，只有四行 BASIC 语言，并且赢得了比赛。策略很简单，就是在游戏的第一次迭代中进行合作; 在此之后，玩家做他或她的对手在前一步中所做的事情。根据具体情况，一个稍微好一点的策略可以是“带着宽恕的心以牙还牙”。当对手叛变时，在下一次博弈中，玩家有时还是会合作，但概率很小(大约1-5%)。这允许博弈能偶尔从陷入叛变循环中恢复过来。确切的概率取决于对手的安排。<br />
<br />
<br />
<br />
By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
<br />
By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
<br />
通过分析得分最高的战略，阿克塞尔罗德阐述了战略成功的几个必要条件。<br />
<br />
<br />
<br />
; Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
<br />
Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
<br />
友好： 最重要的条件是策略必须是好的 ，也就是说，它不会在对手之前叛变(这有时被称为“乐观”算法)。几乎所有得分最高的策略都是友好的; 因此，一个纯粹自私的策略不会出于纯粹自身利益的原因而“欺骗”对手。<br />
<br />
; Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
<br />
Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
<br />
报复: 然而，阿克塞尔罗德认为，成功的战略决不能是盲目的乐观主义。它有时必须进行报复。非报复策略的一个例子就是永远合作。这是一个非常糟糕的选择，因为“肮脏”的策略会无情地剥削这些玩家。<br />
<br />
; Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
<br />
Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
<br />
宽容: 成功的策略也必须是宽容的。虽然玩家会报复，但如果对手不继续叛变，他们将再次回到合作的状态。这阻止了长时间的报复和反报复，最大限度地提高积分。<br />
<br />
; Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
<br />
Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
<br />
不嫉妒: 最后一个品质是不嫉妒，不比对手得分更多。<br />
<br />
<br />
<br />
The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
<br />
The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
<br />
对于一次性的囚徒困境博弈，最优(点数最大化)策略就是简单的叛变; 正如上面所说，无论对手的构成如何，这都是正确的。然而，在迭代囚徒困境博弈中，最优策略取决于可能的对手的策略，以及他们对叛变和合作的反应。例如，考虑一个群体，其中每个人每次都会叛变，除了一个人遵循以牙还牙的策略。那个人就会由于第一回合的失利而处于轻微的不利地位。在这样一个群体中，个体的最佳策略是每次都叛变。在一定比例的总是选择背叛的玩家和其余组成为以牙还牙的玩家的人群中，个人的最佳策略取决于这一比例和博弈的次数。<br />
<br />
<br />
<br />
In the strategy called Pavlov, [[win-stay, lose-switch]], faced with a failure to cooperate, the player switches strategy the next turn.<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref> In certain circumstances,{{specify|date=November 2012}} Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
<br />
In the strategy called Pavlov, win-stay, lose-switch, faced with a failure to cooperate, the player switches strategy the next turn. In certain circumstances, Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
<br />
在所谓的巴甫洛夫策略中，赢-保持，输-变换，面对一次合作失败，玩家将在下一次变换策略。在某些情况下，巴甫洛夫通过给予使用类似策略的合作者优惠待遇打败了所有其他策略。<br />
<br />
<br />
<br />
Deriving the optimal strategy is generally done in two ways:<br />
<br />
Deriving the optimal strategy is generally done in two ways:<br />
<br />
得出最佳策略通常有两种方法:<br />
<br />
* [[Bayesian Nash equilibrium]]: If the statistical distribution of opposing strategies can be determined (e.g. 50% tit for tat, 50% always cooperate) an optimal counter-strategy can be derived analytically.{{efn|1=For example see the 2003 study<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref> for discussion of the concept and whether it can apply in real [[economic]] or strategic situations.}}<br />
<br />
* [[Monte Carlo method|Monte Carlo]] simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a [[genetic algorithm]] for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to produce tit for tat players (see for instance Chess 1988),{{Clarify|date=August 2016}} but no analytic proof exists that this will always occur.<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
<br />
<br />
<br />
Although tit for tat is considered to be the most [[robust]] basic strategy, a team from [[Southampton University]] in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start.<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref> Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show [[University of Southampton]]'s strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between [[computer program|software strategies]] (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian [[Evolutionarily stable strategy|ESS]] simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. [[Richard Dawkins]] showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
<br />
Although tit for tat is considered to be the most robust basic strategy, a team from Southampton University in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show University of Southampton's strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between software strategies (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian ESS simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. Richard Dawkins showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
<br />
尽管以牙还牙认为是最有力的基本策略，来自英格兰南安普敦大学的一个团队在20周年的迭代囚徒困境竞赛中提出了一个新策略，这个策略被证明比以牙还牙更为成功。这种策略依赖于程序之间的串通，以获得单个程序的最高分数。这所大学向比赛提交了60个程序，这些程序的设计目的是在比赛开始时通过一系列的5到10个动作来互相认识。一旦认识建立，一个程序总是合作，另一个程序总是叛变，保证叛变者得到最多的分数。如果这个程序意识到它正在和一个非南安普顿的球员比赛，它会不断地叛变，试图最小化与之竞争程序的得分。因此，2004年囚徒困境锦标赛的结果显示了南安普敦大学战略位居前三名，尽管它比冷酷战略赢得更少，输的更多。(在囚徒困境锦标赛中，比赛的目的不是“赢”比赛——这一点频繁叛变很容易实现)。此外，即使没有软件策略之间的暗中串通(南安普顿队利用了这一点) ，以牙还牙并不总是任何特定锦标赛的绝对赢家; 更准确地说，它是在一系列锦标赛中的长期结果超过了它的竞争对手。(在任何一个事件中，一个给定的策略可以比以牙还牙稍微更好地适应竞争，但是以牙还牙更有力)。这同样适用于带有宽恕变量的以牙还牙，和其他最佳策略: 在任何特定的一天，他们可能不会“赢”一个特定的混合反战略。另一种方法是使用达尔文的 ESS 模拟。在这样的模拟中，以牙还牙几乎总是占主导地位，尽管讨厌的策略会在人群中进进出出，因为使用以牙还牙策略的人群可以通过非报复性的好策略进行渗透，这反过来使他们容易成为讨厌策略的猎物。理查德·道金斯指出，在这里，没有静态的混合策略会形成一个稳定的平衡，系统将始终在界限之间振荡。这种策略最终在比赛中获得了前三名的位置，以及一些接近垫底的位置。<br />
<br />
<br />
<br />
This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of [[minmaxing]]). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book ''[[The Selfish Gene]]'', pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
<br />
This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of minmaxing). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book The Selfish Gene, pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
<br />
这种策略利用了这样一个事实，即在这场特殊的比赛中允许多个参赛项目，并且一支队伍的表现是由得分最高的项目来衡量的(这意味着使用自我牺牲的项目是一种分数最大化的形式)。在一个只能控制一个玩家的比赛中，以牙还牙当然是一个更好的策略。由于这一新规则的存在，与阿克塞尔罗德的具有深远影响的竞赛相比，这种竞赛在分析单个智能体策略时也就没有什么理论意义。然而，它为在分析多智能体框架下，特别是在存在干扰的情况下，如何实现协作策略提供了基础。事实上，早在这场新规则锦标赛开始之前，道金斯就在他的《自私的基因》一书中指出，如果允许多次参赛，这种策略就有可能获胜，但他说，如果提交这种策略的话，阿克塞尔罗德很可能不会允许。因为它依赖于规避囚徒困境的规则，即两个球员之间不允许交流，南安普顿的项目可以说在开场的“十步舞”中就是这样做以认识对方的; 这只是强调了交流对于改变游戏的平衡是多么有影响。<br />
<br />
<br />
<br />
===Stochastic iterated prisoner's dilemma===<br />
<br />
<br />
<br />
In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities".<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref> In an encounter between player ''X'' and player ''Y'', ''X'' 's strategy is specified by a set of probabilities ''P'' of cooperating with ''Y''. ''P'' is a function of the outcomes of their previous encounters or some subset thereof. If ''P'' is a function of only their most recent ''n'' encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that ''X'' will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which ''X'' cooperated and ''Y'' defected, then <math>P_{cd}</math> is the probability that ''X'' will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as ''P''={1,0,1,0}, in which ''X'' responds as ''Y'' did in the previous encounter. Another is the [[win–stay, lose–switch]] strategy written as ''P''={1,0,0,1}, in which ''X'' responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<ref name="Press2012"/><br />
<br />
In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities". In an encounter between player X and player Y, X 's strategy is specified by a set of probabilities P of cooperating with Y. P is a function of the outcomes of their previous encounters or some subset thereof. If P is a function of only their most recent n encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that X will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which X cooperated and Y defected, then <math>P_{cd}</math> is the probability that X will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as P={1,0,1,0}, in which X responds as Y did in the previous encounter. Another is the win–stay, lose–switch strategy written as P={1,0,0,1}, in which X responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<br />
<br />
在随机迭代囚徒困境博弈中，策略由“合作概率”来确定。在玩家 x 和玩家 y 之间的遭遇中，x 的策略由一组与 y 合作的概率 p 确定，p 是他们之前遭遇的结果的函数，或者是其中的一些子集。如果 p 只是它们最近遇到次数 n 的函数，那么它被称为“记忆-n”策略。我们可以用四个合作概率确定一个记忆-1策略:p { cc }、 p { cd }、 p { dc }、 p { dd } ，其中 math遭遇中合作的概率。如果每个概率都是1或0，这种策略称为确定性策略。确定性策略的一个例子是以牙还牙策略，写成 p {1,0,1,0} ，其中 x 的反应和 y 在前一次遭遇中的反应一样。另一种是胜-保持-败-转换策略，它被写成 p {1,0,0,1} ，在这种策略中，如果 x 获得胜利(即:cc 或 dc)，x会做出与上一次遭遇一样的反应 ，但如果失败，x会改变策略(即cd 或 dd)。研究表明，对于任何一种记忆-n 策略，存在一个相应的记忆-1策略，这个策略给出相同的统计结果，因此只需要考虑记忆-1策略。<br />
<br />
<br />
<br />
If we define ''P'' as the above 4-element strategy vector of ''X'' and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of ''Y'', a transition matrix ''M'' may be defined for ''X'' whose ''ij'' th entry is the probability that the outcome of a particular encounter between ''X'' and ''Y'' will be ''j'' given that the previous encounter was ''i'', where ''i'' and ''j'' are one of the four outcome indices: ''cc'', ''cd'', ''dc'', or ''dd''. For example, from ''X'' 's point of view, the probability that the outcome of the present encounter is ''cd'' given that the previous encounter was ''cd'' is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for ''Q'' are from ''Y'' 's point of view: a ''cd'' outcome for ''X'' is a ''dc'' outcome for ''Y''.) Under these definitions, the iterated prisoner's dilemma qualifies as a [[stochastic process]] and ''M'' is a [[stochastic matrix]], allowing all of the theory of stochastic processes to be applied.<ref name="Press2012"/><br />
<br />
If we define P as the above 4-element strategy vector of X and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of Y, a transition matrix M may be defined for X whose ij th entry is the probability that the outcome of a particular encounter between X and Y will be j given that the previous encounter was i, where i and j are one of the four outcome indices: cc, cd, dc, or dd. For example, from X 's point of view, the probability that the outcome of the present encounter is cd given that the previous encounter was cd is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for Q are from Y 's point of view: a cd outcome for X is a dc outcome for Y.) Under these definitions, the iterated prisoner's dilemma qualifies as a stochastic process and M is a stochastic matrix, allowing all of the theory of stochastic processes to be applied.<br />
<br />
如果我们将 p 定义为 x 的上述4元策略向量，并将 q { cc }、 q { cd }、 q { dc }、 q { dd } 定义为 y 的4元策略向量，则对于 x 可以定义一个转移矩阵 m，该 x 的第 j 项是 x 和 y 之间特定遭遇的结果为 j 的概率，前一次遭遇为 i，其中 i 和 j 是 cc、 cd、 dc 或 dd 四个结果索引中的一个。例如，从 x 的角度来看，如果前一次遭遇的结果是 cd，那么这次遭遇的结果是 cd 的概率等于 m { cd，cd } p { cd }(1-Q { dc }) 。(q 的指数是 y 的观点: x 的 cd 结果是 y 的 dc 结果)在这些定义下，重复的囚徒困境被定义为一个随机过程，m 是一个转移矩阵，允许所有的随机过程理论被应用。<br />
<br />
<br />
<br />
One result of stochastic theory is that there exists a stationary vector ''v'' for the matrix ''M'' such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that ''v'' is normalized so that the sum of its four components is unity. The ''ij'' th entry in <math>M^n</math> will give the probability that the outcome of an encounter between ''X'' and ''Y'' will be ''j'' given that the encounter ''n'' steps previous is ''i''. In the limit as ''n'' approaches infinity, ''M'' will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing ''j'' which will be independent of ''i''. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that ''v'' is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to ''v''. Thus the stationary vector specifies the equilibrium outcome probabilities for ''X''. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From ''X'' 's point of view), the equilibrium payoffs for ''X'' and ''Y'' can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.<br />
<br />
One result of stochastic theory is that there exists a stationary vector v for the matrix M such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that v is normalized so that the sum of its four components is unity. The ij th entry in <math>M^n</math> will give the probability that the outcome of an encounter between X and Y will be j given that the encounter n steps previous is i. In the limit as n approaches infinity, M will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing j which will be independent of i. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that v is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to v. Thus the stationary vector specifies the equilibrium outcome probabilities for X. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From X 's point of view), the equilibrium payoffs for X and Y can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies P and Q to be compared for their long term payoffs.<br />
<br />
随机理论的一个结果是，矩阵 m 存在一个平稳向量 v，使得矩阵 m 是一个平稳向量，并且不失一般性，我们可以指定 v 是标准化的，因此它的4个组成部分之和是单位。数学 m ^ n 中的 ij 项给出了 x 和 y 相遇的结果是 j 的概率，前面相遇 n 步的概率是 i。当 n 趋于无穷时，m 收敛于一个具有固定值的矩阵，并给出了产生 j 的长期概率，j 与 i 无关。换句话说， m 的无限次方的行将是相同的，给出了重复囚徒困境的长期平衡结果概率，而不需要明确地计算大量的相互作用。可以看出，v 是数学 m ^ n 特别是 m ^ infty 的平稳向量，因此数学 m的无限次方的每一行都等于 v，因此平稳向量指定 x 的平衡结果概率。将 s，r，s，t，p 和 s y，r，t，s，p 定义为{ cc，cd，dc，dd }结果的短期收益向量(从 x 的角度来看) ，x 和 y 的均衡收益现在可以指定为s_x=v\cdot S_x和s_y=v\cdot S_y ，使得两种P、Q策略能比较他们的长期回报。<br />
<br />
<br />
<br />
====Zero-determinant strategies====<br />
<br />
<br />
<br />
[[File:IPD Venn.svg|right|thumb|upright=2.5|The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram]]. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and [[weak selection]]. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
<br />
The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and weak selection. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
<br />
利用文献[1]中的维恩图，讨论了迭代囚徒困境(IPD)中零行列式(ZD)、合作策略和变节策略之间的关系。合作策略总是与其他合作策略相互配合，而变通策略总是与其他变通策略相抵触。这两种策略都包含在强选择下具有鲁棒性的策略子集，这意味着当它们驻留在一个种群中时，没有其他记忆1策略被选择来入侵这样的策略。只有协作策略包含一个总是鲁棒的子集，这意味着在强选择和弱选择情况下，没有选择其他的记忆-1策略来入侵和替换这些策略。ZD和好的合作策略之间的交集是一套慷慨的 ZD 策略。敲诈策略是 ZD 策略和非鲁棒性叛逃策略的交集。以牙还牙是合作、背叛和 ZD 策略的交集。<br />
<br />
<br />
<br />
In 2012, [[William H. Press]] and [[Freeman Dyson]] published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies.<ref name="Press2012"/> The long term payoffs for encounters between ''X'' and ''Y'' can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector ''v''. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in ''f'', it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where ''U''={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
<br />
In 2012, William H. Press and Freeman Dyson published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies. The long term payoffs for encounters between X and Y can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector v. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in f, it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where U={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
<br />
2012年，威廉· h·普莱斯和弗里曼 · 戴森针对随机迭代囚徒困境提出了一类新的策略，称为“零决定因素”策略。x 和 y 之间的长期收益可以表示为一个矩阵的决定因素，它是两个策略和短期收益向量的函数: 不涉及平稳向量 v 的 s s x d (p，q，sx) 和 s y d (p，q，sy)。 由于行列式函数 s y d (p，q，f) 在 f 中是线性的，因此可以推出alpha s x + βs y + γd (p，q，αs x + βs y + γu)(其中 u {1,1,1})。任何策略的数学 d (p，q， αsx + βsy + gamma u)0 被定义为 ZD 策略，长期收益服从关系式。<br />
<br />
<br />
<br />
Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of [[ultimatum game]]. Specifically, ''X'' is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of ''Y'' 's strategy, offering an opportunity for ''X'' to "extort" player ''Y'' (and vice versa). (It turns out that if ''X'' tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.<ref name="Press2012"/>)<br />
<br />
Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of ultimatum game. Specifically, X is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of Y 's strategy, offering an opportunity for X to "extort" player Y (and vice versa). (It turns out that if X tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.)<br />
<br />
以牙还牙是 ZD 战略，这是“公平”的意义上说，没有占其他玩家的便宜。然而，ZD 空间也包含一些策略，在两个玩家的情况下，允许一个玩家单方面设置另一个玩家的分数，或者强迫一个进化的玩家获得比他自己的分数低一定百分比的回报。被敲诈的玩家可能会叛变，但因此获得较低的回报而受到伤害。因此，敲诈的解决方案将迭代的囚徒困境转化为一种最后通牒博弈。具体来说，x 能够选择一种策略，对于这种策略，数学 d (p，q， beta sy + gamma u)0 单方面地将 s y 设置为一个特定值范围内的特定值，与 y 的策略无关，为 x 提供了一个“勒索”玩家 y 的机会(反之亦然)。(事实证明，如果 x 试图将 s x 设置为一个特定的值，那么可能性的范围要小得多，只包括完全合作或完全叛变。)<br />
<br />
<br />
<br />
An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not [[evolutionarily stable strategy|evolutionarily stable]]. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
<br />
An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<br />
<br />
IPD的一个扩展是进化随机 IPD，其中允许特定策略的相对丰度发生变化，更成功的策略相对增加。这个过程可以通过让不那么成功的玩家模仿更成功的策略来完成，或者通过从游戏中淘汰不那么成功的玩家，同时让更成功的玩家成倍增加。研究表明，不公平的 ZD 策略不是进化稳定策略。关键的直觉告诉我们，简化稳定策略不仅要能够入侵另一个群体(这是敲诈 ZD 策略可以做到的) ，而且还要在同类型的其他玩家面前表现良好(敲诈 ZD 的玩家表现不佳，因为他们减少了彼此的盈余)。<br />
<br />
<br />
<br />
Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and [[win–stay, lose–switch]] agents.<ref name=Hilbe2013 /><br />
<br />
Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.<br />
<br />
理论和模拟证实，超过一个临界种群规模，ZD 勒索失去了在进化竞争对更多的合作策略，结果，平均回报在种群增加。此外，在有些情况下，勒索者甚至可能通过帮助打破一致叛变者与赢-保持-输-转换代理人之间的对峙而促进合作。<br />
<br />
<br />
<br />
While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies ''is'' both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the [[Prisoner's dilemma#Special case: Donation game|donation game]] by Alexander Stewart and Joshua Plotkin in 2013.<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref> Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013)<ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<ref name=Stewart2013 /><br />
<br />
While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies is both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the donation game by Alexander Stewart and Joshua Plotkin in 2013. Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013) to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<br />
<br />
虽然被敲诈的 ZD 策略在人口众多的情况下并不稳定，但另一种被称为“慷慨”的 ZD 策略既稳定又强健。事实上，当人口不是太少的时候，这些策略可以取代任何其他 ZD 策略，甚至在一系列针对迭代囚徒困境的通用策略中表现良好，包括赢-保持，输-转换策略。亚历山大·斯图尔特和约书亚·普洛特金在2013年的捐赠博弈中证明了这一点。慷慨的策略会与其他合作的玩家合作，面对叛变，慷慨的玩家比他的对手失去更多的效用。慷慨策略是 ZD 策略和所谓的“好”策略的交集，Akin (2013)将这两种策略定义为玩家对过去的相互合作作出回应，并在至少获得合作预期收益的情况下平均分配预期收益的策略。在好的策略中，当总体不太小时，慷慨(ZD)子集表现良好。如果总体很少，叛变策略往往占主导地位。<br />
<br />
<br />
<br />
===Continuous iterated prisoner's dilemma===<br />
<br />
Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref> found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from [[Assortative mating|assorting]] with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94.<br />
<br />
Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from assorting with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94.<br />
<br />
关于迭代囚徒困境的研究大多集中在离散情况下，在这种情况下，参与者要么合作，要么叛变，因为这个模型分析起来比较简单。然而，一些研究人员已经研究了连续迭代囚徒困境的模型，在这个模型中，玩家能够对另一个玩家做出可变的贡献。le和Boyd发现，在这种情况下，合作比离散迭代的囚徒困境更难发展。这个结果的基本直觉很简单: 在一个持续的囚徒困境中，如果一个人群开始处于非合作均衡状态，那么只比非合作者稍微多一点合作性的玩家从相互配合中获益不大。相比之下，在离散的囚徒困境中，以牙还牙的合作者相对于非合作者，在非合作均衡中相互配合会获得较大的回报提升。由于自然可以提供更多的机会来进行各种各样的合作，而不是严格地将合作或叛变分为两类，持续的囚徒困境可以帮助解释为什么现实生活中以牙还牙的合作的例子在自然界中极其罕见。（参考汉默斯坦，p.(2003)。《为什么互惠在群居动物中如此罕见？新教徒的呼吁：合作的基因和文化进化》 ，麻省理工学院出版社。83–94页）。<br />
<br />
</ref>) even though tit for tat seems robust in theoretical models.<br />
<br />
</ref>) even though tit for tat seems robust in theoretical models.<br />
<br />
尽管在理论模型中，以牙还牙似乎是有力的。<br />
<br />
<br />
<br />
===Emergence of stable strategies===<br />
<br />
Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies.<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref> Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
<br />
Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies. Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<br />
<br />
玩家似乎不能协调相互合作，因此常常陷入劣势但稳定的叛变策略。通过这种方式，迭代回合可以促进稳定策略的进化。多轮循环往往产生新颖的策略，这对复杂的社会互动有影响。其中一个策略就是“赢-保持-输”的转变。这个策略比一个简单的以牙还牙策略要好——也就是说，如果你能逃脱作弊的惩罚，重复这个行为，但是如果你被抓住了，就改变策略。<br />
<br />
<br />
<br />
The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
<br />
The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
<br />
这种以牙还牙策略的唯一问题是，它们很容易出现信号错误。当一个人因报复而作弊，而另一个人将其单纯解释为欺骗时，问题就出现了。结果，第二个人现在作弊，然后在接下来的连锁反应中开始了反复交替的作弊模式。<br />
<br />
<br />
<br />
==Real-life examples==<br />
<br />
The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the [[social science]]s such as [[economics]], [[politics]], and [[sociology]], as well as to the biological sciences such as [[ethology]] and [[evolutionary biology]]. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
<br />
The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics, and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
<br />
囚犯的设置看起来似乎是人为的，但实际上在人类交往以及自然界的交互中有许多具有相同收益矩阵的例子。囚徒困境是经济学、政治学、社会学等社会科学以及动物行为学、进化生物学等生物学研究的热点问题。许多自然过程都被抽象为生物进行无休止的囚徒困境博弈的模型。这种广泛的适用性让博弈非常重要。<br />
<br />
<br />
<br />
===Environmental studies===<br />
<br />
In [[environmental studies]], the PD is evident in crises such as global [[climate change|climate-change]]. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb [[Carbon dioxide|{{Co2}}]] emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
<br />
In environmental studies, the PD is evident in crises such as global climate-change. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb Carbon dioxide| emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<br />
<br />
在环境研究中，在诸如全球气候变化等危机中，这种差异显而易见。有人认为，所有国家都将从稳定的气候中受益，但是任何一个国家往往都在遏制二氧化碳排放方面犹豫不决。人们错误地认为，如果所有国家的行为都改变，任何一个国家保持目前的行为所带来的直接好处都会大于所谓的最终好处，这就解释了2007年气候变化方面的僵局。<br />
<br />
<br />
<br />
An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
<br />
An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<br />
<br />
气候变化政治与囚徒困境之间的一个重要区别是不确定性; 污染对气候变化的影响程度和速度尚不清楚。因此，政府面临的困境不同于囚徒困境，因为合作的回报是未知的。这种差异表明，各国之间的合作远远少于真正的迭代囚徒困境中的合作，因此避免可能发生的气候灾难的可能性远远小于使用真正的迭代囚徒困境进行的博弈论分析所提出的可能性。<br />
<br />
<br />
<br />
Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of [[Michael Porter]]'s hypothesis, in which government regulation of competing firms is substantial.<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
<br />
Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of Michael Porter's hypothesis, in which government regulation of competing firms is substantial.<br />
<br />
Osang 和 Nandy (2003)提供了一个理论解释，并根据 Michael Porter 的假设，即政府对竞争企业的监管是实质性的，提供了监管驱动的双赢局面的证据。<br />
<br />
<br />
<br />
===Animals===<br />
<br />
Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, [[guppy|guppies]] inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
<br />
Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, guppies inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
<br />
许多动物的合作行为可以被理解为囚徒困境的一个例子。通常动物会有长期的伙伴关系，这种关系可以更具体地模拟为重复的囚徒困境。例如，孔雀鱼成群结队地合作监察捕食者，它们被认为是在惩罚不合作的监察者。<br />
<br />
<br />
<br />
[[Vampire bats]] are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
<br />
Vampire bats are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<br />
<br />
吸血蝙蝠是群居动物，从事相互的食物交换。应用囚徒困境的收益可以帮助解释这种行为:<br />
<br />
* C/C: "Reward: I get blood on my unlucky nights, which saves me from starving. I have to give blood on my lucky nights, which doesn't cost me too much."<br />
合作/合作：回报：我在不幸运的晚上得到了能让我果腹的血，那在幸运的晚上我也应该分出点血，那不会花费多少。<br />
* D/C: "Temptation: You save my life on my poor night. But then I get the added benefit of not having to pay the slight cost of feeding you on my good night."<br />
叛变/合作：诱惑：你在我的不幸的夜里救了我，但在我的幸运夜我不会给你血以让我活的更好。<br />
* C/D: "Sucker's Payoff: I pay the cost of saving your life on my good night. But on my bad night you don't feed me and I run a real risk of starving to death."<br />
合作/叛变：可怜者的回报：在我的幸运夜我救了你的命，但在我的不幸夜里你没有救我，我有饿死的风险。<br />
* D/D: "Punishment: I don't have to pay the slight costs of feeding you on my good nights. But I run a real risk of starving on my poor nights."<br />
叛变/叛变：惩罚：我在我的幸运夜里不必付出代价来救你，但我在我的不幸夜里有挨饿的风险。<br />
<br />
===Psychology===<br />
<br />
In [[addiction]] research / [[behavioral economics]], [[George Ainslie (psychologist)|George Ainslie]] points out<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref> that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, ''defecting'' means ''relapsing'', and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
<br />
In addiction research / behavioral economics, George Ainslie points out that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, defecting means relapsing, and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
<br />
在成瘾研究/行为经济学中，乔治·安斯利指出，成瘾可以被描述为成瘾者现在和未来自我之间的跨期囚徒困境问题。在这种情况下，叛变意味着反复，很容易看出，不在今天和未来叛变是迄今为止最好的结果。如果一个人今天戒了，但在将来又复吸，这是最糟糕的结果——从某种意义上来说，今天戒瘾所包含的纪律和自我牺牲已经被“浪费”了，因为未来的复吸意味着瘾君子又回到了他开始的地方，将不得不重新开始(这相当令人沮丧，也使得重新开始更加困难)。今天和明天复发是一个稍微“更好”的结果，因为当瘾君子仍然上瘾时，他们没有努力去尝试停止。最后一种情况，一个人在今天进行成瘾行为，而在明天弃权，这对于任何一个与成瘾作斗争的人来说都是熟悉的。这里的问题是(和其他囚徒困境一样) ，背叛“今天”有一个明显的好处，但明天这个个人将面临同样的囚徒困境，同样明显的好处将出现，最终导致一连串无休止的叛变。<br />
<br />
<br />
<br />
[[John Gottman]] in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
<br />
John Gottman in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
<br />
John Gottman 在他的研究《信任的科学》中将良好的关系定义为伴侣知道不要进入(叛变，叛变）牢房中或者至少不要陷入这样一个循环中。<br />
<br />
<br />
<br />
===Economics===<br />
<br />
The prisoner's dilemma has been called the ''[[Escherichia coli|E. coli]]'' of social psychology, and it has been used widely to research various topics such as [[Oligopoly|oligopolistic]] competition and collective action to produce a collective good.<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref> <br />
<br />
The prisoner's dilemma has been called the E. coli of social psychology, and it has been used widely to research various topics such as oligopolistic competition and collective action to produce a collective good. <br />
<br />
囚徒困境被称为社会心理学中的大肠杆菌，它被广泛用于研究寡头垄断竞争及其集体行动来产生集体利益等问题。<br />
<br />
<br />
<br />
Advertising is sometimes cited as a real-example of the prisoner's dilemma. When [[cigarette advertising]] was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry.{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} This analysis is likely to be pertinent in many other business situations involving advertising.{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}<br />
<br />
Advertising is sometimes cited as a real-example of the prisoner's dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. This analysis is likely to be pertinent in many other business situations involving advertising.<br />
<br />
广告有时被引用为囚徒困境的一个真实例子。当香烟广告在美国是合法的时候，相互竞争的香烟制造商必须决定在广告上花多少钱。公司 a 的广告效果部分取决于公司 b 的广告效果。同样，公司 b 的广告带来的利润也受到公司 a 的广告影响。如果公司 a 和公司 b 都选择在给定的时间段内做广告，那么一家公司的广告就会抵消另一方的广告，倘若收入保持不变，费用就会因广告成本而增加。两家公司都将从广告减少中获益。然而，如果 b 公司选择不做广告，a 公司就可以通过广告获得巨大的利益。尽管如此，一家公司的最佳广告数量仍取决于另一家公司从事了多少广告。由于最佳策略取决于其他公司的选择，因此这里没有占主导地位的策略，这使得它与囚徒困境略有不同。但结果是相似的，如果两家公司的广告都少于均衡他们的处境会更好。有时合作行为确实会在商业环境中出现。例如，香烟制造商支持立法禁止香烟广告，理解这将降低成本和增加整个行业的利润。这种分析可能适用于许多其他涉及广告的商业情况。<br />
<br />
<br />
<br />
Without enforceable agreements, members of a [[cartel]] are also involved in a (multi-player) prisoner's dilemma.<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. [[Anti-trust]] authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for [[consumer]]s.<br />
<br />
Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoner's dilemma. 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.<br />
<br />
没有可强制执行的协议，卡特尔的成员国也会陷入(多玩家)囚徒困境。“合作”通常意味着将价格保持在预先商定的最低水平。“叛变”意味着在这个最低价格水平下方销售，立即从其他卡特尔成员那里获得业务(和利润)。反垄断机构希望潜在的卡特尔成员相互叛变，确保消费者获得尽可能低的价格。<br />
<br />
<br />
<br />
===Sport===<br />
<br />
[[Doping in sport]] has been cited as an example of a prisoner's dilemma.<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
<br />
Doping in sport has been cited as an example of a prisoner's dilemma.<br />
<br />
体育运动中的兴奋剂被认为是囚徒困境的一个例子。<br />
<br />
<br />
<br />
Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<ref name="wired" /><br />
<br />
Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<br />
<br />
两名参赛运动员可以选择使用非法或危险药物来提高成绩。如果两个运动员都没有服用这种药物，那么他们都不会获得优势。如果只有一个人这样做，那么这个运动员就比他们的竞争对手获得了明显的优势，减少了服用药物的法律或医疗危险。然而，如果两名运动员都服用了这种药物，那么好处就被抵消了，只剩下危险，这使得他们的处境比没有服用兴奋剂的情况更加糟糕。<br />
<br />
<br />
<br />
===International politics===<br />
<br />
In [[international politics|international political theory]], the Prisoner's Dilemma is often used to demonstrate the coherence of [[strategic realism]], which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given [[anarchy (international relations)|international anarchy]]. A classic example is an arms race like the [[Cold War]] and similar conflicts.<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref> During the Cold War the opposing alliances of [[NATO]] and the [[Warsaw Pact]] both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
<br />
In international political theory, the Prisoner's Dilemma is often used to demonstrate the coherence of strategic realism, which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given international anarchy. A classic example is an arms race like the Cold War and similar conflicts. During the Cold War the opposing alliances of NATO and the Warsaw Pact both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
<br />
在国际政治理论中，囚徒困境经常被用来证明战略现实主义的一致性，这种战略现实主义认为，在国际关系中，由于国际无政府状态，所有国家(无论其国内政策或公开宣称的意识形态如何)都会为了自身的理性利益来行动。一个典型的例子是类似冷战和类似冲突的军备竞赛。在冷战期间，北约和华约组织的对立联盟都可以选择武装或解除武装。从双方的观点来看，解除武装而对手继续武装将导致军事劣势和可能的被歼灭。相反，如果武装的时候对手已经解除了武装，那么就会获得优势。如果双方都选择武装自己，那么任何一方都承担不起攻击对方的代价，但是双方都为发展和维持核武库付出了高昂的代价。如果双方都选择裁军，战争就可以避免，也不会有任何代价。<br />
<br />
<br />
<br />
Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a [[War of attrition (game)|war of attrition]] for the next thirty years until the Soviet Union could not withstand the economic cost.<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref> The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
<br />
Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a war of attrition for the next thirty years until the Soviet Union could not withstand the economic cost. The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
<br />
虽然最好的结果是双方解除武装，但是双方的理性选择是武装起来，事实也的确如此。在接下来的三十年里，双方都在军事研究和武器装备的消耗战上上投入了大量的资源，直到苏联无法承受经济损失。同样的逻辑也适用于任何类似的情况，无论是主权国家之间的经济竞争还是技术竞争。<br />
<br />
<br />
<br />
===Multiplayer dilemmas===<br />
<br />
Many real-life dilemmas involve multiple players.<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref> Although metaphorical, [[Garrett Hardin|Hardin's]] [[tragedy of the commons]] may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
<br />
Many real-life dilemmas involve multiple players. Although metaphorical, Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
<br />
许多现实生活中的困境牵涉到多个参与者。虽然是比喻性的，哈丁的公地悲剧可以被看作是囚徒困境的多人泛化的一个例子: 每个村民做出选择是为了个人利益还是为了克制。对于一致(甚至频繁)叛变的集体回报是非常低的回报(代表了对“公共资源”的破坏)。一个大多数人都能理解的共同困境就是在一个共享的房子里洗碗。通过不洗碗，个人可以节省时间，但如果这种行为被每个居民采纳，集体成本是任何人都没有干净的盘子。<br />
<br />
<br />
<br />
The commons are not always exploited: [[William Poundstone]], in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to [[Excludability|take a paper without paying]] (''defecting'') but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by [[Elinor Ostrom]], winner of the 2009 [[Nobel Memorial Prize in Economic Sciences]], hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
<br />
The commons are not always exploited: William Poundstone, in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to take a paper without paying (defecting) but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by Elinor Ostrom, winner of the 2009 Nobel Memorial Prize in Economic Sciences, hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<br />
<br />
公共资源并不总是被利用: 威廉·庞德斯通在一本关于囚徒困境的书(见下文参考文献)中描述了新西兰的一种情况，报纸盒子没有上锁。人们可以不付钱就拿报纸(叛变) ，但很少有人这样做，他们觉得如果他们不付钱，那么其他人也不会付钱，这会摧毁整个体系。2009年诺贝尔经济学奖获得者埃莉诺·奥斯特罗姆随后的研究认为公地悲剧经济学过于简单化，其负面结果受到外部影响。在没有复杂压力的情况下，团体之间为了共同利益进行沟通和管理，执行社会规范以保护资源并为团体实现最大利益，这是影响囚徒困境发展最佳结果的一个例子。<br />
<br />
<br />
<br />
==Related games==<br />
<br />
===Closed-bag exchange===<br />
<br />
[[File:Prisoner's Dilemma briefcase exchange (colorized).svg|thumb|The prisoner's dilemma as a briefcase exchange]]<br />
<br />
The prisoner's dilemma as a briefcase exchange<br />
<br />
囚徒困境是一个公文包的交换<br />
<br />
[[Douglas Hofstadter]]<ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref> once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
<br />
Douglas Hofstadter once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
<br />
侯世达曾经指出，人们通常会发现问题，比如囚徒困境问题，当它以一个简单博弈的形式表现出来时，或者以权衡的方式表现出来时，会更容易理解。他使用的几个例子之一是“封闭式袋子交换” :<br />
<br />
{{quote|Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty bag.}}<br />
<br />
Defection always gives a game-theoretically preferable outcome.<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
<br />
Defection always gives a game-theoretically preferable outcome.<br />
<br />
叛变总是会带来一个理论上更可取的结果。<br />
<br />
<br />
<br />
===''Friend or Foe?''===<br />
<br />
''[[Friend or Foe? (TV series)|Friend or Foe?]]'' is a game show that aired from 2002 to 2005 on the [[Game Show Network]] in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, ''Friend or Foe'' has a rewards model between prisoner's dilemma and the [[Chicken (game)|game of Chicken]].<br />
<br />
Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, Friend or Foe has a rewards model between prisoner's dilemma and the game of Chicken.<br />
<br />
朋友还是敌人？是一个竞赛节目，从2002年至2005年在美国的竞赛节目网络播出。这是囚徒困境博弈在真人身上测试的一个例子，但是是在人为的环境中。在游戏节目中，有三对选手参加比赛。当一对被淘汰时，他们会玩一个类似囚徒困境的游戏来决定奖金如何分配。如果他们都合作(朋友) ，他们分享奖金50-50。如果一方合作而另一方叛变(敌人) ，那么叛变者将得到所有的奖金，而合作者将一无所获。如果双方都叛变，那么双方都将一无所有。请注意，奖励矩阵与上面给出的标准矩阵略有不同，因为“双方都叛变”和“合作而对方叛变”情况下的奖励是相同的。与标准囚徒困境中的严格均衡相比，这使得“两个都叛变”情况成为一个弱均衡。如果一个参赛者知道他们的对手将投票给“敌人” ，那么他们自己的选择不会影响他们自己的奖金。从特定意义上讲，“朋友还是敌人”节目在囚徒困境和“胆小鬼”博弈之间有一个奖励模型。<br />
<br />
<br />
<br />
The rewards matrix is<br />
<br />
The rewards matrix is<br />
<br />
奖励矩阵是<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class“ wikitable”<br />
<br />
! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
<br />
! |}}<br />
<br />
!|}}<br />
<br />
! scope="col" style="width:6em;" | {{color|#900|"Friend"<br />(cooperate)}}<br />
<br />
! scope="col" style="width:6em;" | <br />
<br />
!范围“ col”风格“ width: 6em; ” | <br />
<br />
! scope="col" style="width:6em;" | {{color|#900|"Foe"<br />(defect)}}<br />
<br />
! scope="col" style="width:6em;" | <br />
<br />
!范围“ col”风格“ width: 6em; ” | <br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="row" style="width:6em;" | {{color|#009|"Friend"<br />(cooperate)}}<br />
<br />
! scope="row" style="width:6em;" | <br />
<br />
!范围“行”风格“宽度: 6em; ” | <br />
<br />
| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|"Foe"<br />(defect)}}<br />
<br />
! scope="row" | <br />
<br />
!瞄准镜<br />
<br />
| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
会透明的<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
This payoff matrix has also been used on the [[United Kingdom|British]] [[television]] programmes ''Trust Me'', ''[[Shafted]]'', ''[[The Bank Job (TV series)|The Bank Job]]'' and ''[[Golden Balls]]'', and on the [[United States|American]] shows ''[[Bachelor Pad]]'' and ''[[Take It All (game show)|Take It All]]''. Game data from the ''[[Golden Balls]]'' series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
<br />
This payoff matrix has also been used on the British television programmes Trust Me, Shafted, The Bank Job and Golden Balls, and on the American shows Bachelor Pad and Take It All. Game data from the Golden Balls series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<br />
<br />
英国电视节目《相信我》、《阴影》、《银行工作》和《黄金球》以及美国电视节目《单身公寓》和《全部拿走》也采用了这种奖励矩阵。一个经济学家团队分析了金球系列的游戏数据，他们发现，对于看似重要的金钱数量，现实生活中合作程度“惊人地高” ，但在游戏的背景下，合作程度相对较低。<br />
<br />
<br />
<br />
===Iterated snowdrift===<br />
<br />
{{main|snowdrift game}}<br />
<br />
<br />
<br />
Researchers from the [[University of Lausanne]] and the [[University of Edinburgh]] have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a [[chicken game]], it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a [[snowdrift]], each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
<br />
Researchers from the University of Lausanne and the University of Edinburgh have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a chicken game, it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a snowdrift, each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
<br />
来自洛桑大学和爱丁堡大学的研究人员认为，“迭代雪堆游戏”可能更能反映现实世界的社会状况。虽然这个模型实际上是一个胆小鬼博弈，它将在这里描述。在这个模型中，由于背叛而被剥削的风险较低，个体总是从合作选择中获益。这个雪堆游戏设想两个司机被困在雪堆的两侧，每个司机都可以选择铲雪清理道路，或者留在自己的车里。一个玩家的最高回报来自于让对手自己清除所有的积雪，但是对手名义上仍然因为他们自己的工作而得到回报。<br />
<br />
<br />
<br />
This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
<br />
This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<br />
<br />
这可能更好地反映了现实世界的情景---- 研究人员举了两位科学家合作完成一份报告的例子，如果另一位科学家更加努力地工作，这两位科学家都会受益。“但当你的合作者不做任何工作时，你自己做所有的工作可能会更好。你最终还是会完成一个项目。”<br />
<br />
<br />
<br />
{|<br />
<br />
{|<br />
<br />
{|<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
|<br />
<br />
|<br />
<br />
|<br />
<br />
{| class="wikitable" style="text-align: center;"<br />
<br />
{| class="wikitable" style="text-align: center;"<br />
<br />
{ | 类“ wikitable”样式“ text-align: center; ”<br />
<br />
|+ Example snowdrift payouts (A, B)<br />
<br />
|+ Example snowdrift payouts (A, B)<br />
<br />
| + 例子雪堆补偿(a，b)<br />
<br />
! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
<br />
! !! Cooperates !! Defects<br />
<br />
!!!合作！叛变<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Cooperates<br />
<br />
! Cooperates<br />
<br />
!合作<br />
<br />
| 200, 200 || 100, 300<br />
<br />
| 200, 200 || 100, 300<br />
<br />
| 200, 200 || 100, 300<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Defects<br />
<br />
! Defects<br />
<br />
!缺陷<br />
<br />
| 300, 100 || 0, 0<br />
<br />
| 300, 100 || 0, 0<br />
<br />
| 300, 100 || 0, 0<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
||<br />
<br />
||<br />
<br />
||<br />
<br />
{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
{ | class“ wikitable”样式“ text-align: center; margin-left: 2em; ”<br />
<br />
|+ Example PD payouts (A, B)<br />
<br />
|+ Example PD payouts (A, B)<br />
<br />
| + PD 支出示例(a，b)<br />
<br />
! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
<br />
! !! Cooperates !! Defects<br />
<br />
!!!合作！叛变<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Cooperates<br />
<br />
! Cooperates<br />
<br />
!合作<br />
<br />
| 200, 200 || -100, 300<br />
<br />
| 200, 200 || -100, 300<br />
<br />
| 200, 200 || -100, 300<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Defects<br />
<br />
! Defects<br />
<br />
!叛变<br />
<br />
| 300, -100 || 0, 0<br />
<br />
| 300, -100 || 0, 0<br />
<br />
| 300, -100 || 0, 0<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
===Coordination games===<br />
<br />
{{main|coordination games}}<br />
<br />
In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local [[left- and right-hand traffic]] convention helps to co-ordinate their actions.<br />
<br />
In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local left- and right-hand traffic convention helps to co-ordinate their actions.<br />
<br />
在协调博弈中，参与者必须协调他们的策略以获得一个好的结果。一个例子是两辆车在暴风雪中突然相遇，每辆车必须选择是左转还是右转。如果两辆车都向左转弯，或者都向右转弯，那么两辆车就不会相撞。当地的左右向交通惯例有助于协调他们的行动。<br />
<br />
<br />
<br />
Symmetrical co-ordination games include [[Stag hunt]] and [[Bach or Stravinsky]].<br />
<br />
Symmetrical co-ordination games include Stag hunt and Bach or Stravinsky.<br />
<br />
对称的协调游戏包括猎鹿和巴赫或斯特拉文斯基。<br />
<br />
<br />
<br />
===Asymmetric prisoner's dilemmas===<br />
<br />
A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an [[alibi]], whence the term "alibi game".<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
<br />
A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an alibi, whence the term "alibi game".<br />
<br />
一个更一般的博弈集是不对称的。就像在囚徒困境中一样，最好的结果是合作，而叛变是有动机的。不像对称的囚徒困境，一方比另一方有更多的损失或获得。有些这样的博弈被描述为囚徒困境，其中一个囚徒有不在场证明，这就是术语“不在场证明游戏”的由来。<br />
<br />
<br />
<br />
In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
<br />
In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<br />
<br />
在实验中，重复博弈中获得不平等收益的参与者可能会寻求利润最大化，但是只有在两个参与者获得相同收益的条件下，这可能导致一个稳定的均衡策略，即弱势参与者在每个 x 博弈中都会叛变，而另一个参与者总是合作。这种行为可能取决于实验围绕公平的社会规范。<br />
<br />
<br />
<br />
==Software==<br />
<br />
<br />
<br />
Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
<br />
Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
<br />
一些软件包已经被创建来运行囚徒困境模拟和比赛，其中一些有可用的源代码。<br />
<br />
* The source code for the [[The Evolution of Cooperation|second tournament]] run by Robert Axelrod (written by Axelrod and many contributors in [[Fortran]]) is available [http://www-personal.umich.edu/~axe/research/Software/CC/CC2.html online]<br />
<br />
* [https://web.archive.org/web/19991010053242/http://www.lifl.fr/IPD/ipd.frame.html Prison], a library written in [[Java (programming language)|Java]], last updated in 1998<br />
<br />
* [https://github.com/Axelrod-Python/Axelrod Axelrod-Python], written in [[Python (programming language)|Python]]<br />
<br />
* [http://selborne.nl/ipd/ play the Iterative Prisoner's Dilemma in the browser], play against strategies or let strategies play against other strategies<br />
<br />
<br />
<br />
==In fiction==<br />
<br />
[[Hannu Rajaniemi]] set the opening scene of his ''[[The Quantum Thief]]'' trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in [[mathematical physics]]&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, ''[[The Fractal Prince]]'' and ''[[The Causal Angel]]'', published in 2012 and 2014, respectively.<br />
<br />
Hannu Rajaniemi set the opening scene of his The Quantum Thief trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in mathematical physics&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively.<br />
<br />
汉努 · 拉贾尼埃米将他的《量子窃贼》三部曲的开场场景设置在一个“进退两难的监狱”中。该系列的主题被描述为“双重宇宙的不足” ，最终的对手是一个叫做全面叛变者的角色。拉贾尼埃米作为一个处理这个问题的艺术家尤其有趣，因为他是剑桥大学培养的数学家，拥有数学物理学博士学位——物质和信息的可互换性是这本书的一个主要特征，它发生在“后奇点”的未来。该系列的第一本书于2010年出版，其续集《分形王子》和《因果天使》分别于2012年和2014年出版。<br />
<br />
<br />
<br />
A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game ''[[Zero Escape: Virtue's Last Reward]]'' and a minor part in its 2016 sequel ''[[Zero Escape: Zero Time Dilemma]]''.<br />
<br />
A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time Dilemma.<br />
<br />
一个模仿迭代囚徒困境的游戏《零度逃脱: 美德的最后奖励》是2012年电子游戏的中心焦点，也是2016年续集《零度逃脱: 极限脱出刻之困境》的一个次要部分。<br />
<br />
<br />
<br />
In ''The Mysterious Benedict Society and the Prisoner's Dilemma'' by [[Trenton Lee Stewart]], the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
<br />
In The Mysterious Benedict Society and the Prisoner's Dilemma by Trenton Lee Stewart, the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
<br />
在特伦顿· 李 ·斯图尔特的《神秘的本尼迪克特社会和囚徒困境》中，主要角色从玩一个版本的游戏开始，然后一起逃离“监狱”。后来他们变成了真正的囚犯，再次越狱。<br />
<br />
<br />
<br />
In ''[[The Adventure Zone]]: Balance'' during ''The Suffering Game'' subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
<br />
In The Adventure Zone: Balance during The Suffering Game subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
<br />
在冒险区: 苦难游戏的平衡中，玩家角色在他们在两个领域的时间内两次被呈现囚徒困境，一次是合作，一次是叛变。<br />
<br />
<br />
<br />
In the 8th novel from the author James S. A. Corey [[Tiamat's Wrath]] . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. {{cn|date=April 2020}}<br />
<br />
In the 8th novel from the author James S. A. Corey Tiamat's Wrath . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. <br />
<br />
在作者詹姆斯·S·A·科里·提亚玛特的《愤怒》的第八部小说中。温斯顿•杜阿尔特向他14岁的女儿特蕾莎解释了面临的囚徒困境，以训练她的战略思维。<br />
<br />
<br />
<br />
==See also==<br />
请参阅<br />
{{div col|colwidth=18em}}<br />
<br />
* [[Abilene paradox]]<br />
* [[阿背伦悖论]]<br />
* [[Centipede game]]<br />
* [[蜈蚣博弈]]<br />
* [[Christmas truce]]<br />
* [[圣诞休战]]<br />
* [[Folk theorem (game theory)]]<br />
* [[无名氏定理（博弈论）]]<br />
* [[Free-rider problem]]<br />
* [[搭便车问题]]<br />
* [[Hobbesian trap]]<br />
* [[霍布斯主义陷阱]]<br />
* [[Innocent prisoner's dilemma]]<br />
* [[无辜囚徒困局]]<br />
* [[Liar Game]]<br />
* [[说谎者博弈]]<br />
* [[Optional prisoner's dilemma]]<br />
* [[可选择囚徒困境]]<br />
* [[Robert H. Frank#Prisoner's dilemma and cooperation|Prisoner's dilemma and cooperation]]<br />
* [[罗伯特·H·弗兰克囚徒的困境和合作]]<br />
* [[Public goods game]]<br />
* [[公共商品博弈]]<br />
* [[Gift-exchange game]]<br />
* [[互利博弈]]<br />
* [[Reciprocal altruism]]<br />
* [[相互利他行为]]<br />
* [[Social preferences]]<br />
* [[社会偏好]]<br />
* [[Swift trust theory]]<br />
* [[快速信任理论]]<br />
* [[Unscrupulous diner's dilemma]]<br />
* [[无道德食客困境]]<br />
{{div col end}}<br />
<br />
<br />
<br />
==References==<br />
==参考==<br />
{{notelist}}<br />
<br />
{{reflist|colwidth=30em}}<br />
<br />
<br />
<br />
==Further reading==<br />
==拓展阅读==<br />
{{refbegin|30em}}<br />
<br />
* [[S.M. Amadae|Amadae, S.]] (2016). 'Prisoner's Dilemma,' ''Prisoners of Reason.'' [[Cambridge University Press]], NY, pp.&nbsp;24–61.<br />
<br />
* {{cite book |first1=Robert |last1=Aumann |authorlink=Robert Aumann |chapter=Acceptable points in general cooperative ''n''-person games |editor1-first=R. D. |editor1-last=Luce |editor2-first=A. W. |editor2-last=Tucker |title=Contributions to the Theory 23 of Games IV |series=Annals of Mathematics Study |volume=40 |pages=287–324 |publisher=Princeton University Press |location=Princeton NJ |year=1959 |mr=0104521}}<br />
<br />
* [[Robert Axelrod|Axelrod, R.]] (1984). ''[[The Evolution of Cooperation]]''. {{isbn|0-465-02121-2}}<br />
<br />
* [[Cristina Bicchieri|Bicchieri, Cristina]] (1993). Rationality and Coordination. [[Cambridge University Press]].<br />
<br />
* {{cite journal |first1=David M. |last1=Chess |date=December 1988 |title=Simulating the evolution of behavior: the iterated prisoners' dilemma problem |url=http://www.complex-systems.com/pdf/02-6-4.pdf |journal=Complex Systems |volume=2 |issue=6 |pages=663–70}}<br />
<br />
* [[Melvin Dresher|Dresher, M.]] (1961). ''The Mathematics of Games of Strategy: Theory and Applications'' [[Prentice-Hall]], Englewood Cliffs, NJ.<br />
<br />
* Greif, A. (2006). ''Institutions and the Path to the Modern Economy: Lessons from Medieval Trade.'' Cambridge University Press, [[Cambridge]], UK.<br />
<br />
* [[Anatol Rapoport|Rapoport, Anatol]] and Albert M. Chammah (1965). ''Prisoner's Dilemma''. [[University of Michigan Press]].<br />
<br />
{{refend}}<br />
<br />
<br />
<br />
==External links==<br />
<br />
*{{Commonscat-inline}}<br />
<br />
* [http://plato.stanford.edu/entries/prisoner-dilemma/ Prisoner's Dilemma (''Stanford Encyclopedia of Philosophy'')]<br />
<br />
* [http://www.msri.org/ext/larryg/pages/15.htm The Bowerbird's Dilemma] The Prisoner's Dilemma in ornithology&nbsp;– mathematical cartoon by Larry Gonick.<br />
<br />
* [https://www.youtube.com/watch?v=_1SEXTVsxjk The Prisoner's Dilemma] The Prisoner's Dilemma with Lego minifigures.<br />
<br />
* {{cite encyclopedia |last1=Dixit |first1=Avinash |authorlink1=Avinash Dixit |last2= Nalebuff |first2=Barry |authorlink2=Barry Nalebuff |editor=[[David R. Henderson]]|encyclopedia=[[Concise Encyclopedia of Economics]] |title=Prisoner's Dilemma |url=http://www.econlib.org/library/Enc/PrisonersDilemma.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0865976658 |oclc=237794267}}<br />
<br />
* [http://gametheory101.com/The_Prisoner_s_Dilemma.html Game Theory 101: Prisoner's Dilemma]<br />
<br />
* [https://www.youtube.com/watch?v=I71mjZefg8g Dawkins: Nice Guys Finish First]<br />
<br />
* [https://axelrod.readthedocs.io/en/stable/ Axelrod] Iterated Prisoner's Dilemma [[Python (programming language)|Python]] library<br />
<br />
* [http://gametheorygames.nl/index.html Play the Iterated Prisoner's Dilemma on gametheorygames.nl]<br />
<br />
* [https://web.archive.org/web/20141011014608/http://demo.otree.org/demo/Prisoner%27s+Dilemma/ Play Prisoner's Dilemma on ''oTree''] (N/A 11-5-17)<br />
<br />
* Nicky Case's [https://web.archive.org/web/20181229222135/https://ncase.me/trust/ Evolution of Trust], an example of the donation game<br />
<br />
* [http://iterated-prisoners-dilemma.info Iterated Prisoner's Dilemma online game] by Wayne Davis<br />
<br />
{{Decision theory paradoxes}}<br />
<br />
{{Game theory}}<br />
<br />
<br />
<br />
{{Authority control}}<br />
<br />
<br />
<br />
[[Category:Non-cooperative games]]<br />
<br />
Category:Non-cooperative games<br />
<br />
类别: 非合作性游戏<br />
<br />
[[Category:Thought experiments]]<br />
<br />
Category:Thought experiments<br />
<br />
类别: 思维实验<br />
<br />
[[Category:Dilemmas]]<br />
<br />
Category:Dilemmas<br />
<br />
类别: 困境<br />
<br />
[[Category:Environmental studies]]<br />
<br />
Category:Environmental studies<br />
<br />
类别: 环境研究<br />
<br />
[[Category:Social psychology]]<br />
<br />
Category:Social psychology<br />
<br />
类别: 社会心理学<br />
<br />
[[Category:Moral psychology]]<br />
<br />
Category:Moral psychology<br />
<br />
范畴: 道德心理学<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Prisoner's dilemma]]. Its edit history can be viewed at [[囚徒困境/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=%E8%87%AA%E7%94%B1%E6%84%8F%E5%BF%97%E5%AE%9A%E7%90%86_Free_Will_Theorem&diff=14485自由意志定理 Free Will Theorem2020-09-27T04:00:44Z<p>趣木木：/* 公理背景——量子力学中的自由意志定理 */</p>
<hr />
<div>{{#seo:<br />
* |keywords=自由意志定理,the free will theorem,John Horton Conway,自由意志<br />
* |description=自由意志定理,the free will theorem,John Horton Conway,自由意志<br />
* }}<br />
[[File:freewill.jpeg|200px|缩略图|自由意志是不受阻碍地在不同可能的行动路线之间进行选择的能力|right]]<br />
'''自由意志定理 Free Will Theorem'''的形式描述为：在某些条件下，如果实验者可以自由决定在特定实验中测量什么量，那么基本粒子必须能够自由选择其自旋，以使测量结果与物理定律一致。该定理由[[约翰·何顿·康威 John Horton Conway]]和Simon B. Kochen提出，他们指出：如果我们拥有自由意志（即我们的选择与过去时间无关），那么在一定的假设前提下，一些基本粒子必须表现出类似的行为。 Conway和Kochen的论文发表在2006年的《物理学基础 Foundations of Physics》上。<ref>{{cite journal | last = Conway | first = John |author2=Simon Kochen | year = 2006 | title = The Free Will Theorem | journal = Foundations of Physics | volume = 36 | issue = 10 | pages = 1441 | doi = 10.1007/s10701-006-9068-6 |arxiv = quant-ph/0604079 |bibcode = 2006FoPh...36.1441C }}</ref> 2009年，Conway在AMS中发布了该定理的一个加强版本。<ref name=Later>{{cite journal |author1=Conway, John H. |author2=Simon Kochen |title=The strong free will theorem |journal= Notices of the AMS |volume=56 |issue=2 |year=2009 |pages=226–232 |url=http://www.ams.org/notices/200902/rtx090200226p.pdf?q=will&sa=U&ei=k71jU8X7DoypyASw9YGoCA&ved=0CCAQFjAB&usg=AFQjCNE7L-k87yWE32ru0rDjkLOdg12LRQ}}</ref>后来，在2017年，Kochen对其中一些细节进行更进一步的阐释论证。<ref name=":0">Kochen S., (2017), [https://arxiv.org/abs/1710.00868 ''Born's Rule, EPR, and the Free Will Theorem''] [[arxiv]]</ref><br />
<br />
==公理背景——量子力学中的自由意志定理==<br />
<br />
<br />
量子力学自建立后近一个世纪以来，已在科学技术的各个领域取得了巨大的成功。而与此同时，量子力学也是一个充满争议的理论。自爱因斯坦提出量子力学是不完备的理论以来，对其的补充或替代理论的追寻也从未停止。也许是习惯了经典力学的决定论性特点，20世纪初的物理学家们大多认为，像一辆小车、一个电子这样的“死物”，其行为应该是可以通过力学方程严格预测的,爱因斯坦一言蔽之：“上帝不掷骰子。”<br><br />
<br />
基于这种观点，量子论所描述的粒子的概率行为当然令人生疑。一个自然的想法是：由于缺乏足够的信息和理解，所以对粒子行为不能准确把握；而当我们拥有了足够的信息、更深的理论理解，就能准确预测粒子行为。这种想法催生了一类隐参量理论。贝尔 John Stewart Bell 在寻找玻姆式的隐参量理论时，发现该类理论一旦结合定域性条件，将对纠缠态粒子的可能关联程度建立一个严格的数学限制，即贝尔不等式，而该不等式在量子力学中却不一定成立。随着贝尔不等式被阿莱恩·阿斯派克特 Alain Aspect等人的实验证伪，定域性的隐参量理论被否定。<br><br />
<br />
贝尔本人也认为：“任何定域隐变量理论都不可能重现量子力学的全部统计性预言。”然而，决定论并没有就此被终结，寻找其他的决定性力学理论的努力至今仍在继续，其影响根深蒂固，让人怀疑量子论只是权宜之计。<br><br />
<br />
进入21世纪，普林斯顿大学的康韦 John Conway 和寇辰 Simon Kochen 教授提出了自由意志定理，再次给决定论以沉重打击。<br><br />
<br />
==公理内容==<br />
[[File:entanglement.jpeg|200px|缩略图|量子纠缠|right]]<br />
自由意志定理的出发点之一就是：我们人类是拥有自由意志的。并且康韦等认为这点上毋庸置疑，也没有争论的意义与必要。<br><br />
<br />
康韦 John Conway 和寇辰 Simon Kochen 教授提出了三个公理，他们称其为“ '''鳍式 FIN'''”，“'''自旋 SPIN'''”和“'''孪生 TWIN'''”。自旋和孪生公理可以通过纠缠实验验证，鳍式是相对论的一个结果。<br />
*鳍式：信息的传播有一个最大的速度（不一定是光速）。康威和Kochen说这是“有效因果关系 effective causality”的结果。<br />
*自旋：在三个正交方向上获得的自旋一的某些基本粒子的平方自旋分量，将是（1,1,0）的排列。<br />
*孪生：这是可以“缠结”的两个基本粒子，并将它们隔开很大的距离，如果在平行方向上进行测量，它们具有相同的平方自旋结果。假设有两个实验者，如果第一个实验者a（在地球上）对这个框架（x，y，z）进行三重实验，得到结果：<math>x \rightarrow j, y \rightarrow k , z \rightarrow l</math>这是'''量子纠缠'''的结果。而第二个实验者b（在火星上，至少5光分以外）测量方向w的单一自旋，那么如果w是x，y，z中的一个，结果分别是<math>w \rightarrow j, k 或 l</math>。所以“孪生”公理指明离子间的纠缠关系，但是对于“孪生”公理来说，完全纠缠不是必需的（纠缠是充分不必要条件）。<br />
<br />
在他们2009年的论文“强自由意志定理”<ref name = Later />中，Conway和Kochen用一个更弱的定理“Min”代替了鳍公理。 Min断言：两个以类似空间的方式分离的实验者可以独立地做出测量结果的选择。 特别地，假定中所有信息的传输速度没有受到最大限制，而仅受有关测量选择的特定信息的限制。在2017年，Kochen辩称Min可以由Lin代替实验可验证（Lorentz covariance）。<ref name =":0"/><br />
<br />
== 定理概要==<br />
自由意志定理指出：<br />
<br />
'''{{quotation|根据公理，如果所讨论的两个实验者可以自由选择要进行的测量，那么测量结果就不能由实验之前的任何事情来确定。}}'''<br />
这是“结果开放 outcome open”定理：<br />
<br />
'''{{quotation |如果实验的结果是公开的，那么一个或两个实验者可能会自由地选择所要采取的行动。}}'''<br />
<br />
由于该定理适用于与公理一致的任何物理理论，因此它不能以特殊的方式将信息放入宇宙的过去进行研究。该论点源自'''Kochen–Specker定理'''，该结果表明，对自旋的任何单独测量的结果都不是独立于测量选择而固定的。正如Cator和Landsman关于'''隐藏变量理论 hidden-variable theories'''所述<ref name=Cator>{{cite journal |author1=Cator, Eric |author2=Klaas Landsman |title=Constraints on determinism: Bell versus Conway–Kochen |journal=Foundations of Physics |volume=44 |issue=7 |year=2014 |pages=781–791 |doi=10.1007/s10701-014-9815-z|arxiv = 1402.1972 |bibcode = 2014FoPh...44..781C }}</ref>：“隐藏变量（在相关的因果关系上）一方面应包括与实验有关的所有本体信息，但另一方面应该让实验对象自由选择他们倾向的任何设置。”<br />
<br />
==讨论==<br />
根据Cator和Landsman <ref name = Cator />的说法，Conway和Kochen证明“确定性与许多'先验'理想假设不相容”。 Cator和Landsman将'''Min'''假设与'''Bell定理'''中的局部性假设进行了比较，并得出加强版自由意志定理的结论，因为它使用的假设比Bell 1964年的定理更少（因为它没有用到概率论的相关内容）。哲学家戴维·霍奇森 David Hodgson 支持该定理，因为该结论非常明确地表明“科学不支持决定论”：比如量子力学证明粒子的确以与过去不同的方式运动。<ref>{{cite book |author=David Hodgson |title=Rationality + Consciousness = Free Will |chapter=Chapter 7: Science and determinism |isbn=9780199845309 |year=2012 |publisher=Oxford University Press |chapter-url=https://books.google.com/books?id=4SGsmowYARsC&pg=PA121&dq=%22Conway+and+Kochen+call+the+free+will+theorem%22&hl=en&sa=X&ei=UiMYVeTBII3woATFkoKAAQ&ved=0CB4Q6AEwAA#v=onepage&q=%22Conway%20and%20Kochen%20call%20the%20free%20will%20theorem%22&f=false}}</ref>但有一些言论认为这个定理只适应于确定的模型。 <ref>Sheldon Goldstein, Daniel V. Tausk, Roderich Tumulka, and Nino Zanghì (2010). [http://www.ams.org/notices/201011/rtx101101451p.pdf What Does the Free Will Theorem Actually Prove?] ''Notices of the AMS'', December, 1451–1453.</ref><br />
<br />
==文献引用==<br />
<references /><br />
<br />
==其他参考文献==<br />
* Conway and Kochen, [http://www.ams.org/notices/200902/rtx090200226p.pdf The Strong Free Will Theorem], published in Notices of the AMS. Volume 56, Number 2, February 2009.<br />
<br />
[https://kns.cnki.net/KNS8/Detail?sfield=fn&QueryID=0&CurRec=3&recid=&FileName=ZXFX201605009&DbName=CJFDLAST2016&DbCode=CJFD&yx=&pr=&URLID= 量子力学中的自由意志定理]<br />
*{{Cite journal<br />
| last =Rehmeyer<br />
| first =Julie<br />
| title = Do Subatomic Particles Have Free Will?<br />
| journal = Science News<br />
| volume = <br />
| issue = <br />
| pages = <br />
| date = August 15, 2008<br />
| url = http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_subatomic_particles_have_free_will%3F<br />
| doi =<br />
| postscript =<!--None--> }}<br />
*[https://mediacentral.princeton.edu/tag/tagid/free%20will Introduction to the Free Will Theorem], videos of six lectures given by J. H. Conway, Mar. 2009.<br />
* {{cite encyclopedia<br />
|last= Wüthrich<br />
|first= Christian<br />
|editor1-first= Claus<br />
|editor1-last= Beisbart<br />
|editor2-first= Stephan<br />
|editor2-last= Hartmann<br />
|encyclopedia= Probabilities in Physics<br />
|title= Can the world be shown to be indeterministic after all?<br />
|trans-title=<br />
|date= September 2011<br />
|publisher= Oxford University Press<br />
|isbn= 978-0199577439<br />
|doi= 10.1093/acprof:oso/9780199577439.003.0014<br />
|pages= 365–389<br />
|chapter-url= http://philsci-archive.pitt.edu/8437/<br />
|chapter= Can the World Beshown to be Indeterministic after all?<br />
|url= http://philsci-archive.pitt.edu/8437/1/WuthrichChristian2010PhilSci_IndeterministicWorld.pdf<br />
}}<br />
==相关链接==<br />
*[http://www.informationphilosopher.com/freedom/free_will_theorem.html The Free Will Theorem of Conway and Kochen]<br />
<br />
<br><br />
<br />
==编者推荐==<br />
[[File:Uncertainty.jpg|140px|缩略图|复杂系统]]<br />
*[https://pattern.swarma.org/path?id=32 长文综述：复杂系统科学及其应用]<br />
自由意志定理证明复杂系统是具有不可预测性和不确定性的。<br />
<br />
如何理解复杂系统？如何分析复杂系统？如何设计复杂系统？这是研究和学习复杂性科学会遇到的问题。<br />
<br />
本文对研究复杂系统与不确定性（COMPLEX SYSTEMS AND UNCERTAINTY）的研究做了一个长文综述。<br />
----<br />
本中文词条由[[用户:费米子|费米子]]编辑，欢迎在讨论页面留言。<br />
<br />
'''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''<br />
[[Category:Physics theorems]]<br />
[[Category:Free will]]<br />
[[Category:自由意志定理]]</div>趣木木https://wiki.swarma.org/index.php?title=%E8%87%AA%E7%94%B1%E6%84%8F%E5%BF%97%E5%AE%9A%E7%90%86_Free_Will_Theorem&diff=14484自由意志定理 Free Will Theorem2020-09-27T04:00:04Z<p>趣木木：/* 公理背景——量子力学中的自由意志定理 */</p>
<hr />
<div>{{#seo:<br />
* |keywords=自由意志定理,the free will theorem,John Horton Conway,自由意志<br />
* |description=自由意志定理,the free will theorem,John Horton Conway,自由意志<br />
* }}<br />
[[File:freewill.jpeg|200px|缩略图|自由意志是不受阻碍地在不同可能的行动路线之间进行选择的能力|right]]<br />
'''自由意志定理 Free Will Theorem'''的形式描述为：在某些条件下，如果实验者可以自由决定在特定实验中测量什么量，那么基本粒子必须能够自由选择其自旋，以使测量结果与物理定律一致。该定理由[[约翰·何顿·康威 John Horton Conway]]和Simon B. Kochen提出，他们指出：如果我们拥有自由意志（即我们的选择与过去时间无关），那么在一定的假设前提下，一些基本粒子必须表现出类似的行为。 Conway和Kochen的论文发表在2006年的《物理学基础 Foundations of Physics》上。<ref>{{cite journal | last = Conway | first = John |author2=Simon Kochen | year = 2006 | title = The Free Will Theorem | journal = Foundations of Physics | volume = 36 | issue = 10 | pages = 1441 | doi = 10.1007/s10701-006-9068-6 |arxiv = quant-ph/0604079 |bibcode = 2006FoPh...36.1441C }}</ref> 2009年，Conway在AMS中发布了该定理的一个加强版本。<ref name=Later>{{cite journal |author1=Conway, John H. |author2=Simon Kochen |title=The strong free will theorem |journal= Notices of the AMS |volume=56 |issue=2 |year=2009 |pages=226–232 |url=http://www.ams.org/notices/200902/rtx090200226p.pdf?q=will&sa=U&ei=k71jU8X7DoypyASw9YGoCA&ved=0CCAQFjAB&usg=AFQjCNE7L-k87yWE32ru0rDjkLOdg12LRQ}}</ref>后来，在2017年，Kochen对其中一些细节进行更进一步的阐释论证。<ref name=":0">Kochen S., (2017), [https://arxiv.org/abs/1710.00868 ''Born's Rule, EPR, and the Free Will Theorem''] [[arxiv]]</ref><br />
<br />
==公理背景——量子力学中的自由意志定理==<br />
<br />
<br />
量子力学自建立后近一个世纪以来，已在科学技术的各个领域取得了巨大的成功。而与此同时，量子力学也是一个充满争议的理论。自爱因斯坦提出量子力学是不完备的理论以来，对其的补充或替代理论的追寻也从未停止。也许是习惯了经典力学的决定论性特点，20世纪初的物理学家们大多认为，像一辆小车、一个电子这样的“死物”，其行为应该 是可以通过力学方程严格预测的,爱因斯坦一言蔽之：“上帝不掷骰子。”<br><br />
<br />
基于这种观点，量子论所描述的粒子的概率行为当然令人生疑。一个自然的想法是：由于缺乏足够的信息和理解，所以对粒子行为不能准确把握；而当我们拥有了足够的信息、更深的理论理解，就能准确预测粒子行为。这种想法催生了一类隐参量理论。贝尔 John Stewart Bell 在寻找玻姆式的隐参量理论时，发现该类理论一旦结合定域性条件，将对纠缠态粒子的可能关联程度建立一个严格的数学限制，即贝尔不等式，而该不等式在量子力学中却不一定成立。随着贝尔不等式被阿莱恩·阿斯派克特 Alain Aspect等人的实验证伪，定域性的隐参量理论被否定。<br><br />
<br />
贝尔本人也认为：“任何定域隐变量理论都不可能重现量子力学的全部统计性预言。”然而，决定论并没有就此被终结，寻找其他的决定性力学理论的努力至今仍在继续，其影响根深蒂固，让人怀疑量子论只是权宜之计。<br><br />
<br />
进入21世纪，普林斯顿大学的康韦 John Conway 和寇辰 Simon Kochen 教授提出了自由意志定理，再次给决定论以沉重打击。<br><br />
<br />
==公理内容==<br />
[[File:entanglement.jpeg|200px|缩略图|量子纠缠|right]]<br />
自由意志定理的出发点之一就是：我们人类是拥有自由意志的。并且康韦等认为这点上毋庸置疑，也没有争论的意义与必要。<br><br />
<br />
康韦 John Conway 和寇辰 Simon Kochen 教授提出了三个公理，他们称其为“ '''鳍式 FIN'''”，“'''自旋 SPIN'''”和“'''孪生 TWIN'''”。自旋和孪生公理可以通过纠缠实验验证，鳍式是相对论的一个结果。<br />
*鳍式：信息的传播有一个最大的速度（不一定是光速）。康威和Kochen说这是“有效因果关系 effective causality”的结果。<br />
*自旋：在三个正交方向上获得的自旋一的某些基本粒子的平方自旋分量，将是（1,1,0）的排列。<br />
*孪生：这是可以“缠结”的两个基本粒子，并将它们隔开很大的距离，如果在平行方向上进行测量，它们具有相同的平方自旋结果。假设有两个实验者，如果第一个实验者a（在地球上）对这个框架（x，y，z）进行三重实验，得到结果：<math>x \rightarrow j, y \rightarrow k , z \rightarrow l</math>这是'''量子纠缠'''的结果。而第二个实验者b（在火星上，至少5光分以外）测量方向w的单一自旋，那么如果w是x，y，z中的一个，结果分别是<math>w \rightarrow j, k 或 l</math>。所以“孪生”公理指明离子间的纠缠关系，但是对于“孪生”公理来说，完全纠缠不是必需的（纠缠是充分不必要条件）。<br />
<br />
在他们2009年的论文“强自由意志定理”<ref name = Later />中，Conway和Kochen用一个更弱的定理“Min”代替了鳍公理。 Min断言：两个以类似空间的方式分离的实验者可以独立地做出测量结果的选择。 特别地，假定中所有信息的传输速度没有受到最大限制，而仅受有关测量选择的特定信息的限制。在2017年，Kochen辩称Min可以由Lin代替实验可验证（Lorentz covariance）。<ref name =":0"/><br />
<br />
== 定理概要==<br />
自由意志定理指出：<br />
<br />
'''{{quotation|根据公理，如果所讨论的两个实验者可以自由选择要进行的测量，那么测量结果就不能由实验之前的任何事情来确定。}}'''<br />
这是“结果开放 outcome open”定理：<br />
<br />
'''{{quotation |如果实验的结果是公开的，那么一个或两个实验者可能会自由地选择所要采取的行动。}}'''<br />
<br />
由于该定理适用于与公理一致的任何物理理论，因此它不能以特殊的方式将信息放入宇宙的过去进行研究。该论点源自'''Kochen–Specker定理'''，该结果表明，对自旋的任何单独测量的结果都不是独立于测量选择而固定的。正如Cator和Landsman关于'''隐藏变量理论 hidden-variable theories'''所述<ref name=Cator>{{cite journal |author1=Cator, Eric |author2=Klaas Landsman |title=Constraints on determinism: Bell versus Conway–Kochen |journal=Foundations of Physics |volume=44 |issue=7 |year=2014 |pages=781–791 |doi=10.1007/s10701-014-9815-z|arxiv = 1402.1972 |bibcode = 2014FoPh...44..781C }}</ref>：“隐藏变量（在相关的因果关系上）一方面应包括与实验有关的所有本体信息，但另一方面应该让实验对象自由选择他们倾向的任何设置。”<br />
<br />
==讨论==<br />
根据Cator和Landsman <ref name = Cator />的说法，Conway和Kochen证明“确定性与许多'先验'理想假设不相容”。 Cator和Landsman将'''Min'''假设与'''Bell定理'''中的局部性假设进行了比较，并得出加强版自由意志定理的结论，因为它使用的假设比Bell 1964年的定理更少（因为它没有用到概率论的相关内容）。哲学家戴维·霍奇森 David Hodgson 支持该定理，因为该结论非常明确地表明“科学不支持决定论”：比如量子力学证明粒子的确以与过去不同的方式运动。<ref>{{cite book |author=David Hodgson |title=Rationality + Consciousness = Free Will |chapter=Chapter 7: Science and determinism |isbn=9780199845309 |year=2012 |publisher=Oxford University Press |chapter-url=https://books.google.com/books?id=4SGsmowYARsC&pg=PA121&dq=%22Conway+and+Kochen+call+the+free+will+theorem%22&hl=en&sa=X&ei=UiMYVeTBII3woATFkoKAAQ&ved=0CB4Q6AEwAA#v=onepage&q=%22Conway%20and%20Kochen%20call%20the%20free%20will%20theorem%22&f=false}}</ref>但有一些言论认为这个定理只适应于确定的模型。 <ref>Sheldon Goldstein, Daniel V. Tausk, Roderich Tumulka, and Nino Zanghì (2010). [http://www.ams.org/notices/201011/rtx101101451p.pdf What Does the Free Will Theorem Actually Prove?] ''Notices of the AMS'', December, 1451–1453.</ref><br />
<br />
==文献引用==<br />
<references /><br />
<br />
==其他参考文献==<br />
* Conway and Kochen, [http://www.ams.org/notices/200902/rtx090200226p.pdf The Strong Free Will Theorem], published in Notices of the AMS. Volume 56, Number 2, February 2009.<br />
<br />
[https://kns.cnki.net/KNS8/Detail?sfield=fn&QueryID=0&CurRec=3&recid=&FileName=ZXFX201605009&DbName=CJFDLAST2016&DbCode=CJFD&yx=&pr=&URLID= 量子力学中的自由意志定理]<br />
*{{Cite journal<br />
| last =Rehmeyer<br />
| first =Julie<br />
| title = Do Subatomic Particles Have Free Will?<br />
| journal = Science News<br />
| volume = <br />
| issue = <br />
| pages = <br />
| date = August 15, 2008<br />
| url = http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_subatomic_particles_have_free_will%3F<br />
| doi =<br />
| postscript =<!--None--> }}<br />
*[https://mediacentral.princeton.edu/tag/tagid/free%20will Introduction to the Free Will Theorem], videos of six lectures given by J. H. Conway, Mar. 2009.<br />
* {{cite encyclopedia<br />
|last= Wüthrich<br />
|first= Christian<br />
|editor1-first= Claus<br />
|editor1-last= Beisbart<br />
|editor2-first= Stephan<br />
|editor2-last= Hartmann<br />
|encyclopedia= Probabilities in Physics<br />
|title= Can the world be shown to be indeterministic after all?<br />
|trans-title=<br />
|date= September 2011<br />
|publisher= Oxford University Press<br />
|isbn= 978-0199577439<br />
|doi= 10.1093/acprof:oso/9780199577439.003.0014<br />
|pages= 365–389<br />
|chapter-url= http://philsci-archive.pitt.edu/8437/<br />
|chapter= Can the World Beshown to be Indeterministic after all?<br />
|url= http://philsci-archive.pitt.edu/8437/1/WuthrichChristian2010PhilSci_IndeterministicWorld.pdf<br />
}}<br />
==相关链接==<br />
*[http://www.informationphilosopher.com/freedom/free_will_theorem.html The Free Will Theorem of Conway and Kochen]<br />
<br />
<br><br />
<br />
==编者推荐==<br />
[[File:Uncertainty.jpg|140px|缩略图|复杂系统]]<br />
*[https://pattern.swarma.org/path?id=32 长文综述：复杂系统科学及其应用]<br />
自由意志定理证明复杂系统是具有不可预测性和不确定性的。<br />
<br />
如何理解复杂系统？如何分析复杂系统？如何设计复杂系统？这是研究和学习复杂性科学会遇到的问题。<br />
<br />
本文对研究复杂系统与不确定性（COMPLEX SYSTEMS AND UNCERTAINTY）的研究做了一个长文综述。<br />
----<br />
本中文词条由[[用户:费米子|费米子]]编辑，欢迎在讨论页面留言。<br />
<br />
'''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''<br />
[[Category:Physics theorems]]<br />
[[Category:Free will]]<br />
[[Category:自由意志定理]]</div>趣木木https://wiki.swarma.org/index.php?title=%E8%87%AA%E7%94%B1%E6%84%8F%E5%BF%97%E5%AE%9A%E7%90%86_Free_Will_Theorem&diff=14482自由意志定理 Free Will Theorem2020-09-27T03:59:38Z<p>趣木木：</p>
<hr />
<div>{{#seo:<br />
* |keywords=自由意志定理,the free will theorem,John Horton Conway,自由意志<br />
* |description=自由意志定理,the free will theorem,John Horton Conway,自由意志<br />
* }}<br />
[[File:freewill.jpeg|200px|缩略图|自由意志是不受阻碍地在不同可能的行动路线之间进行选择的能力|right]]<br />
'''自由意志定理 Free Will Theorem'''的形式描述为：在某些条件下，如果实验者可以自由决定在特定实验中测量什么量，那么基本粒子必须能够自由选择其自旋，以使测量结果与物理定律一致。该定理由[[约翰·何顿·康威 John Horton Conway]]和Simon B. Kochen提出，他们指出：如果我们拥有自由意志（即我们的选择与过去时间无关），那么在一定的假设前提下，一些基本粒子必须表现出类似的行为。 Conway和Kochen的论文发表在2006年的《物理学基础 Foundations of Physics》上。<ref>{{cite journal | last = Conway | first = John |author2=Simon Kochen | year = 2006 | title = The Free Will Theorem | journal = Foundations of Physics | volume = 36 | issue = 10 | pages = 1441 | doi = 10.1007/s10701-006-9068-6 |arxiv = quant-ph/0604079 |bibcode = 2006FoPh...36.1441C }}</ref> 2009年，Conway在AMS中发布了该定理的一个加强版本。<ref name=Later>{{cite journal |author1=Conway, John H. |author2=Simon Kochen |title=The strong free will theorem |journal= Notices of the AMS |volume=56 |issue=2 |year=2009 |pages=226–232 |url=http://www.ams.org/notices/200902/rtx090200226p.pdf?q=will&sa=U&ei=k71jU8X7DoypyASw9YGoCA&ved=0CCAQFjAB&usg=AFQjCNE7L-k87yWE32ru0rDjkLOdg12LRQ}}</ref>后来，在2017年，Kochen对其中一些细节进行更进一步的阐释论证。<ref name=":0">Kochen S., (2017), [https://arxiv.org/abs/1710.00868 ''Born's Rule, EPR, and the Free Will Theorem''] [[arxiv]]</ref><br />
<br />
==公理背景——量子力学中的自由意志定理==<br />
量子力学自建立后近一个世纪以来，已在科学技术的各个领域取得了巨大的成功。而与此同时，量子力学也是一个充满争议的理论。自爱因斯坦提出量子力学是不完备的理论以来，对其的补充或替代理论的追寻也从未停止。也许是习惯了经典力学的决定论性特点，20世纪初的物理学家们大多认为，像一辆小车、一个电子这样的“死物”，其行为应该 是可以通过力学方程严格预测的,爱因斯坦一言蔽之：“上帝不掷骰子。”<br><br />
基于这种观点，量子论所描述的粒子的概率行为当然令人生疑。一个自然的想法是：由于缺乏足够的信息和理解，所以对粒子行为不能准确把握；而当我们拥有了足够的信息、更深的理论理解，就能准确预测粒子行为。这种想法催生了一类隐参量理论。贝尔 John Stewart Bell 在寻找玻姆式的隐参量理论时，发现该类理论一旦结合定域性条件，将对纠缠态粒子的可能关联程度建立一个严格的数学限制，即贝尔不等式，而该不等式在量子力学中却不一定成立。随着贝尔不等式被阿莱恩·阿斯派克特 Alain Aspect等人的实验证伪，定域性的隐参量理论被否定。<br><br />
贝尔本人也认为：“任何定域隐变量理论都不可能重现量子力学的全部统计性预言。”然而，决定论并没有就此被终结，寻找其他的决定性力学理论的努力至今仍在继续，其影响根深蒂固，让人怀疑量子论只是权宜之计。<br><br />
<br />
进入21世纪，普林斯顿大学的康韦 John Conway 和寇辰 Simon Kochen 教授提出了自由意志定理，再次给决定论以沉重打击。<br><br />
<br />
<br />
==公理内容==<br />
[[File:entanglement.jpeg|200px|缩略图|量子纠缠|right]]<br />
自由意志定理的出发点之一就是：我们人类是拥有自由意志的。并且康韦等认为这点上毋庸置疑，也没有争论的意义与必要。<br><br />
<br />
康韦 John Conway 和寇辰 Simon Kochen 教授提出了三个公理，他们称其为“ '''鳍式 FIN'''”，“'''自旋 SPIN'''”和“'''孪生 TWIN'''”。自旋和孪生公理可以通过纠缠实验验证，鳍式是相对论的一个结果。<br />
*鳍式：信息的传播有一个最大的速度（不一定是光速）。康威和Kochen说这是“有效因果关系 effective causality”的结果。<br />
*自旋：在三个正交方向上获得的自旋一的某些基本粒子的平方自旋分量，将是（1,1,0）的排列。<br />
*孪生：这是可以“缠结”的两个基本粒子，并将它们隔开很大的距离，如果在平行方向上进行测量，它们具有相同的平方自旋结果。假设有两个实验者，如果第一个实验者a（在地球上）对这个框架（x，y，z）进行三重实验，得到结果：<math>x \rightarrow j, y \rightarrow k , z \rightarrow l</math>这是'''量子纠缠'''的结果。而第二个实验者b（在火星上，至少5光分以外）测量方向w的单一自旋，那么如果w是x，y，z中的一个，结果分别是<math>w \rightarrow j, k 或 l</math>。所以“孪生”公理指明离子间的纠缠关系，但是对于“孪生”公理来说，完全纠缠不是必需的（纠缠是充分不必要条件）。<br />
<br />
在他们2009年的论文“强自由意志定理”<ref name = Later />中，Conway和Kochen用一个更弱的定理“Min”代替了鳍公理。 Min断言：两个以类似空间的方式分离的实验者可以独立地做出测量结果的选择。 特别地，假定中所有信息的传输速度没有受到最大限制，而仅受有关测量选择的特定信息的限制。在2017年，Kochen辩称Min可以由Lin代替实验可验证（Lorentz covariance）。<ref name =":0"/><br />
<br />
== 定理概要==<br />
自由意志定理指出：<br />
<br />
'''{{quotation|根据公理，如果所讨论的两个实验者可以自由选择要进行的测量，那么测量结果就不能由实验之前的任何事情来确定。}}'''<br />
这是“结果开放 outcome open”定理：<br />
<br />
'''{{quotation |如果实验的结果是公开的，那么一个或两个实验者可能会自由地选择所要采取的行动。}}'''<br />
<br />
由于该定理适用于与公理一致的任何物理理论，因此它不能以特殊的方式将信息放入宇宙的过去进行研究。该论点源自'''Kochen–Specker定理'''，该结果表明，对自旋的任何单独测量的结果都不是独立于测量选择而固定的。正如Cator和Landsman关于'''隐藏变量理论 hidden-variable theories'''所述<ref name=Cator>{{cite journal |author1=Cator, Eric |author2=Klaas Landsman |title=Constraints on determinism: Bell versus Conway–Kochen |journal=Foundations of Physics |volume=44 |issue=7 |year=2014 |pages=781–791 |doi=10.1007/s10701-014-9815-z|arxiv = 1402.1972 |bibcode = 2014FoPh...44..781C }}</ref>：“隐藏变量（在相关的因果关系上）一方面应包括与实验有关的所有本体信息，但另一方面应该让实验对象自由选择他们倾向的任何设置。”<br />
<br />
==讨论==<br />
根据Cator和Landsman <ref name = Cator />的说法，Conway和Kochen证明“确定性与许多'先验'理想假设不相容”。 Cator和Landsman将'''Min'''假设与'''Bell定理'''中的局部性假设进行了比较，并得出加强版自由意志定理的结论，因为它使用的假设比Bell 1964年的定理更少（因为它没有用到概率论的相关内容）。哲学家戴维·霍奇森 David Hodgson 支持该定理，因为该结论非常明确地表明“科学不支持决定论”：比如量子力学证明粒子的确以与过去不同的方式运动。<ref>{{cite book |author=David Hodgson |title=Rationality + Consciousness = Free Will |chapter=Chapter 7: Science and determinism |isbn=9780199845309 |year=2012 |publisher=Oxford University Press |chapter-url=https://books.google.com/books?id=4SGsmowYARsC&pg=PA121&dq=%22Conway+and+Kochen+call+the+free+will+theorem%22&hl=en&sa=X&ei=UiMYVeTBII3woATFkoKAAQ&ved=0CB4Q6AEwAA#v=onepage&q=%22Conway%20and%20Kochen%20call%20the%20free%20will%20theorem%22&f=false}}</ref>但有一些言论认为这个定理只适应于确定的模型。 <ref>Sheldon Goldstein, Daniel V. Tausk, Roderich Tumulka, and Nino Zanghì (2010). [http://www.ams.org/notices/201011/rtx101101451p.pdf What Does the Free Will Theorem Actually Prove?] ''Notices of the AMS'', December, 1451–1453.</ref><br />
<br />
==文献引用==<br />
<references /><br />
<br />
==其他参考文献==<br />
* Conway and Kochen, [http://www.ams.org/notices/200902/rtx090200226p.pdf The Strong Free Will Theorem], published in Notices of the AMS. Volume 56, Number 2, February 2009.<br />
<br />
[https://kns.cnki.net/KNS8/Detail?sfield=fn&QueryID=0&CurRec=3&recid=&FileName=ZXFX201605009&DbName=CJFDLAST2016&DbCode=CJFD&yx=&pr=&URLID= 量子力学中的自由意志定理]<br />
*{{Cite journal<br />
| last =Rehmeyer<br />
| first =Julie<br />
| title = Do Subatomic Particles Have Free Will?<br />
| journal = Science News<br />
| volume = <br />
| issue = <br />
| pages = <br />
| date = August 15, 2008<br />
| url = http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_subatomic_particles_have_free_will%3F<br />
| doi =<br />
| postscript =<!--None--> }}<br />
*[https://mediacentral.princeton.edu/tag/tagid/free%20will Introduction to the Free Will Theorem], videos of six lectures given by J. H. Conway, Mar. 2009.<br />
* {{cite encyclopedia<br />
|last= Wüthrich<br />
|first= Christian<br />
|editor1-first= Claus<br />
|editor1-last= Beisbart<br />
|editor2-first= Stephan<br />
|editor2-last= Hartmann<br />
|encyclopedia= Probabilities in Physics<br />
|title= Can the world be shown to be indeterministic after all?<br />
|trans-title=<br />
|date= September 2011<br />
|publisher= Oxford University Press<br />
|isbn= 978-0199577439<br />
|doi= 10.1093/acprof:oso/9780199577439.003.0014<br />
|pages= 365–389<br />
|chapter-url= http://philsci-archive.pitt.edu/8437/<br />
|chapter= Can the World Beshown to be Indeterministic after all?<br />
|url= http://philsci-archive.pitt.edu/8437/1/WuthrichChristian2010PhilSci_IndeterministicWorld.pdf<br />
}}<br />
==相关链接==<br />
*[http://www.informationphilosopher.com/freedom/free_will_theorem.html The Free Will Theorem of Conway and Kochen]<br />
<br />
<br><br />
<br />
==编者推荐==<br />
[[File:Uncertainty.jpg|140px|缩略图|复杂系统]]<br />
*[https://pattern.swarma.org/path?id=32 长文综述：复杂系统科学及其应用]<br />
自由意志定理证明复杂系统是具有不可预测性和不确定性的。<br />
<br />
如何理解复杂系统？如何分析复杂系统？如何设计复杂系统？这是研究和学习复杂性科学会遇到的问题。<br />
<br />
本文对研究复杂系统与不确定性（COMPLEX SYSTEMS AND UNCERTAINTY）的研究做了一个长文综述。<br />
----<br />
本中文词条由[[用户:费米子|费米子]]编辑，欢迎在讨论页面留言。<br />
<br />
'''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''<br />
[[Category:Physics theorems]]<br />
[[Category:Free will]]<br />
[[Category:自由意志定理]]</div>趣木木https://wiki.swarma.org/index.php?title=80/20%E5%8E%9F%E5%88%99&diff=1439880/20原则2020-09-26T07:35:16Z<p>趣木木：</p>
<hr />
<div>本词条由11初步翻译<br />
<br />
{{for|the optimal allocation of resources|Pareto efficiency}}<br />
{{为了资源的优化配置|帕累托效率}}<br />
<br />
{{short description|Statistical principle about ratio of effects to causes}}<br />
{{简述|关于效果与原因之比的统计原则}}<br />
<br />
[[File:Pareto principle applied to community fundraising.jpg|thumb|right|Pareto principle applied to community fundraising]]<br />
[[文件:应用于社区筹款的帕累托原则.jpg|thumb|right|应用于社区筹款的帕累托原则]]<br />
<br />
Pareto principle applied to community fundraising<br />
<br />
应用于社区筹款的帕累托原则<br />
<br />
The '''Pareto principle''' (also known as the '''80/20 rule''', the '''law of the vital few,''' or the '''principle of factor sparsity''')<ref>{{cite news|url=https://www.nytimes.com/2008/03/03/business/03juran.html|title=Joseph Juran, 103, Pioneer in Quality Control, Dies|last1=Bunkley|first1=Nick|date=March 3, 2008|work=New York Times|accessdate=25 January 2018|archiveurl=https://web.archive.org/web/20170906182706/http://www.nytimes.com/2008/03/03/business/03juran.html|archivedate=September 6, 2017}}</ref><ref>{{cite journal|last1=Box|first1=George E.P.|last2=Meyer|first2=R. Daniel|date=1986|title=An Analysis for Unreplicated Fractional Factorials|journal=Technometrics|volume=28|issue=1|pages=11–18|doi=10.1080/00401706.1986.10488093}}</ref> states that, for many events, roughly 80% of the effects come from 20% of the causes.<ref name="NYT">{{cite news|url=https://www.nytimes.com/2008/03/03/business/03juran.html|title=Joseph Juran, 103, Pioneer in Quality Control, Dies|last=Bunkley|first=Nick|date=March 3, 2008|work=[[The New York Times]]}}</ref> <br />
<br />
The Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes. <br />
<br />
'''<font color="#ff8000"> 帕累托原则</font>'''（又称80/20法则、至关重要的少数人法则或因素稀少原则）指出，对于许多事件，大约80%的影响来自20%的原因。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】注意专业名词后面需要添加大写开头的对应英文“帕累托原则 Pareto Principle” 下同<br />
<br />
<br />
[[Management consultant]] [[Joseph M. Juran]] suggested the principle and named it after Italian [[economist]] [[Vilfredo Pareto]], who noted the 80/20 connection while at the [[University of Lausanne]] in 1896. In his first work, ''Cours d'économie politique'', Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. The Pareto principle is only tangentially related to [[Pareto efficiency]]. Pareto developed both concepts in the context of the [[distribution of income]] and wealth among the population.<br />
<br />
Management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who noted the 80/20 connection while at the University of Lausanne in 1896. In his first work, Cours d'économie politique, Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. The Pareto principle is only tangentially related to Pareto efficiency. Pareto developed both concepts in the context of the distribution of income and wealth among the population.<br />
<br />
管理顾问 Joseph M. Juran 提出了这个原则，并以意大利经济学家 Vilfredo Pareto 的名字命名，后者于1896年在洛桑大学指出了80/20的联系。帕雷托在他的第一部著作《政治经济学》中指出，意大利约80% 的土地为20% 的人口所拥有。帕雷托原则与帕累托最优的相关性不大。帕累托在人口的收入和财富分配的背景下发展出了这两个概念。<br />
<br />
<br />
<br />
Mathematically, the 80/20 rule is roughly followed by a [[power law]] distribution (also known as a [[Pareto distribution]]) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution.<ref>{{cite journal|url=https://arxiv.org/PS_cache/cond-mat/pdf/0412/0412004v3.pdf|title=Power laws, Pareto Distributions, and Zipf's law|journal=Contemporary Physics|volume=46|issue=5|pages=323–351|last=Newman|first=MEJ|access-date=10 April 2011|bibcode=2005ConPh..46..323N|year=2005|arxiv=cond-mat/0412004|doi=10.1080/00107510500052444|s2cid=202719165}}</ref> It is an axiom of business management that "80% of sales come from 20% of clients".<ref>{{Cite news|last=Marshall|first=Perry|url=https://www.entrepreneur.com/article/229294|title=The 80/20 Rule of Sales: How to Find Your Best Customers|date=2013-10-09|work=Entrepreneur|access-date=2018-01-05|language=en}}</ref><br />
<br />
Mathematically, the 80/20 rule is roughly followed by a power law distribution (also known as a Pareto distribution) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution. It is an axiom of business management that "80% of sales come from 20% of clients".<br />
<br />
在数学上，80/20原则对于一组特定的参数大致遵循'''<font color="#ff8000"> 幂律分布</font>'''(也称为'''<font color="#ff8000"> 帕累托分布</font>''') ，许多自然现象已经由试验证明呈现这样的分布。“80% 的销售额来自20% 的客户”是企业管理的一条公理。<br />
<br />
<br />
<br />
== In economics ==<br />
在经济学中<br />
<br />
<br />
<br />
The original observation was in connection with population and wealth. Pareto noticed that approximately 80% of Italy's land was owned by 20% of the population.<ref>{{citation|title=''Translation of'' Manuale di economia politica ("Manual of political economy") |first1=Vilfredo|last1=Pareto|first2=Alfred N.|last2=Page|publisher=A.M. Kelley|year=1971|isbn=978-0-678-00881-2|postscript=<!--none-->}}</ref> He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.<br />
<br />
The original observation was in connection with population and wealth. Pareto noticed that approximately 80% of Italy's land was owned by 20% of the population. He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.<br />
<br />
最初的观察结果与人口和财富有关。帕累托注意到，意大利约80% 的土地为20% 的人口所拥有。他随后对许多其他国家进行了调查，令他惊讶的是，类似的分布也同样适用。<br />
<br />
<br />
<br />
A chart that gave the inequality a very visible and comprehensible form, the so-called "champagne glass" effect,<ref>{{citation|first=Xabier|last=Gorostiaga|title=World has become a 'champagne glass' globalization will fill it fuller for a wealthy few|journal=National Catholic Reporter|date=January 27, 1995|postscript=<!--none-->}}</ref> was contained in the 1992 [[United Nations Development Programme|United Nations Development Program]] Report, which showed that distribution of global income is very uneven, with the richest 20% of the world's population controlling 82.7% of the world's income.<ref>{{citation|author=United Nations Development Program|title=1992 Human Development Report|year=1992|location=New York|publisher=Oxford University Press|postscript=<!--none-->}}</ref> Still, the [[Gini index]] of the world shows that nations have wealth distributions that vary greatly.<br />
<br />
A chart that gave the inequality a very visible and comprehensible form, the so-called "champagne glass" effect, was contained in the 1992 United Nations Development Program Report, which showed that distribution of global income is very uneven, with the richest 20% of the world's population controlling 82.7% of the world's income. Still, the Gini index of the world shows that nations have wealth distributions that vary greatly.<br />
<br />
1992年《联合国开发计划署报告》中的一张图表以非常明显和易懂的形式呈现了不平等，即所谓的 "香槟酒杯 "效应，该图表显示，全球收入分配非常不均衡，世界上最富有的20% 人口控制着82.7%的世界收入。不过，世界基尼系数显示，各国的财富分配差异很大。<br />
<br />
<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class = “ wikitable”<br />
<br />
|+ Distribution of world GDP, 1989<ref name="1992 Human Development Report, Chapter 3">{{citation|url=http://hdr.undp.org/en/reports/global/hdr1992/chapters/|title=Human Development Report 1992, Chapter 3|accessdate=2007-07-08|postscript=<!--none-->}}</ref><br />
<br />
|+ Distribution of world GDP, 1989<br />
<br />
| + 世界 GDP 分布，1989年<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="col" | Quintile of population<br />
<br />
! scope="col" | Quintile of population<br />
<br />
!范围 = “ col” | 五分之一人口<br />
<br />
! scope="col" | Income<br />
<br />
! scope="col" | Income<br />
<br />
!范围 = “ col” | 收入<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Richest 20%<br />
<br />
| Richest 20%<br />
<br />
最富有的20% <br />
<br />
| 82.70%<br />
<br />
| 82.70%<br />
<br />
| 82.70%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Second 20%<br />
<br />
| Second 20%<br />
<br />
第二个20% <br />
<br />
| 11.75%<br />
<br />
| 11.75%<br />
<br />
| 11.75%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Third 20%<br />
<br />
| Third 20%<br />
<br />
第三20% <br />
<br />
| 2.30%<br />
<br />
| 2.30%<br />
<br />
| 2.30%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Fourth 20%<br />
<br />
| Fourth 20%<br />
<br />
第四个20% <br />
<br />
| 1.85%<br />
<br />
| 1.85%<br />
<br />
| 1.85%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Poorest 20%<br />
<br />
| Poorest 20%<br />
<br />
最穷的20% <br />
<br />
| 1.40%<br />
<br />
| 1.40%<br />
<br />
| 1.40%<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
The Pareto principle also could be seen as applying to taxation. In the US, the top 20% of earners have paid roughly 80-90% of Federal income taxes in 2000 and 2006,<ref>Curtis Dubay (May 4, 2009) [https://www.heritage.org/poverty-and-inequality/report/the-rich-pay-more-taxes-top-20-percent-pay-record-share-income-taxes The Rich Pay More Taxes: Top 20 Percent Pay Record Share of Income Taxes], Heritage.org, accessed 12 April 2018</ref> and again in 2018.<ref>Laura Sanders (April 6, 2018) [https://www.wsj.com/articles/top-20-of-americans-will-pay-87-of-income-tax-1523007001 Top 20% of Americans Will Pay 87% of Income Tax], Wall Street Journal, accessed 12 April 2018</ref><br />
<br />
The Pareto principle also could be seen as applying to taxation. In the US, the top 20% of earners have paid roughly 80-90% of Federal income taxes in 2000 and 2006, and again in 2018.<br />
<br />
欧洲帕雷托法则也可以被视为适用于税收。在美国，收入最高的20%的人在2000年和2006年缴纳了大约80%-90%的联邦所得税，2018年又是如此。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】帕雷托法则 注意全文的专业名词统一性 是统一用原则还是法则<br />
<br />
<br />
However, it is important to note that while there have been associations of such with [[meritocracy]], the principle should not be confused with further reaching implications. As Alessandro Pluchino at the University of Catania in Italy points out, other attributes do not necessarily correlate. Using talent as an example, he and other researchers state, “The maximum success never coincides with the maximum talent, and vice-versa,” and that such factors are the result of chance.<ref>Emerging Technology from the arXiv (March 1, 2018) [https://www.technologyreview.com/s/610395/if-youre-so-smart-why-arent-you-rich-turns-out-its-just-chance/ If you’re so smart, why aren’t you rich? Turns out it’s just chance.], TechnologyReview.com, accessed 1 January 2019</ref><br />
<br />
However, it is important to note that while there have been associations of such with meritocracy, the principle should not be confused with further reaching implications. As Alessandro Pluchino at the University of Catania in Italy points out, other attributes do not necessarily correlate. Using talent as an example, he and other researchers state, “The maximum success never coincides with the maximum talent, and vice-versa,” and that such factors are the result of chance.<br />
<br />
然而，必须指出的是，虽然有这与精英管理体制有联系，但这一原则不应与进一步的影响混为一谈。正如意大利卡塔尼亚大学的 Alessandro Pluchino 指出的那样，其他属性并不一定相互关联。以天赋为例，他和其他研究人员指出，“最大的成功从来没有与最大的天赋相吻合，反之亦然”，这样的因素是偶然的结果。<br />
<br />
<br />
The physicist Victor Yakovenko of the [[University of Maryland, College Park]] and AC Silva analyzed income data from the US Internal Revenue Service from 1983 to 2001, and found that the income distribution among the upper class (1–3% of the population) follows Pareto's principle.<ref>{{Citation|last1=Yakovenko|first1=Victor M.|title=Two-class Structure of Income Distribution in the USA: Exponential Bulk and Power-law Tail|date=2005|work=Econophysics of Wealth Distributions: Econophys-Kolkata I|pages=15–23|editor-last=Chatterjee|editor-first=Arnab|series=New Economic Windows|publisher=Springer Milan|language=en|doi=10.1007/88-470-0389-x_2|isbn=978-88-470-0389-7|last2=Silva|first2=A. Christian|editor2-last=Yarlagadda|editor2-first=Sudhakar|editor3-last=Chakrabarti|editor3-first=Bikas K.}}</ref><br />
<br />
The physicist Victor Yakovenko of the University of Maryland, College Park and AC Silva analyzed income data from the US Internal Revenue Service from 1983 to 2001, and found that the income distribution among the upper class (1–3% of the population) follows Pareto's principle.<br />
<br />
马里兰大学学院帕克分校的物理学家Victor Yakovenko和AC Silva分析了美国国税局1983年到2001年的收入数据，发现上层阶级(占总人口的1-3%)的收入分配遵循帕累托原则。<br />
<br />
<br />
<br />
== In computing ==<br />
在计算领域<br />
<br />
In [[computer science]] the Pareto principle can be applied to [[optimization (computer science)|optimization]] efforts.<ref name=optimization>{{citation|first1=M.|last1=Gen|first2=R.|last2=Cheng|title=Genetic Algorithms and Engineering Optimization|location=New York|publisher=Wiley|year=2002|postscript=<!--none-->}}</ref> For example, [[Microsoft]] noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated.<ref>{{citation|url=http://www.crn.com/news/security/18821726/microsofts-ceo-80-20-rule-applies-to-bugs-not-just-features.htm|title=Microsoft's CEO: 80–20 Rule Applies To Bugs, Not Just Features|first=Paula|last=Rooney|date=October 3, 2002|publisher=ChannelWeb|postscript=<!--none-->}}</ref> [[Lowell Arthur]] expressed that "20 percent of the code has 80 percent of the errors. Find them, fix them!"<ref>Pressman, Roger S. (2010). Software Engineering: A Practitioner's Approach (7th ed.). Boston, Mass: McGraw-Hill, 2010. {{ISBN|978-0-07-337597-7}}.</ref> It was also discovered that in general the 80% of a certain piece of software can be written in 20% of the total allocated time. Conversely, the hardest 20% of the code takes 80% of the time. This factor is usually a part of [[COCOMO]] estimating for software coding.<br />
<br />
In computer science the Pareto principle can be applied to optimization efforts. For example, Microsoft noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated. Lowell Arthur expressed that "20 percent of the code has 80 percent of the errors. Find them, fix them!" It was also discovered that in general the 80% of a certain piece of software can be written in 20% of the total allocated time. Conversely, the hardest 20% of the code takes 80% of the time. This factor is usually a part of COCOMO estimating for software coding.<br />
<br />
在计算机科学中，帕雷托原则可以应用于优化工作。例如，微软指出，通过修复前20%的报告最多的错误，可以消除给定系统中80%的相关错误和崩溃。Lowell Arthur表示“20% 的代码有80% 的错误。找到它们，修复它们!”人们还发现，一般来说，某个软件的80%可以在总分配时间的20%内编写完。相反，最难的20%的代码占用了80%的时间。这个因素通常是软件编码的COCOMO估算的一部分。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）帕雷托原则 帕累托原则 80/20原则 全文注意名词的统一性 翻译完后一定一定通读 按照自审清单走一遍<br />
<br />
== In sports ==<br />
在体育领域<br />
<br />
It has been inferred that the Pareto principle applies to athletic training, where roughly 20% of the exercises and habits have 80% of the impact, and the trainee should not focus so much on a varied training.<ref>{{citation |url= http://speedendurance.com/2008/11/20/training-and-the-80-20-rule-of-paretos-principle/ |title=Training and the 80-20 rule of Pareto's Principle |date=21 November 2008 }}</ref> This does not necessarily mean that having a healthy diet or going to the gym are not important, but they are not as significant as the key activities. It is also important to note this 80/20 rule has yet to be scientifically tested in controlled studies of athletic training.<br />
<br />
It has been inferred that the Pareto principle applies to athletic training, where roughly 20% of the exercises and habits have 80% of the impact, and the trainee should not focus so much on a varied training. This does not necessarily mean that having a healthy diet or going to the gym are not important, but they are not as significant as the key activities. It is also important to note this 80/20 rule has yet to be scientifically tested in controlled studies of athletic training.<br />
<br />
据推测，帕雷托原则适用于运动训练，其中大约20%的训练和习惯有80%的影响，受训者不应该过多地注重多样化的训练。这并不一定意味着健康饮食或去健身房不重要，只是它们不如那些关键活动重要。另外需要注意的是，这个80/20原则还没有在运动训练的对照研究中得到科学验证。<br />
<br />
<br />
<br />
In [[baseball]], the Pareto principle has been perceived in [[Wins Above Replacement]] (an attempt to combine multiple statistics to determine a player's overall importance to a team). "15% of all the players last year produced 85% of the total wins with the other 85% of the players creating 15% of the wins. The Pareto principle holds up pretty soundly when it is applied to baseball."<ref>Jeff Zimmerman (Jun 4, 2010). [https://www.beyondtheboxscore.com/2010/6/4/1501048/applying-the-parento-principle-80 Applying the Pareto Principle (80-20 Rule) to Baseball], BeyondTheBoxScore.com, accessed 12 April 2018</ref><br />
<br />
In baseball, the Pareto principle has been perceived in Wins Above Replacement (an attempt to combine multiple statistics to determine a player's overall importance to a team). "15% of all the players last year produced 85% of the total wins with the other 85% of the players creating 15% of the wins. The Pareto principle holds up pretty soundly when it is applied to baseball."<br />
<br />
在棒球比赛中，帕雷托原则已经在Wins Above Replacement(试图结合多种统计数据来确定一个球员对一个球队的整体重要性)中被认识到。“去年15%的球员创造了85%的总胜利，其他85%的球员创造了15%的胜利。帕雷托原则在棒球比赛中得到了充分体现。”<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】“中被认识到” 避免被动语态<br />
<br />
== Occupational health and safety ==<br />
职业健康和安全<br />
<br />
[[Occupational health and safety]] professionals use the Pareto principle to underline the importance of hazard prioritization. Assuming 20% of the hazards account for 80% of the injuries, and by categorizing hazards, safety professionals can target those 20% of the hazards that cause 80% of the injuries or accidents. Alternatively, if hazards are addressed in random order, a safety professional is more likely to fix one of the 80% of hazards that account only for some fraction of the remaining 20% of injuries.<ref>{{cite book |last=Woodcock |first=Kathryn |title=Safety Evaluation Techniques |year=2010 |publisher= Ryerson University |location= Toronto, ON |pages=86 |url= http://www.ryerson.ca/woodcock/}}</ref><br />
<br />
Occupational health and safety professionals use the Pareto principle to underline the importance of hazard prioritization. Assuming 20% of the hazards account for 80% of the injuries, and by categorizing hazards, safety professionals can target those 20% of the hazards that cause 80% of the injuries or accidents. Alternatively, if hazards are addressed in random order, a safety professional is more likely to fix one of the 80% of hazards that account only for some fraction of the remaining 20% of injuries.<br />
<br />
职业健康和安全方面的专业人士使用帕雷托原则来强调危害优先级的重要性。假设20% 的危险占伤害的80% ，通过对危险进行分类，安全专业人员可以有针对性地解决造成80%伤害或事故的那20%的危害。或者，如果危害按随机顺序处理，安全专业人员更有可能解决那80%的危害中的一个，而这个危害只占其余20%伤害的某一部分。<br />
<br />
<br />
<br />
Aside from ensuring efficient accident prevention practices, the Pareto principle also ensures hazards are addressed in an economical order, because the technique ensures the utilized resources are best used to prevent the most accidents.<ref name=USCG001>{{cite web|title=Introduction to Risk-based Decision-Making |url= http://www.uscg.mil/hq/cg5/cg5211/docs/RBDM_Files/PDF/RBDM_Guidelines/Volume%202/Volume%202-Chapter%206.pdf |work=USCG Safety Program |publisher= United States Coast Guard |accessdate= 14 January 2012}}</ref><br />
<br />
Aside from ensuring efficient accident prevention practices, the Pareto principle also ensures hazards are addressed in an economical order, because the technique ensures the utilized resources are best used to prevent the most accidents.<br />
<br />
除了确保有效的事故预防措施，帕雷托法则安全管理局原则还能确保以经济的顺序处理危险，因为该技术能确保所利用的资源被最好地用于预防最多的事故。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】“帕雷托法则安全管理局原则”此处是否没有经过人工翻译？<br />
<br />
== Other applications ==<br />
其他应用<br />
<br />
In engineering control theory, such as for electromechanical energy converters, the 80/20 principle applies to optimization efforts.<ref name=optimization/><br />
<br />
In engineering control theory, such as for electromechanical energy converters, the 80/20 principle applies to optimization efforts.<br />
<br />
在工程控制理论中，如对于机电式能量转换器，80/20原则适用于优化工作。<br />
<br />
<br />
<br />
The law of the few can be also seen in betting, where it is said that with 20% effort you can match the accuracy of 80% of the bettors.<ref>{{citation|title=The Pareto Principle of Prediction|url=https://www.pinnacle.com/en/betting-articles/betting-strategy/the-pareto-principle-of-prediction}}</ref><br />
<br />
In the systems science discipline, Joshua M. Epstein and Robert Axtell created an agent-based simulation model called Sugarscape, from a decentralized modeling approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 principle became emergent in their results, which suggests the principle is a collective consequence of these individual rules.<br />
<br />
在系统科学领域，Joshua M. Epstein和Robert Axtell从分散建模方法出发，基于为经济中的每个代理人定义的个人行为规则创建了创建了一个名为Sugarscape的基于代理的仿真模型。财富分配原则和帕累托80/20原则在其结果中突现，这表明这一原则是这些个体规则的集体结果。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】“创建了创建了一个” 下次需要认真细心<br />
<br />
<br />
In the systems science discipline, [[Joshua M. Epstein]] and [[Robert Axtell]] created an [[Agent-based social simulation|agent-based simulation]] model called [[Sugarscape]], from a [[Decentralised system|decentralized modeling]] approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 principle became emergent in their results, which suggests the principle is a collective consequence of these individual rules.<ref>{{Citation|last1=Epstein|first1=Joshua|title=Growing Artificial Societies: Social Science from the Bottom-Up|url=https://books.google.com/books?id=xXvelSs2caQC|page=208|year=1996|postscript=<!--none-->|publisher=[[MIT Press]]|isbn=0-262-55025-3|last2=Axtell|first2=Robert}}<br />
<br />
The Pareto principle has many applications in quality control. It is the basis for the Pareto chart, one of the key tools used in total quality control and Six Sigma techniques. The Pareto principle serves as a baseline for ABC-analysis and XYZ-analysis, widely used in logistics and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.<br />
<br />
帕雷托原则在质量控制方面有很多应用。它是帕累托图的基础，帕累托图是用于全面质量控制和六西格玛技术的关键工具之一。帕雷托原则分析作为ABC分析法和XYZ分析法的基准，广泛应用于物流和采购，目的是优化库存以及保存和补充库存的成本。<br />
<br />
</ref><br />
<br />
<br />
<br />
In health care in the United States, in one instance 20% of patients have been found to use 80% of health care resources.<br />
<br />
在美国的医疗服务中，一个事例发现20%的病人使用了80%的医疗资源。<br />
<br />
The Pareto principle has many applications in quality control.<ref>{{Cite book|url=https://books.google.com/books?id=QtVmCgAAQBAJ&pg=PA8&lpg=PA8&dq=The+Pareto+principle+has+many+applications+in+quality+control#v=onepage|title=The Pareto Principle for Business Management: Expand your business with the 80/20 rule|last=50MINUTES.COM|date=2015-08-17|publisher=50 Minutes|isbn=9782806265869|language=en}}</ref> It is the basis for the [[Pareto chart]], one of the key tools used in [[total quality management|total quality control]] and [[Six Sigma]] techniques. The Pareto principle serves as a baseline for [[time management#abc analysis|ABC-analysis]] and XYZ-analysis, widely used in [[logistics]] and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.<ref>{{harvtxt|Rushton|Oxley|Croucher|2000}}, pp. 107–108.</ref><br />
<br />
<br />
<br />
Some cases of super-spreading conform to the 20/80 rule, where approximately 20% of infected individuals are responsible for 80% of transmissions, although super-spreading can still be said to occur when super-spreaders account for a higher or lower percentage of transmissions. In epidemics with super-spreading, the majority of individuals infect relatively few secondary contacts.<br />
<br />
一些超级传播病例符合20/80原则，其中大约20%的感染者要为80%的传播负责，尽管当超级传播者占传播的比例较高或较低时，仍然可以说发生了超级传播。在超级传播的流行病中，大多数个体感染的二次接触者相对较少。<br />
<br />
In health care in the United States, in one instance 20% of patients have been found to use 80% of health care resources.<ref>[http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html Myrl Weinberg: In health-care reform, the 20-80 solution | Contributors | projo.com | The Providence Journal<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20090802002952/http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|date=2009-08-02}}</ref><ref>{{cite web|url=http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|archiveurl=https://archive.today/20090802002952/http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|url-status=dead|title=Myrl Weinberg: In health-care reform, the 20-80 solution - Contributo…|date=2 August 2009|archivedate=2 August 2009|website=archive.li}}</ref><ref>{{cite web |last1=Sawyer and Claxton |first1=Bradley and Gary |title=How do health expenditures vary across the population? |url=https://www.healthsystemtracker.org/chart-collection/health-expenditures-vary-across-population/#item-discussion-of-health-spending-often-focus-on-averages-but-a-small-share-of-the-population-incurs-most-of-the-cost_2016 |website=Peterson-Kaiser Health System Tracker |publisher=Peterson Center on Healthcare and the Kaiser Family Foundation |accessdate=13 March 2019}}</ref><br />
<br />
<br />
<br />
The Dunedin Study has found 80% of crimes are committed by 20% of criminals. This statistic has been used to support both stop-and-frisk policies and broken windows policing, as catching those criminals committing minor crimes will supposedly net many criminals wanted for (or who would normally commit) larger ones.<br />
<br />
达尼丁研究发现80%的犯罪是20%的罪犯所为。这一统计数据被用来支持拦截搜查政策和破窗执法，因为抓获那些犯有轻罪的罪犯，可能会让许多想犯(或通常会犯)重罪的通缉犯落网。<br />
<br />
Some cases of [[Super-spreader|super-spreading]] conform to the 20/80 rule,<ref>{{cite journal|last1=Galvani|first1=Alison P.|last2=May|first2=Robert M.|year=2005|title=Epidemiology: Dimensions of superspreading|url=|journal=Nature|volume=438|issue=7066|pages=293–295|doi=10.1038/438293a|pmid=16292292|bibcode=2005Natur.438..293G|pmc=7095140}}</ref> where approximately 20% of infected individuals are responsible for 80% of transmissions, although super-spreading can still be said to occur when super-spreaders account for a higher or lower percentage of transmissions.<ref name="Lloyd-Smith JO 2005">{{cite journal|last1=Lloyd-Smith|first1=JO|last2=Schreiber|first2=SJ|last3=Kopp|first3=PE|last4=Getz|first4=WM|year=2005|title=Superspreading and the effect of individual variation on disease emergence|url=|journal=Nature|volume=438|issue=7066|pages=355–359|doi=10.1038/nature04153|pmid=16292310|bibcode=2005Natur.438..355L|pmc=7094981}}</ref> In [[epidemic]]s with super-spreading, the majority of individuals infect relatively few [[contact tracing|secondary contacts]].<br />
<br />
<br />
<br />
Many video rental shops reported in 1988 that 80% of revenue came from 20% of videotapes. A video-chain executive discussed the "Gone with the Wind syndrome", however, in which every store had to offer classics like Gone with the Wind, Casablanca, or The African Queen to appear to have a large inventory, even if customers very rarely rented them.<br />
<br />
1988年，许多录像带出租店报告说，80%的收入来自20%的录像带。然而，一家视频连锁店的高管谈到了“乱世佳人综合症”，即每家商店都必须提供《飘》、《卡萨布兰卡》或《非洲女王号》等经典影片，以显得其库存庞大，即使顾客很少租用这些影片。<br />
<br />
The [[Dunedin Multidisciplinary Health and Development Study|Dunedin Study]] has found 80% of crimes are committed by 20% of criminals.<ref>{{Citation|last=Nicola|first=Davis|title='High social cost' adults can be predicted from as young as three, says study|url=https://www.theguardian.com/science/2016/dec/12/high-social-cost-adults-can-be-identified-from-as-young-as-three-says-study|year=2016|postscript=<!--none-->|publisher=[[The Guardian]]}}<br />
<br />
</ref> This statistic has been used to support both [[stop-and-frisk]] policies and [[broken windows]] policing, as catching those criminals committing minor crimes will supposedly net many criminals wanted for (or who would normally commit) larger ones.<br />
<br />
<br />
<br />
Many [[video rental shop]]s reported in 1988 that 80% of revenue came from 20% of videotapes. A video-chain executive discussed the "''Gone with the Wind'' syndrome", however, in which every store had to offer classics like ''[[Gone with the Wind (film)|Gone with the Wind]]'', ''[[Casablanca (film)|Casablanca]]'', or ''[[The African Queen (film)|The African Queen]]'' to appear to have a large inventory, even if customers very rarely rented them.<ref name="kleinfield19880501">{{Cite news |url=https://www.nytimes.com/1988/05/01/business/a-tight-squeeze-at-video-stores.html |title=A Tight Squeeze at Video Stores |last=Kleinfield |first=N. R. |date=1988-05-01 |work=The New York Times |access-date=2019-02-08 |language=en-US |issn=0362-4331}}</ref><br />
<br />
The idea has a rule of thumb application in many places, but it is commonly misused. For example, it is a misuse to state a solution to a problem "fits the 80/20 rule" just because it fits 80% of the cases; it must also be that the solution requires only 20% of the resources that would be needed to solve all cases. Additionally, it is a misuse of the 80/20 rule to interpret a small number of categories or observations.<br />
<br />
这个想法在很多地方都有经验法则的应用，但它通常被误用。例如，仅仅因为一个问题的解决方案符合80/20原则，就声称其“符合80/20原则” ，这是一种误用;该解决方案还必须只需要解决所有案例所需资源的20% 。此外，用80/20原则来解释少数类别或意见也是一种滥用。<br />
<br />
<br />
<br />
== Mathematical notes ==<br />
数学说明<br />
<br />
This is a special case of the wider phenomenon of Pareto distributions. If the Pareto index&nbsp;α, which is one of the parameters characterizing a Pareto distribution, is chosen as α&nbsp;=&nbsp;log45&nbsp;≈&nbsp;1.16, then one has 80% of effects coming from 20% of causes.<br />
<br />
这是更广泛的帕累托分布现象的一个特例。如果选择帕累托指数α作为帕累托分布的参数之一，α=log45≈1.16，那么80%的效应来自20%的原因。<br />
<br />
{{or-section|date=May 2020}}<br />
<br />
The idea has a rule of thumb application in many places, but it is commonly misused. For example, it is a misuse to state a solution to a problem "fits the 80/20 rule" just because it fits 80% of the cases; it must also be that the solution requires only 20% of the resources that would be needed to solve all cases. Additionally, it is a misuse of the 80/20 rule to interpret a small number of categories or observations.<br />
<br />
It follows that one also has 80% of that top 80% of effects coming from 20% of that top 20% of causes, and so on. Eighty percent of 80% is 64%; 20% of 20% is 4%, so this implies a "64/4" law; and similarly implies a "51.2/0.8" law. Similarly for the bottom 80% of causes and bottom 20% of effects, the bottom 80% of the bottom 80% only cause 20% of the remaining 20%. This is broadly in line with the world population/wealth table above, where the bottom 60% of the people own 5.5% of the wealth, approximating to a 64/4 connection.<br />
<br />
因此，前80%的影响中，有80%来自前20%的原因，以此类推。80%的80%是64%，20%的20%是4%，所以这意味着一个“64/4”原则，同样意味着一个“51.2/0.8”原则。同样，对于底层80% 的原因和底层20%的结果，底层80%的80%只造成剩下的20%的20% 。这与上面的世界人口财富表基本一致，那里底层60%的人拥有5.5%的财富，接近于64/4的联系。<br />
<br />
<br />
<br />
This is a special case of the wider phenomenon of [[Pareto distribution]]s. If the [[Pareto index]]&nbsp;'''α''', which is one of the parameters characterizing a Pareto distribution, is chosen as '''α'''&nbsp;=&nbsp;log<sub>4</sub>5&nbsp;≈&nbsp;1.16, then one has 80% of effects coming from 20% of causes.<br />
<br />
The 64/4 correlation also implies a 32% 'fair' area between the 4% and 64%, where the lower 80% of the top 20% (16%) and upper 20% of the bottom 80% (also 16%) relates to the corresponding lower top and upper bottom of effects (32%). This is also broadly in line with the world population table above, where the second 20% control 12% of the wealth, and the bottom of the top 20% (presumably) control 16% of the wealth.<br />
<br />
64/4的相关性还意味着在4%和64%之间有32%的”公平”区域，其中前20% 的后80%(16%)和后80%的前20% (也是16%)与相应的下层和上层的效果（32%）有关。这也与上面的世界人口表基本一致，其中第二层的20%控制着12%的财富，前20%的底层(大概)控制着16%的财富。<br />
<br />
<br />
<br />
It follows that one also has 80% of that top 80% of effects coming from 20% of that top 20% of causes, and so on. Eighty percent of 80% is 64%; 20% of 20% is 4%, so this implies a "64/4" law; and similarly implies a "51.2/0.8" law. Similarly for the bottom 80% of causes and bottom 20% of effects, the bottom 80% of the bottom 80% only cause 20% of the remaining 20%. This is broadly in line with the world population/wealth table above, where the bottom 60% of the people own 5.5% of the wealth, approximating to a 64/4 connection.<br />
<br />
The term 80/20 is only a shorthand for the general principle at work. In individual cases, the distribution could just as well be, say, nearer to 90/10 or 70/30. There is no need for the two numbers to add up to the number 100, as they are measures of different things, (e.g., 'number of customers' vs 'amount spent'). However, each case in which they do not add up to 100%, is equivalent to one in which they do. For example, as noted above, the "64/4 law" (in which the two numbers do not add up to 100%) is equivalent to the "80/20 law" (in which they do add up to 100%). Thus, specifying two percentages independently does not lead to a broader class of distributions than what one gets by specifying the larger one and letting the smaller one be its complement relative to 100%. Thus, there is only one degree of freedom in the choice of that parameter.<br />
<br />
术语80/20只是一般工作原则的简写。在个别情况下，分布也可能接近90/10或70/30。这两个数字加起来不必等于100，因为它们是对不同事物的度量(例如，“客户数量”和“消费金额”)。然而，每一个他们加起来不到100%的情况，都等同于他们加起来是100%的情况。例如，如上文所述，“64/4法则”(两个数字之和不等于100%)相当于80/20原则(两者之和等于100%)。因此，单独指定两个百分比并不会比指定较大的百分比并让较小的百分比作为其相对于100% 的补充得到更广泛的一类分布。因此，在选择该参数时只有一个自由度。<br />
<br />
<br />
<br />
The 64/4 correlation also implies a 32% 'fair' area between the 4% and 64%, where the lower 80% of the top 20% (16%) and upper 20% of the bottom 80% (also 16%) relates to the corresponding lower top and upper bottom of effects (32%). This is also broadly in line with the world population table above, where the second 20% control 12% of the wealth, and the bottom of the top 20% (presumably) control 16% of the wealth.<br />
<br />
Adding up to 100 leads to a nice symmetry. For example, if 80% of effects come from the top 20% of sources, then the remaining 20% of effects come from the lower 80% of sources. This is called the "joint ratio", and can be used to measure the degree of imbalance: a joint ratio of 96:4 is extremely imbalanced, 80:20 is highly imbalanced (Gini index: 76%), 70:30 is moderately imbalanced (Gini index: 28%), and 55:45 is just slightly imbalanced (Gini index 14%).<br />
<br />
100加起来就是一个完美的对称。例如，如果80%的影响来自前20%的来源，那么剩下的20%的影响来自后80%的来源。这就是所谓的“联合比率” ，可以用来衡量不平衡的程度: 96:4的联合比率极不平衡，80:20的联合比率高度不平衡(基尼指数: 76%) ，70:30的联合比率中度不平衡(基尼指数: 28%) ，55:45的联合比率略不平衡(基尼指数14%)。<br />
<br />
<br />
<br />
The term 80/20 is only a shorthand for the general principle at work. In individual cases, the distribution could just as well be, say, nearer to 90/10 or 70/30. There is no need for the two numbers to add up to the number 100, as they are measures of different things, (e.g., 'number of customers' vs 'amount spent'). However, each case in which they do not add up to 100%, is equivalent to one in which they do. For example, as noted above, the "64/4 law" (in which the two numbers do not add up to 100%) is equivalent to the "80/20 law" (in which they do add up to 100%). Thus, specifying two percentages independently does not lead to a broader class of distributions than what one gets by specifying the larger one and letting the smaller one be its complement relative to 100%. Thus, there is only one degree of freedom in the choice of that parameter.<br />
<br />
The Pareto principle is an illustration of a "power law" relationship, which also occurs in phenomena such as brush fires and earthquakes.<br />
<br />
帕累托原则是“幂律”关系的一个例证，这种关系也发生在诸如丛林火灾和地震等现象中。<br />
<br />
<br />
<br />
Because it is self-similar over a wide range of magnitudes, it produces outcomes completely different from Normal or Gaussian distribution phenomena. This fact explains the frequent breakdowns of sophisticated financial instruments, which are modeled on the assumption that a Gaussian relationship is appropriate to something like stock price movements.<br />
<br />
因为它在很大范围内是自相似的，所以它产生的结果与正态或高斯分布现象完全不同。这一事实解释了复杂金融工具频繁崩溃的原因，因为这些金融工具是建立在高斯关系适用于类似股票价格波动的假设之上的。<br />
<br />
Adding up to 100 leads to a nice symmetry. For example, if 80% of effects come from the top 20% of sources, then the remaining 20% of effects come from the lower 80% of sources. This is called the "joint ratio", and can be used to measure the degree of imbalance: a joint ratio of 96:4 is extremely imbalanced, 80:20 is highly imbalanced ([[Gini index]]: 76%), 70:30 is moderately imbalanced (Gini index: 28%), and 55:45 is just slightly imbalanced (Gini index 14%).<br />
<br />
<br />
<br />
The Pareto principle is an illustration of a "[[power law]]" relationship, which also occurs in phenomena such as [[brush fire]]s and earthquakes.<ref>{{Citation|last=Bak|first=Per|title=How Nature Works: the science of self-organized criticality|page=89|year=1999|publisher=Springer|isbn=0-387-94791-4|authorlink=Per Bak}}</ref><br />
<br />
Because it is self-similar over a wide range of magnitudes, it produces outcomes completely different from [[Normal distribution|Normal or Gaussian distribution]] phenomena. This fact explains the frequent breakdowns of sophisticated financial instruments, which are modeled on the assumption that a Gaussian relationship is appropriate to something like stock price movements.<ref>{{Citation|last=Taleb|first=Nassim|title=The Black Swan|pages=229–252, 274–285|year=2007|postscript=<!--none-->|authorlink=Nassim Taleb|title-link=The Black Swan (Taleb book)}}</ref><br />
<br />
<br />
<br />
== Equality measures ==<br />
平等措施<br />
<br />
Using the "A&nbsp;:&nbsp;B" notation (for example, 0.8:0.2) and with&nbsp;A&nbsp;+&nbsp;B&nbsp;=&nbsp;1, inequality measures like the Gini index (G) and the Hoover index (H) can be computed. In this case both are the same.<br />
<br />
使用“A:B”符号(例如，0.8:0.2)和a+b=1，可以计算基尼指数(G)和胡佛指数(H)等不平等度量。在这种情况下，两者是相同的。<br />
<br />
<br />
<br />
=== Gini coefficient and Hoover index ===<br />
基尼系数和胡佛指数<br />
<br />
H=G=|2A-1|=|1-2B| \, <br />
<br />
H = G = | 2A-1 | = | 1-2B | ,<br />
<br />
<br />
<br />
Using the "''A''&nbsp;:&nbsp;''B''" notation (for example, 0.8:0.2) and with&nbsp;''A''&nbsp;+&nbsp;''B''&nbsp;=&nbsp;1, [[Income inequality metrics|inequality measures]] like the [[Gini index]] (G) ''and'' the [[Hoover index]] (H) can be computed. In this case both are the same.<br />
使用“A:B”符号(例如，0.8:0.2)和a+b=1，可以计算基尼指数(G)和胡佛指数(H)等不平等度量。在这种情况下，两者是相同的。<br />
<br />
<br />
A:B = \left( \frac{1+H} 2 \right): \left( \frac{1-H} 2 \right)<br />
<br />
A: B = left (frac {1 + H }2 right) : left (frac {1-H }2 right)<br />
<br />
<br />
<br />
: <math>H=G=|2A-1|=|1-2B| \, </math><br />
<br />
<br />
<br />
: <math>A:B = \left( \frac{1+H} 2 \right): \left( \frac{1-H} 2 \right)</math><br />
<br />
<br />
<br />
== See also ==<br />
另见<br />
<br />
{{div col|colwidth=22em}}<br />
<br />
*[[1% rule (Internet culture)]]<br />
*[[1%规则（互联网文化）]]<br />
<br />
*[[10/90 gap]]<br />
*[[10/90差距]]<br />
<br />
*[[Benford's law]]<br />
*[[本福德定律]]<br />
<br />
*[[Diminishing returns]]<br />
*[[收益递减]]<br />
<br />
*[[Elephant flow]]<br />
*[[大象流]]<br />
<br />
*[[Keystone species]]<br />
*[[关键物种]]<br />
<br />
*[[Long tail]]<br />
*[[长尾]]<br />
<br />
*[[Matthew effect]]<br />
*[[马太效应]]<br />
<br />
*[[Mathematical economics]]<br />
*[[数学经济学]]<br />
<br />
*[[Megadiverse countries]]<br />
*[[巨型多样化国家]]<br />
<br />
*[[Ninety-ninety rule]]<br />
*[[90-90法则]]<br />
<br />
*[[Pareto distribution]]<br />
*[[帕累托分布]]<br />
<br />
*[[Pareto priority index]]<br />
*[[帕累托优先权指数]]<br />
<br />
*[[Parkinson's law]]<br />
*[[帕金森定律]]<br />
<br />
*[[Derek J. de Solla Price|Price's law]]<br />
*[[普赖斯定律]]<br />
<br />
*[[Principle of least effort]]<br />
*[[最小努力原则]]<br />
<br />
*[[Profit risk]]<br />
*[[利润风险]]<br />
<br />
*[[Rank-size distribution]]<br />
*[[等级分布]]<br />
<br />
*[[Sturgeon's law]]<br />
*[[斯特金法则]]<br />
<br />
*[[Vitality curve]]<br />
*[[生命力曲线]]<br />
<br />
*[[Wealth concentration]]<br />
*[[财富集中]]<br />
<br />
*[[Zipf's law]]<br />
*[[齐普夫定律]]<br />
<br />
*[[Free-to-play#Comparison with traditional model|Microtransaction whale]]<br />
*[[免费游戏#与传统模式比较|微交易鲸]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== References ==<br />
参考<br />
<br />
{{Reflist|30em}}<br />
<br />
<br />
<br />
== Further reading ==<br />
进一步阅读<br />
<br />
*{{Citation |last=Bookstein |first=Abraham |authorlink= |year=1990 |title=Informetric distributions, part I: Unified overview |journal=Journal of the American Society for Information Science |volume=41 |issue= 5|pages=368–375 |doi=10.1002/(SICI)1097-4571(199007)41:5<368::AID-ASI8>3.0.CO;2-C |url= |accessdate= |quote= |postscript=<!--none--> }}<br />
<br />
*{{Citation |authors=Klass, O. S.; Biham, O.; Levy, M.; Malcai, O.; Soloman, S. |year=2006 |title=The Forbes 400 and the Pareto wealth distribution |journal=Economics Letters |volume=90 |issue=2 |pages=290–295 |doi=10.1016/j.econlet.2005.08.020 |url= |accessdate= |quote= |postscript=<!--none--> }}<br />
<br />
*{{Citation |title=The 80/20 Principle: The Secret of Achieving More with Less |last=Koch |first=R. |authorlink= |year=2001 |publisher=Nicholas Brealey Publishing |location=London |isbn= |pages= |url=https://www.scribd.com/doc/3664882/The-8020-Principle-The-Secret-to-Success-by-Achieving-More-with-Less |postscript=<!--none--> }}<br />
<br />
*{{Citation |title=Living the 80/20 Way: Work Less, Worry Less, Succeed More, Enjoy More |last=Koch |first=R. |authorlink= |year=2004 |publisher=Nicholas Brealey Publishing |location=London |isbn=1-85788-331-4 |pages= |url= |postscript=<!--none--> }}<br />
<br />
*{{Citation |last=Reed |first=W. J. |authorlink= |year=2001 |title=The Pareto, Zipf and other power laws |journal=Economics Letters |volume=74 |issue=1 |pages=15–19 |doi=10.1016/S0165-1765(01)00524-9 |url= |accessdate= |quote= |postscript=<!--none--> }}<br />
<br />
*{{Citation |doi=10.1016/0094-1190(80)90043-1 |authors=Rosen, K. T.; Resnick, M. |year=1980 |title=The size distribution of cities: an examination of the Pareto law and primacy |journal=Journal of Urban Economics |volume=8 |issue= 2|pages=165–186 |id= |url= https://escholarship.org/uc/item/9tt5c711|accessdate= |quote= |postscript=<!--none--> }}<br />
<br />
*{{citation |title=The handbook of logistics and distribution management |last1=Rushton |first1=A. |last2=Oxley|first2= J.|last3= Croucher|first3= P. |year=2000 |edition=2nd |publisher=Kogan Page |location=London |isbn=978-0-7494-3365-9 |postscript=<!--none-->}}.<br />
<br />
<br />
<br />
== External links ==<br />
外部链接<br />
*<br />
<br />
*<br />
<br />
{{Commons category|Pareto principle}}<br />
<br />
<br />
<br />
*[https://www.paretorule.cf/?m=1 ParetoRule.cf : Pareto Rule]<br />
<br />
*<br />
<br />
* [https://www.paretorule.cf/2018/12/the-pareto-Rule.html?m=1 ParetoRule.cf : The Pareto Rule]<br />
<br />
* [http://management.about.com/cs/generalmanagement/a/Pareto081202.htm About.com: Pareto's Principle]<br />
<br />
* [https://web.archive.org/web/20080528063231/http://www.ma.hw.ac.uk/~des/HWM00-26.pdf Wealth Condensation in Pareto Macro-Economies]<br />
<br />
* [http://buildthefire.com/pareto-principle-accomplishing-goals-with-purpose/ The Pareto Principle: Accomplishing goals with purpose]<br />
<br />
Category:Statistical laws<br />
<br />
类别: 统计法<br />
<br />
<br />
<br />
Category:Rules of thumb<br />
<br />
类别: 经验法则<br />
<br />
{{authority control}}<br />
<br />
Category:Tails of probability distributions<br />
<br />
类别: 概率分布的尾部<br />
<br />
<br />
<br />
Category:Statistical principles<br />
<br />
类别: 统计原则<br />
<br />
[[Category:Statistical laws]]<br />
<br />
Category:Adages<br />
<br />
分类: 格言<br />
<br />
[[Category:Rules of thumb]]<br />
<br />
Category:Vilfredo Pareto<br />
<br />
类别: Vilfredo Pareto<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Pareto principle]]. Its edit history can be viewed at [[80/20原则/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=80/20%E5%8E%9F%E5%88%99&diff=1439780/20原则2020-09-26T07:34:27Z<p>趣木木：</p>
<hr />
<div>本词条由11初步翻译<br />
<br />
{{for|the optimal allocation of resources|Pareto efficiency}}<br />
{{为了资源的优化配置|帕累托效率}}<br />
<br />
{{short description|Statistical principle about ratio of effects to causes}}<br />
{{简述|关于效果与原因之比的统计原则}}<br />
<br />
[[File:Pareto principle applied to community fundraising.jpg|thumb|right|Pareto principle applied to community fundraising]]<br />
[[文件:应用于社区筹款的帕累托原则.jpg|thumb|right|应用于社区筹款的帕累托原则]]<br />
<br />
Pareto principle applied to community fundraising<br />
<br />
应用于社区筹款的帕累托原则<br />
<br />
The '''Pareto principle''' (also known as the '''80/20 rule''', the '''law of the vital few,''' or the '''principle of factor sparsity''')<ref>{{cite news|url=https://www.nytimes.com/2008/03/03/business/03juran.html|title=Joseph Juran, 103, Pioneer in Quality Control, Dies|last1=Bunkley|first1=Nick|date=March 3, 2008|work=New York Times|accessdate=25 January 2018|archiveurl=https://web.archive.org/web/20170906182706/http://www.nytimes.com/2008/03/03/business/03juran.html|archivedate=September 6, 2017}}</ref><ref>{{cite journal|last1=Box|first1=George E.P.|last2=Meyer|first2=R. Daniel|date=1986|title=An Analysis for Unreplicated Fractional Factorials|journal=Technometrics|volume=28|issue=1|pages=11–18|doi=10.1080/00401706.1986.10488093}}</ref> states that, for many events, roughly 80% of the effects come from 20% of the causes.<ref name="NYT">{{cite news|url=https://www.nytimes.com/2008/03/03/business/03juran.html|title=Joseph Juran, 103, Pioneer in Quality Control, Dies|last=Bunkley|first=Nick|date=March 3, 2008|work=[[The New York Times]]}}</ref> <br />
<br />
The Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes. <br />
<br />
'''<font color="#ff8000"> 帕累托原则</font>'''（又称80/20法则、至关重要的少数人法则或因素稀少原则）指出，对于许多事件，大约80%的影响来自20%的原因。<br />
<br />
<br />
<br />
[[Management consultant]] [[Joseph M. Juran]] suggested the principle and named it after Italian [[economist]] [[Vilfredo Pareto]], who noted the 80/20 connection while at the [[University of Lausanne]] in 1896. In his first work, ''Cours d'économie politique'', Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. The Pareto principle is only tangentially related to [[Pareto efficiency]]. Pareto developed both concepts in the context of the [[distribution of income]] and wealth among the population.<br />
<br />
Management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who noted the 80/20 connection while at the University of Lausanne in 1896. In his first work, Cours d'économie politique, Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. The Pareto principle is only tangentially related to Pareto efficiency. Pareto developed both concepts in the context of the distribution of income and wealth among the population.<br />
<br />
管理顾问 Joseph M. Juran 提出了这个原则，并以意大利经济学家 Vilfredo Pareto 的名字命名，后者于1896年在洛桑大学指出了80/20的联系。帕雷托在他的第一部著作《政治经济学》中指出，意大利约80% 的土地为20% 的人口所拥有。帕雷托原则与帕累托最优的相关性不大。帕累托在人口的收入和财富分配的背景下发展出了这两个概念。<br />
<br />
<br />
<br />
Mathematically, the 80/20 rule is roughly followed by a [[power law]] distribution (also known as a [[Pareto distribution]]) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution.<ref>{{cite journal|url=https://arxiv.org/PS_cache/cond-mat/pdf/0412/0412004v3.pdf|title=Power laws, Pareto Distributions, and Zipf's law|journal=Contemporary Physics|volume=46|issue=5|pages=323–351|last=Newman|first=MEJ|access-date=10 April 2011|bibcode=2005ConPh..46..323N|year=2005|arxiv=cond-mat/0412004|doi=10.1080/00107510500052444|s2cid=202719165}}</ref> It is an axiom of business management that "80% of sales come from 20% of clients".<ref>{{Cite news|last=Marshall|first=Perry|url=https://www.entrepreneur.com/article/229294|title=The 80/20 Rule of Sales: How to Find Your Best Customers|date=2013-10-09|work=Entrepreneur|access-date=2018-01-05|language=en}}</ref><br />
<br />
Mathematically, the 80/20 rule is roughly followed by a power law distribution (also known as a Pareto distribution) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution. It is an axiom of business management that "80% of sales come from 20% of clients".<br />
<br />
在数学上，80/20原则对于一组特定的参数大致遵循'''<font color="#ff8000"> 幂律分布</font>'''(也称为'''<font color="#ff8000"> 帕累托分布</font>''') ，许多自然现象已经由试验证明呈现这样的分布。“80% 的销售额来自20% 的客户”是企业管理的一条公理。<br />
<br />
<br />
<br />
== In economics ==<br />
在经济学中<br />
<br />
<br />
<br />
The original observation was in connection with population and wealth. Pareto noticed that approximately 80% of Italy's land was owned by 20% of the population.<ref>{{citation|title=''Translation of'' Manuale di economia politica ("Manual of political economy") |first1=Vilfredo|last1=Pareto|first2=Alfred N.|last2=Page|publisher=A.M. Kelley|year=1971|isbn=978-0-678-00881-2|postscript=<!--none-->}}</ref> He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.<br />
<br />
The original observation was in connection with population and wealth. Pareto noticed that approximately 80% of Italy's land was owned by 20% of the population. He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.<br />
<br />
最初的观察结果与人口和财富有关。帕累托注意到，意大利约80% 的土地为20% 的人口所拥有。他随后对许多其他国家进行了调查，令他惊讶的是，类似的分布也同样适用。<br />
<br />
<br />
<br />
A chart that gave the inequality a very visible and comprehensible form, the so-called "champagne glass" effect,<ref>{{citation|first=Xabier|last=Gorostiaga|title=World has become a 'champagne glass' globalization will fill it fuller for a wealthy few|journal=National Catholic Reporter|date=January 27, 1995|postscript=<!--none-->}}</ref> was contained in the 1992 [[United Nations Development Programme|United Nations Development Program]] Report, which showed that distribution of global income is very uneven, with the richest 20% of the world's population controlling 82.7% of the world's income.<ref>{{citation|author=United Nations Development Program|title=1992 Human Development Report|year=1992|location=New York|publisher=Oxford University Press|postscript=<!--none-->}}</ref> Still, the [[Gini index]] of the world shows that nations have wealth distributions that vary greatly.<br />
<br />
A chart that gave the inequality a very visible and comprehensible form, the so-called "champagne glass" effect, was contained in the 1992 United Nations Development Program Report, which showed that distribution of global income is very uneven, with the richest 20% of the world's population controlling 82.7% of the world's income. Still, the Gini index of the world shows that nations have wealth distributions that vary greatly.<br />
<br />
1992年《联合国开发计划署报告》中的一张图表以非常明显和易懂的形式呈现了不平等，即所谓的 "香槟酒杯 "效应，该图表显示，全球收入分配非常不均衡，世界上最富有的20% 人口控制着82.7%的世界收入。不过，世界基尼系数显示，各国的财富分配差异很大。<br />
<br />
<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class = “ wikitable”<br />
<br />
|+ Distribution of world GDP, 1989<ref name="1992 Human Development Report, Chapter 3">{{citation|url=http://hdr.undp.org/en/reports/global/hdr1992/chapters/|title=Human Development Report 1992, Chapter 3|accessdate=2007-07-08|postscript=<!--none-->}}</ref><br />
<br />
|+ Distribution of world GDP, 1989<br />
<br />
| + 世界 GDP 分布，1989年<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="col" | Quintile of population<br />
<br />
! scope="col" | Quintile of population<br />
<br />
!范围 = “ col” | 五分之一人口<br />
<br />
! scope="col" | Income<br />
<br />
! scope="col" | Income<br />
<br />
!范围 = “ col” | 收入<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Richest 20%<br />
<br />
| Richest 20%<br />
<br />
最富有的20% <br />
<br />
| 82.70%<br />
<br />
| 82.70%<br />
<br />
| 82.70%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Second 20%<br />
<br />
| Second 20%<br />
<br />
第二个20% <br />
<br />
| 11.75%<br />
<br />
| 11.75%<br />
<br />
| 11.75%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Third 20%<br />
<br />
| Third 20%<br />
<br />
第三20% <br />
<br />
| 2.30%<br />
<br />
| 2.30%<br />
<br />
| 2.30%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Fourth 20%<br />
<br />
| Fourth 20%<br />
<br />
第四个20% <br />
<br />
| 1.85%<br />
<br />
| 1.85%<br />
<br />
| 1.85%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Poorest 20%<br />
<br />
| Poorest 20%<br />
<br />
最穷的20% <br />
<br />
| 1.40%<br />
<br />
| 1.40%<br />
<br />
| 1.40%<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
The Pareto principle also could be seen as applying to taxation. In the US, the top 20% of earners have paid roughly 80-90% of Federal income taxes in 2000 and 2006,<ref>Curtis Dubay (May 4, 2009) [https://www.heritage.org/poverty-and-inequality/report/the-rich-pay-more-taxes-top-20-percent-pay-record-share-income-taxes The Rich Pay More Taxes: Top 20 Percent Pay Record Share of Income Taxes], Heritage.org, accessed 12 April 2018</ref> and again in 2018.<ref>Laura Sanders (April 6, 2018) [https://www.wsj.com/articles/top-20-of-americans-will-pay-87-of-income-tax-1523007001 Top 20% of Americans Will Pay 87% of Income Tax], Wall Street Journal, accessed 12 April 2018</ref><br />
<br />
The Pareto principle also could be seen as applying to taxation. In the US, the top 20% of earners have paid roughly 80-90% of Federal income taxes in 2000 and 2006, and again in 2018.<br />
<br />
欧洲帕雷托法则也可以被视为适用于税收。在美国，收入最高的20%的人在2000年和2006年缴纳了大约80%-90%的联邦所得税，2018年又是如此。<br />
<br />
<br />
<br />
However, it is important to note that while there have been associations of such with [[meritocracy]], the principle should not be confused with further reaching implications. As Alessandro Pluchino at the University of Catania in Italy points out, other attributes do not necessarily correlate. Using talent as an example, he and other researchers state, “The maximum success never coincides with the maximum talent, and vice-versa,” and that such factors are the result of chance.<ref>Emerging Technology from the arXiv (March 1, 2018) [https://www.technologyreview.com/s/610395/if-youre-so-smart-why-arent-you-rich-turns-out-its-just-chance/ If you’re so smart, why aren’t you rich? Turns out it’s just chance.], TechnologyReview.com, accessed 1 January 2019</ref><br />
<br />
However, it is important to note that while there have been associations of such with meritocracy, the principle should not be confused with further reaching implications. As Alessandro Pluchino at the University of Catania in Italy points out, other attributes do not necessarily correlate. Using talent as an example, he and other researchers state, “The maximum success never coincides with the maximum talent, and vice-versa,” and that such factors are the result of chance.<br />
<br />
然而，必须指出的是，虽然有这与精英管理体制有联系，但这一原则不应与进一步的影响混为一谈。正如意大利卡塔尼亚大学的 Alessandro Pluchino 指出的那样，其他属性并不一定相互关联。以天赋为例，他和其他研究人员指出，“最大的成功从来没有与最大的天赋相吻合，反之亦然”，这样的因素是偶然的结果。<br />
<br />
<br />
The physicist Victor Yakovenko of the [[University of Maryland, College Park]] and AC Silva analyzed income data from the US Internal Revenue Service from 1983 to 2001, and found that the income distribution among the upper class (1–3% of the population) follows Pareto's principle.<ref>{{Citation|last1=Yakovenko|first1=Victor M.|title=Two-class Structure of Income Distribution in the USA: Exponential Bulk and Power-law Tail|date=2005|work=Econophysics of Wealth Distributions: Econophys-Kolkata I|pages=15–23|editor-last=Chatterjee|editor-first=Arnab|series=New Economic Windows|publisher=Springer Milan|language=en|doi=10.1007/88-470-0389-x_2|isbn=978-88-470-0389-7|last2=Silva|first2=A. Christian|editor2-last=Yarlagadda|editor2-first=Sudhakar|editor3-last=Chakrabarti|editor3-first=Bikas K.}}</ref><br />
<br />
The physicist Victor Yakovenko of the University of Maryland, College Park and AC Silva analyzed income data from the US Internal Revenue Service from 1983 to 2001, and found that the income distribution among the upper class (1–3% of the population) follows Pareto's principle.<br />
<br />
马里兰大学学院帕克分校的物理学家Victor Yakovenko和AC Silva分析了美国国税局1983年到2001年的收入数据，发现上层阶级(占总人口的1-3%)的收入分配遵循帕累托原则。<br />
<br />
<br />
<br />
== In computing ==<br />
在计算领域<br />
<br />
In [[computer science]] the Pareto principle can be applied to [[optimization (computer science)|optimization]] efforts.<ref name=optimization>{{citation|first1=M.|last1=Gen|first2=R.|last2=Cheng|title=Genetic Algorithms and Engineering Optimization|location=New York|publisher=Wiley|year=2002|postscript=<!--none-->}}</ref> For example, [[Microsoft]] noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated.<ref>{{citation|url=http://www.crn.com/news/security/18821726/microsofts-ceo-80-20-rule-applies-to-bugs-not-just-features.htm|title=Microsoft's CEO: 80–20 Rule Applies To Bugs, Not Just Features|first=Paula|last=Rooney|date=October 3, 2002|publisher=ChannelWeb|postscript=<!--none-->}}</ref> [[Lowell Arthur]] expressed that "20 percent of the code has 80 percent of the errors. Find them, fix them!"<ref>Pressman, Roger S. (2010). Software Engineering: A Practitioner's Approach (7th ed.). Boston, Mass: McGraw-Hill, 2010. {{ISBN|978-0-07-337597-7}}.</ref> It was also discovered that in general the 80% of a certain piece of software can be written in 20% of the total allocated time. Conversely, the hardest 20% of the code takes 80% of the time. This factor is usually a part of [[COCOMO]] estimating for software coding.<br />
<br />
In computer science the Pareto principle can be applied to optimization efforts. For example, Microsoft noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated. Lowell Arthur expressed that "20 percent of the code has 80 percent of the errors. Find them, fix them!" It was also discovered that in general the 80% of a certain piece of software can be written in 20% of the total allocated time. Conversely, the hardest 20% of the code takes 80% of the time. This factor is usually a part of COCOMO estimating for software coding.<br />
<br />
在计算机科学中，帕雷托原则可以应用于优化工作。例如，微软指出，通过修复前20%的报告最多的错误，可以消除给定系统中80%的相关错误和崩溃。Lowell Arthur表示“20% 的代码有80% 的错误。找到它们，修复它们!”人们还发现，一般来说，某个软件的80%可以在总分配时间的20%内编写完。相反，最难的20%的代码占用了80%的时间。这个因素通常是软件编码的COCOMO估算的一部分。<br />
<br />
<br />
<br />
== In sports ==<br />
在体育领域<br />
<br />
It has been inferred that the Pareto principle applies to athletic training, where roughly 20% of the exercises and habits have 80% of the impact, and the trainee should not focus so much on a varied training.<ref>{{citation |url= http://speedendurance.com/2008/11/20/training-and-the-80-20-rule-of-paretos-principle/ |title=Training and the 80-20 rule of Pareto's Principle |date=21 November 2008 }}</ref> This does not necessarily mean that having a healthy diet or going to the gym are not important, but they are not as significant as the key activities. It is also important to note this 80/20 rule has yet to be scientifically tested in controlled studies of athletic training.<br />
<br />
It has been inferred that the Pareto principle applies to athletic training, where roughly 20% of the exercises and habits have 80% of the impact, and the trainee should not focus so much on a varied training. This does not necessarily mean that having a healthy diet or going to the gym are not important, but they are not as significant as the key activities. It is also important to note this 80/20 rule has yet to be scientifically tested in controlled studies of athletic training.<br />
<br />
据推测，帕雷托原则适用于运动训练，其中大约20%的训练和习惯有80%的影响，受训者不应该过多地注重多样化的训练。这并不一定意味着健康饮食或去健身房不重要，只是它们不如那些关键活动重要。另外需要注意的是，这个80/20原则还没有在运动训练的对照研究中得到科学验证。<br />
<br />
<br />
<br />
In [[baseball]], the Pareto principle has been perceived in [[Wins Above Replacement]] (an attempt to combine multiple statistics to determine a player's overall importance to a team). "15% of all the players last year produced 85% of the total wins with the other 85% of the players creating 15% of the wins. The Pareto principle holds up pretty soundly when it is applied to baseball."<ref>Jeff Zimmerman (Jun 4, 2010). [https://www.beyondtheboxscore.com/2010/6/4/1501048/applying-the-parento-principle-80 Applying the Pareto Principle (80-20 Rule) to Baseball], BeyondTheBoxScore.com, accessed 12 April 2018</ref><br />
<br />
In baseball, the Pareto principle has been perceived in Wins Above Replacement (an attempt to combine multiple statistics to determine a player's overall importance to a team). "15% of all the players last year produced 85% of the total wins with the other 85% of the players creating 15% of the wins. The Pareto principle holds up pretty soundly when it is applied to baseball."<br />
<br />
在棒球比赛中，帕雷托原则已经在Wins Above Replacement(试图结合多种统计数据来确定一个球员对一个球队的整体重要性)中被认识到。“去年15%的球员创造了85%的总胜利，其他85%的球员创造了15%的胜利。帕雷托原则在棒球比赛中得到了充分体现。”<br />
<br />
<br />
<br />
== Occupational health and safety ==<br />
职业健康和安全<br />
<br />
[[Occupational health and safety]] professionals use the Pareto principle to underline the importance of hazard prioritization. Assuming 20% of the hazards account for 80% of the injuries, and by categorizing hazards, safety professionals can target those 20% of the hazards that cause 80% of the injuries or accidents. Alternatively, if hazards are addressed in random order, a safety professional is more likely to fix one of the 80% of hazards that account only for some fraction of the remaining 20% of injuries.<ref>{{cite book |last=Woodcock |first=Kathryn |title=Safety Evaluation Techniques |year=2010 |publisher= Ryerson University |location= Toronto, ON |pages=86 |url= http://www.ryerson.ca/woodcock/}}</ref><br />
<br />
Occupational health and safety professionals use the Pareto principle to underline the importance of hazard prioritization. Assuming 20% of the hazards account for 80% of the injuries, and by categorizing hazards, safety professionals can target those 20% of the hazards that cause 80% of the injuries or accidents. Alternatively, if hazards are addressed in random order, a safety professional is more likely to fix one of the 80% of hazards that account only for some fraction of the remaining 20% of injuries.<br />
<br />
职业健康和安全方面的专业人士使用帕雷托原则来强调危害优先级的重要性。假设20% 的危险占伤害的80% ，通过对危险进行分类，安全专业人员可以有针对性地解决造成80%伤害或事故的那20%的危害。或者，如果危害按随机顺序处理，安全专业人员更有可能解决那80%的危害中的一个，而这个危害只占其余20%伤害的某一部分。<br />
<br />
<br />
<br />
Aside from ensuring efficient accident prevention practices, the Pareto principle also ensures hazards are addressed in an economical order, because the technique ensures the utilized resources are best used to prevent the most accidents.<ref name=USCG001>{{cite web|title=Introduction to Risk-based Decision-Making |url= http://www.uscg.mil/hq/cg5/cg5211/docs/RBDM_Files/PDF/RBDM_Guidelines/Volume%202/Volume%202-Chapter%206.pdf |work=USCG Safety Program |publisher= United States Coast Guard |accessdate= 14 January 2012}}</ref><br />
<br />
Aside from ensuring efficient accident prevention practices, the Pareto principle also ensures hazards are addressed in an economical order, because the technique ensures the utilized resources are best used to prevent the most accidents.<br />
<br />
除了确保有效的事故预防措施，帕雷托法则安全管理局原则还能确保以经济的顺序处理危险，因为该技术能确保所利用的资源被最好地用于预防最多的事故。<br />
<br />
<br />
== Other applications ==<br />
其他应用<br />
<br />
In engineering control theory, such as for electromechanical energy converters, the 80/20 principle applies to optimization efforts.<ref name=optimization/><br />
<br />
In engineering control theory, such as for electromechanical energy converters, the 80/20 principle applies to optimization efforts.<br />
<br />
在工程控制理论中，如对于机电式能量转换器，80/20原则适用于优化工作。<br />
<br />
<br />
<br />
The law of the few can be also seen in betting, where it is said that with 20% effort you can match the accuracy of 80% of the bettors.<ref>{{citation|title=The Pareto Principle of Prediction|url=https://www.pinnacle.com/en/betting-articles/betting-strategy/the-pareto-principle-of-prediction}}</ref><br />
<br />
In the systems science discipline, Joshua M. Epstein and Robert Axtell created an agent-based simulation model called Sugarscape, from a decentralized modeling approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 principle became emergent in their results, which suggests the principle is a collective consequence of these individual rules.<br />
<br />
在系统科学领域，Joshua M. Epstein和Robert Axtell从分散建模方法出发，基于为经济中的每个代理人定义的个人行为规则创建了创建了一个名为Sugarscape的基于代理的仿真模型。财富分配原则和帕累托80/20原则在其结果中突现，这表明这一原则是这些个体规则的集体结果。<br />
<br />
<br />
<br />
In the systems science discipline, [[Joshua M. Epstein]] and [[Robert Axtell]] created an [[Agent-based social simulation|agent-based simulation]] model called [[Sugarscape]], from a [[Decentralised system|decentralized modeling]] approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 principle became emergent in their results, which suggests the principle is a collective consequence of these individual rules.<ref>{{Citation|last1=Epstein|first1=Joshua|title=Growing Artificial Societies: Social Science from the Bottom-Up|url=https://books.google.com/books?id=xXvelSs2caQC|page=208|year=1996|postscript=<!--none-->|publisher=[[MIT Press]]|isbn=0-262-55025-3|last2=Axtell|first2=Robert}}<br />
<br />
The Pareto principle has many applications in quality control. It is the basis for the Pareto chart, one of the key tools used in total quality control and Six Sigma techniques. The Pareto principle serves as a baseline for ABC-analysis and XYZ-analysis, widely used in logistics and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.<br />
<br />
帕雷托原则在质量控制方面有很多应用。它是帕累托图的基础，帕累托图是用于全面质量控制和六西格玛技术的关键工具之一。帕雷托原则分析作为ABC分析法和XYZ分析法的基准，广泛应用于物流和采购，目的是优化库存以及保存和补充库存的成本。<br />
<br />
</ref><br />
<br />
<br />
<br />
In health care in the United States, in one instance 20% of patients have been found to use 80% of health care resources.<br />
<br />
在美国的医疗服务中，一个事例发现20%的病人使用了80%的医疗资源。<br />
<br />
The Pareto principle has many applications in quality control.<ref>{{Cite book|url=https://books.google.com/books?id=QtVmCgAAQBAJ&pg=PA8&lpg=PA8&dq=The+Pareto+principle+has+many+applications+in+quality+control#v=onepage|title=The Pareto Principle for Business Management: Expand your business with the 80/20 rule|last=50MINUTES.COM|date=2015-08-17|publisher=50 Minutes|isbn=9782806265869|language=en}}</ref> It is the basis for the [[Pareto chart]], one of the key tools used in [[total quality management|total quality control]] and [[Six Sigma]] techniques. The Pareto principle serves as a baseline for [[time management#abc analysis|ABC-analysis]] and XYZ-analysis, widely used in [[logistics]] and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.<ref>{{harvtxt|Rushton|Oxley|Croucher|2000}}, pp. 107–108.</ref><br />
<br />
<br />
<br />
Some cases of super-spreading conform to the 20/80 rule, where approximately 20% of infected individuals are responsible for 80% of transmissions, although super-spreading can still be said to occur when super-spreaders account for a higher or lower percentage of transmissions. In epidemics with super-spreading, the majority of individuals infect relatively few secondary contacts.<br />
<br />
一些超级传播病例符合20/80原则，其中大约20%的感染者要为80%的传播负责，尽管当超级传播者占传播的比例较高或较低时，仍然可以说发生了超级传播。在超级传播的流行病中，大多数个体感染的二次接触者相对较少。<br />
<br />
In health care in the United States, in one instance 20% of patients have been found to use 80% of health care resources.<ref>[http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html Myrl Weinberg: In health-care reform, the 20-80 solution | Contributors | projo.com | The Providence Journal<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20090802002952/http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|date=2009-08-02}}</ref><ref>{{cite web|url=http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|archiveurl=https://archive.today/20090802002952/http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|url-status=dead|title=Myrl Weinberg: In health-care reform, the 20-80 solution - Contributo…|date=2 August 2009|archivedate=2 August 2009|website=archive.li}}</ref><ref>{{cite web |last1=Sawyer and Claxton |first1=Bradley and Gary |title=How do health expenditures vary across the population? |url=https://www.healthsystemtracker.org/chart-collection/health-expenditures-vary-across-population/#item-discussion-of-health-spending-often-focus-on-averages-but-a-small-share-of-the-population-incurs-most-of-the-cost_2016 |website=Peterson-Kaiser Health System Tracker |publisher=Peterson Center on Healthcare and the Kaiser Family Foundation |accessdate=13 March 2019}}</ref><br />
<br />
<br />
<br />
The Dunedin Study has found 80% of crimes are committed by 20% of criminals. This statistic has been used to support both stop-and-frisk policies and broken windows policing, as catching those criminals committing minor crimes will supposedly net many criminals wanted for (or who would normally commit) larger ones.<br />
<br />
达尼丁研究发现80%的犯罪是20%的罪犯所为。这一统计数据被用来支持拦截搜查政策和破窗执法，因为抓获那些犯有轻罪的罪犯，可能会让许多想犯(或通常会犯)重罪的通缉犯落网。<br />
<br />
Some cases of [[Super-spreader|super-spreading]] conform to the 20/80 rule,<ref>{{cite journal|last1=Galvani|first1=Alison P.|last2=May|first2=Robert M.|year=2005|title=Epidemiology: Dimensions of superspreading|url=|journal=Nature|volume=438|issue=7066|pages=293–295|doi=10.1038/438293a|pmid=16292292|bibcode=2005Natur.438..293G|pmc=7095140}}</ref> where approximately 20% of infected individuals are responsible for 80% of transmissions, although super-spreading can still be said to occur when super-spreaders account for a higher or lower percentage of transmissions.<ref name="Lloyd-Smith JO 2005">{{cite journal|last1=Lloyd-Smith|first1=JO|last2=Schreiber|first2=SJ|last3=Kopp|first3=PE|last4=Getz|first4=WM|year=2005|title=Superspreading and the effect of individual variation on disease emergence|url=|journal=Nature|volume=438|issue=7066|pages=355–359|doi=10.1038/nature04153|pmid=16292310|bibcode=2005Natur.438..355L|pmc=7094981}}</ref> In [[epidemic]]s with super-spreading, the majority of individuals infect relatively few [[contact tracing|secondary contacts]].<br />
<br />
<br />
<br />
Many video rental shops reported in 1988 that 80% of revenue came from 20% of videotapes. A video-chain executive discussed the "Gone with the Wind syndrome", however, in which every store had to offer classics like Gone with the Wind, Casablanca, or The African Queen to appear to have a large inventory, even if customers very rarely rented them.<br />
<br />
1988年，许多录像带出租店报告说，80%的收入来自20%的录像带。然而，一家视频连锁店的高管谈到了“乱世佳人综合症”，即每家商店都必须提供《飘》、《卡萨布兰卡》或《非洲女王号》等经典影片，以显得其库存庞大，即使顾客很少租用这些影片。<br />
<br />
The [[Dunedin Multidisciplinary Health and Development Study|Dunedin Study]] has found 80% of crimes are committed by 20% of criminals.<ref>{{Citation|last=Nicola|first=Davis|title='High social cost' adults can be predicted from as young as three, says study|url=https://www.theguardian.com/science/2016/dec/12/high-social-cost-adults-can-be-identified-from-as-young-as-three-says-study|year=2016|postscript=<!--none-->|publisher=[[The Guardian]]}}<br />
<br />
</ref> This statistic has been used to support both [[stop-and-frisk]] policies and [[broken windows]] policing, as catching those criminals committing minor crimes will supposedly net many criminals wanted for (or who would normally commit) larger ones.<br />
<br />
<br />
<br />
Many [[video rental shop]]s reported in 1988 that 80% of revenue came from 20% of videotapes. A video-chain executive discussed the "''Gone with the Wind'' syndrome", however, in which every store had to offer classics like ''[[Gone with the Wind (film)|Gone with the Wind]]'', ''[[Casablanca (film)|Casablanca]]'', or ''[[The African Queen (film)|The African Queen]]'' to appear to have a large inventory, even if customers very rarely rented them.<ref name="kleinfield19880501">{{Cite news |url=https://www.nytimes.com/1988/05/01/business/a-tight-squeeze-at-video-stores.html |title=A Tight Squeeze at Video Stores |last=Kleinfield |first=N. R. |date=1988-05-01 |work=The New York Times |access-date=2019-02-08 |language=en-US |issn=0362-4331}}</ref><br />
<br />
The idea has a rule of thumb application in many places, but it is commonly misused. For example, it is a misuse to state a solution to a problem "fits the 80/20 rule" just because it fits 80% of the cases; it must also be that the solution requires only 20% of the resources that would be needed to solve all cases. Additionally, it is a misuse of the 80/20 rule to interpret a small number of categories or observations.<br />
<br />
这个想法在很多地方都有经验法则的应用，但它通常被误用。例如，仅仅因为一个问题的解决方案符合80/20原则，就声称其“符合80/20原则” ，这是一种误用;该解决方案还必须只需要解决所有案例所需资源的20% 。此外，用80/20原则来解释少数类别或意见也是一种滥用。<br />
<br />
<br />
<br />
== Mathematical notes ==<br />
数学说明<br />
<br />
This is a special case of the wider phenomenon of Pareto distributions. If the Pareto index&nbsp;α, which is one of the parameters characterizing a Pareto distribution, is chosen as α&nbsp;=&nbsp;log45&nbsp;≈&nbsp;1.16, then one has 80% of effects coming from 20% of causes.<br />
<br />
这是更广泛的帕累托分布现象的一个特例。如果选择帕累托指数α作为帕累托分布的参数之一，α=log45≈1.16，那么80%的效应来自20%的原因。<br />
<br />
{{or-section|date=May 2020}}<br />
<br />
The idea has a rule of thumb application in many places, but it is commonly misused. For example, it is a misuse to state a solution to a problem "fits the 80/20 rule" just because it fits 80% of the cases; it must also be that the solution requires only 20% of the resources that would be needed to solve all cases. Additionally, it is a misuse of the 80/20 rule to interpret a small number of categories or observations.<br />
<br />
It follows that one also has 80% of that top 80% of effects coming from 20% of that top 20% of causes, and so on. Eighty percent of 80% is 64%; 20% of 20% is 4%, so this implies a "64/4" law; and similarly implies a "51.2/0.8" law. Similarly for the bottom 80% of causes and bottom 20% of effects, the bottom 80% of the bottom 80% only cause 20% of the remaining 20%. This is broadly in line with the world population/wealth table above, where the bottom 60% of the people own 5.5% of the wealth, approximating to a 64/4 connection.<br />
<br />
因此，前80%的影响中，有80%来自前20%的原因，以此类推。80%的80%是64%，20%的20%是4%，所以这意味着一个“64/4”原则，同样意味着一个“51.2/0.8”原则。同样，对于底层80% 的原因和底层20%的结果，底层80%的80%只造成剩下的20%的20% 。这与上面的世界人口财富表基本一致，那里底层60%的人拥有5.5%的财富，接近于64/4的联系。<br />
<br />
<br />
<br />
This is a special case of the wider phenomenon of [[Pareto distribution]]s. If the [[Pareto index]]&nbsp;'''α''', which is one of the parameters characterizing a Pareto distribution, is chosen as '''α'''&nbsp;=&nbsp;log<sub>4</sub>5&nbsp;≈&nbsp;1.16, then one has 80% of effects coming from 20% of causes.<br />
<br />
The 64/4 correlation also implies a 32% 'fair' area between the 4% and 64%, where the lower 80% of the top 20% (16%) and upper 20% of the bottom 80% (also 16%) relates to the corresponding lower top and upper bottom of effects (32%). This is also broadly in line with the world population table above, where the second 20% control 12% of the wealth, and the bottom of the top 20% (presumably) control 16% of the wealth.<br />
<br />
64/4的相关性还意味着在4%和64%之间有32%的”公平”区域，其中前20% 的后80%(16%)和后80%的前20% (也是16%)与相应的下层和上层的效果（32%）有关。这也与上面的世界人口表基本一致，其中第二层的20%控制着12%的财富，前20%的底层(大概)控制着16%的财富。<br />
<br />
<br />
<br />
It follows that one also has 80% of that top 80% of effects coming from 20% of that top 20% of causes, and so on. Eighty percent of 80% is 64%; 20% of 20% is 4%, so this implies a "64/4" law; and similarly implies a "51.2/0.8" law. Similarly for the bottom 80% of causes and bottom 20% of effects, the bottom 80% of the bottom 80% only cause 20% of the remaining 20%. This is broadly in line with the world population/wealth table above, where the bottom 60% of the people own 5.5% of the wealth, approximating to a 64/4 connection.<br />
<br />
The term 80/20 is only a shorthand for the general principle at work. In individual cases, the distribution could just as well be, say, nearer to 90/10 or 70/30. There is no need for the two numbers to add up to the number 100, as they are measures of different things, (e.g., 'number of customers' vs 'amount spent'). However, each case in which they do not add up to 100%, is equivalent to one in which they do. For example, as noted above, the "64/4 law" (in which the two numbers do not add up to 100%) is equivalent to the "80/20 law" (in which they do add up to 100%). Thus, specifying two percentages independently does not lead to a broader class of distributions than what one gets by specifying the larger one and letting the smaller one be its complement relative to 100%. Thus, there is only one degree of freedom in the choice of that parameter.<br />
<br />
术语80/20只是一般工作原则的简写。在个别情况下，分布也可能接近90/10或70/30。这两个数字加起来不必等于100，因为它们是对不同事物的度量(例如，“客户数量”和“消费金额”)。然而，每一个他们加起来不到100%的情况，都等同于他们加起来是100%的情况。例如，如上文所述，“64/4法则”(两个数字之和不等于100%)相当于80/20原则(两者之和等于100%)。因此，单独指定两个百分比并不会比指定较大的百分比并让较小的百分比作为其相对于100% 的补充得到更广泛的一类分布。因此，在选择该参数时只有一个自由度。<br />
<br />
<br />
<br />
The 64/4 correlation also implies a 32% 'fair' area between the 4% and 64%, where the lower 80% of the top 20% (16%) and upper 20% of the bottom 80% (also 16%) relates to the corresponding lower top and upper bottom of effects (32%). This is also broadly in line with the world population table above, where the second 20% control 12% of the wealth, and the bottom of the top 20% (presumably) control 16% of the wealth.<br />
<br />
Adding up to 100 leads to a nice symmetry. For example, if 80% of effects come from the top 20% of sources, then the remaining 20% of effects come from the lower 80% of sources. This is called the "joint ratio", and can be used to measure the degree of imbalance: a joint ratio of 96:4 is extremely imbalanced, 80:20 is highly imbalanced (Gini index: 76%), 70:30 is moderately imbalanced (Gini index: 28%), and 55:45 is just slightly imbalanced (Gini index 14%).<br />
<br />
100加起来就是一个完美的对称。例如，如果80%的影响来自前20%的来源，那么剩下的20%的影响来自后80%的来源。这就是所谓的“联合比率” ，可以用来衡量不平衡的程度: 96:4的联合比率极不平衡，80:20的联合比率高度不平衡(基尼指数: 76%) ，70:30的联合比率中度不平衡(基尼指数: 28%) ，55:45的联合比率略不平衡(基尼指数14%)。<br />
<br />
<br />
<br />
The term 80/20 is only a shorthand for the general principle at work. In individual cases, the distribution could just as well be, say, nearer to 90/10 or 70/30. There is no need for the two numbers to add up to the number 100, as they are measures of different things, (e.g., 'number of customers' vs 'amount spent'). However, each case in which they do not add up to 100%, is equivalent to one in which they do. For example, as noted above, the "64/4 law" (in which the two numbers do not add up to 100%) is equivalent to the "80/20 law" (in which they do add up to 100%). Thus, specifying two percentages independently does not lead to a broader class of distributions than what one gets by specifying the larger one and letting the smaller one be its complement relative to 100%. Thus, there is only one degree of freedom in the choice of that parameter.<br />
<br />
The Pareto principle is an illustration of a "power law" relationship, which also occurs in phenomena such as brush fires and earthquakes.<br />
<br />
帕累托原则是“幂律”关系的一个例证，这种关系也发生在诸如丛林火灾和地震等现象中。<br />
<br />
<br />
<br />
Because it is self-similar over a wide range of magnitudes, it produces outcomes completely different from Normal or Gaussian distribution phenomena. This fact explains the frequent breakdowns of sophisticated financial instruments, which are modeled on the assumption that a Gaussian relationship is appropriate to something like stock price movements.<br />
<br />
因为它在很大范围内是自相似的，所以它产生的结果与正态或高斯分布现象完全不同。这一事实解释了复杂金融工具频繁崩溃的原因，因为这些金融工具是建立在高斯关系适用于类似股票价格波动的假设之上的。<br />
<br />
Adding up to 100 leads to a nice symmetry. For example, if 80% of effects come from the top 20% of sources, then the remaining 20% of effects come from the lower 80% of sources. This is called the "joint ratio", and can be used to measure the degree of imbalance: a joint ratio of 96:4 is extremely imbalanced, 80:20 is highly imbalanced ([[Gini index]]: 76%), 70:30 is moderately imbalanced (Gini index: 28%), and 55:45 is just slightly imbalanced (Gini index 14%).<br />
<br />
<br />
<br />
The Pareto principle is an illustration of a "[[power law]]" relationship, which also occurs in phenomena such as [[brush fire]]s and earthquakes.<ref>{{Citation|last=Bak|first=Per|title=How Nature Works: the science of self-organized criticality|page=89|year=1999|publisher=Springer|isbn=0-387-94791-4|authorlink=Per Bak}}</ref><br />
<br />
Because it is self-similar over a wide range of magnitudes, it produces outcomes completely different from [[Normal distribution|Normal or Gaussian distribution]] phenomena. This fact explains the frequent breakdowns of sophisticated financial instruments, which are modeled on the assumption that a Gaussian relationship is appropriate to something like stock price movements.<ref>{{Citation|last=Taleb|first=Nassim|title=The Black Swan|pages=229–252, 274–285|year=2007|postscript=<!--none-->|authorlink=Nassim Taleb|title-link=The Black Swan (Taleb book)}}</ref><br />
<br />
<br />
<br />
== Equality measures ==<br />
平等措施<br />
<br />
Using the "A&nbsp;:&nbsp;B" notation (for example, 0.8:0.2) and with&nbsp;A&nbsp;+&nbsp;B&nbsp;=&nbsp;1, inequality measures like the Gini index (G) and the Hoover index (H) can be computed. In this case both are the same.<br />
<br />
使用“A:B”符号(例如，0.8:0.2)和a+b=1，可以计算基尼指数(G)和胡佛指数(H)等不平等度量。在这种情况下，两者是相同的。<br />
<br />
<br />
<br />
=== Gini coefficient and Hoover index ===<br />
基尼系数和胡佛指数<br />
<br />
H=G=|2A-1|=|1-2B| \, <br />
<br />
H = G = | 2A-1 | = | 1-2B | ,<br />
<br />
<br />
<br />
Using the "''A''&nbsp;:&nbsp;''B''" notation (for example, 0.8:0.2) and with&nbsp;''A''&nbsp;+&nbsp;''B''&nbsp;=&nbsp;1, [[Income inequality metrics|inequality measures]] like the [[Gini index]] (G) ''and'' the [[Hoover index]] (H) can be computed. In this case both are the same.<br />
使用“A:B”符号(例如，0.8:0.2)和a+b=1，可以计算基尼指数(G)和胡佛指数(H)等不平等度量。在这种情况下，两者是相同的。<br />
<br />
<br />
A:B = \left( \frac{1+H} 2 \right): \left( \frac{1-H} 2 \right)<br />
<br />
A: B = left (frac {1 + H }2 right) : left (frac {1-H }2 right)<br />
<br />
<br />
<br />
: <math>H=G=|2A-1|=|1-2B| \, </math><br />
<br />
<br />
<br />
: <math>A:B = \left( \frac{1+H} 2 \right): \left( \frac{1-H} 2 \right)</math><br />
<br />
<br />
<br />
== See also ==<br />
另见<br />
<br />
{{div col|colwidth=22em}}<br />
<br />
*[[1% rule (Internet culture)]]<br />
*[[1%规则（互联网文化）]]<br />
<br />
*[[10/90 gap]]<br />
*[[10/90差距]]<br />
<br />
*[[Benford's law]]<br />
*[[本福德定律]]<br />
<br />
*[[Diminishing returns]]<br />
*[[收益递减]]<br />
<br />
*[[Elephant flow]]<br />
*[[大象流]]<br />
<br />
*[[Keystone species]]<br />
*[[关键物种]]<br />
<br />
*[[Long tail]]<br />
*[[长尾]]<br />
<br />
*[[Matthew effect]]<br />
*[[马太效应]]<br />
<br />
*[[Mathematical economics]]<br />
*[[数学经济学]]<br />
<br />
*[[Megadiverse countries]]<br />
*[[巨型多样化国家]]<br />
<br />
*[[Ninety-ninety rule]]<br />
*[[90-90法则]]<br />
<br />
*[[Pareto distribution]]<br />
*[[帕累托分布]]<br />
<br />
*[[Pareto priority index]]<br />
*[[帕累托优先权指数]]<br />
<br />
*[[Parkinson's law]]<br />
*[[帕金森定律]]<br />
<br />
*[[Derek J. de Solla Price|Price's law]]<br />
*[[普赖斯定律]]<br />
<br />
*[[Principle of least effort]]<br />
*[[最小努力原则]]<br />
<br />
*[[Profit risk]]<br />
*[[利润风险]]<br />
<br />
*[[Rank-size distribution]]<br />
*[[等级分布]]<br />
<br />
*[[Sturgeon's law]]<br />
*[[斯特金法则]]<br />
<br />
*[[Vitality curve]]<br />
*[[生命力曲线]]<br />
<br />
*[[Wealth concentration]]<br />
*[[财富集中]]<br />
<br />
*[[Zipf's law]]<br />
*[[齐普夫定律]]<br />
<br />
*[[Free-to-play#Comparison with traditional model|Microtransaction whale]]<br />
*[[免费游戏#与传统模式比较|微交易鲸]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== References ==<br />
参考<br />
<br />
{{Reflist|30em}}<br />
<br />
<br />
<br />
== Further reading ==<br />
进一步阅读<br />
<br />
*{{Citation |last=Bookstein |first=Abraham |authorlink= |year=1990 |title=Informetric distributions, part I: Unified overview |journal=Journal of the American Society for Information Science |volume=41 |issue= 5|pages=368–375 |doi=10.1002/(SICI)1097-4571(199007)41:5<368::AID-ASI8>3.0.CO;2-C |url= |accessdate= |quote= |postscript=<!--none--> }}<br />
<br />
*{{Citation |authors=Klass, O. S.; Biham, O.; Levy, M.; Malcai, O.; Soloman, S. |year=2006 |title=The Forbes 400 and the Pareto wealth distribution |journal=Economics Letters |volume=90 |issue=2 |pages=290–295 |doi=10.1016/j.econlet.2005.08.020 |url= |accessdate= |quote= |postscript=<!--none--> }}<br />
<br />
*{{Citation |title=The 80/20 Principle: The Secret of Achieving More with Less |last=Koch |first=R. |authorlink= |year=2001 |publisher=Nicholas Brealey Publishing |location=London |isbn= |pages= |url=https://www.scribd.com/doc/3664882/The-8020-Principle-The-Secret-to-Success-by-Achieving-More-with-Less |postscript=<!--none--> }}<br />
<br />
*{{Citation |title=Living the 80/20 Way: Work Less, Worry Less, Succeed More, Enjoy More |last=Koch |first=R. |authorlink= |year=2004 |publisher=Nicholas Brealey Publishing |location=London |isbn=1-85788-331-4 |pages= |url= |postscript=<!--none--> }}<br />
<br />
*{{Citation |last=Reed |first=W. J. |authorlink= |year=2001 |title=The Pareto, Zipf and other power laws |journal=Economics Letters |volume=74 |issue=1 |pages=15–19 |doi=10.1016/S0165-1765(01)00524-9 |url= |accessdate= |quote= |postscript=<!--none--> }}<br />
<br />
*{{Citation |doi=10.1016/0094-1190(80)90043-1 |authors=Rosen, K. T.; Resnick, M. |year=1980 |title=The size distribution of cities: an examination of the Pareto law and primacy |journal=Journal of Urban Economics |volume=8 |issue= 2|pages=165–186 |id= |url= https://escholarship.org/uc/item/9tt5c711|accessdate= |quote= |postscript=<!--none--> }}<br />
<br />
*{{citation |title=The handbook of logistics and distribution management |last1=Rushton |first1=A. |last2=Oxley|first2= J.|last3= Croucher|first3= P. |year=2000 |edition=2nd |publisher=Kogan Page |location=London |isbn=978-0-7494-3365-9 |postscript=<!--none-->}}.<br />
<br />
<br />
<br />
== External links ==<br />
外部链接<br />
*<br />
<br />
*<br />
<br />
{{Commons category|Pareto principle}}<br />
<br />
<br />
<br />
*[https://www.paretorule.cf/?m=1 ParetoRule.cf : Pareto Rule]<br />
<br />
*<br />
<br />
* [https://www.paretorule.cf/2018/12/the-pareto-Rule.html?m=1 ParetoRule.cf : The Pareto Rule]<br />
<br />
* [http://management.about.com/cs/generalmanagement/a/Pareto081202.htm About.com: Pareto's Principle]<br />
<br />
* [https://web.archive.org/web/20080528063231/http://www.ma.hw.ac.uk/~des/HWM00-26.pdf Wealth Condensation in Pareto Macro-Economies]<br />
<br />
* [http://buildthefire.com/pareto-principle-accomplishing-goals-with-purpose/ The Pareto Principle: Accomplishing goals with purpose]<br />
<br />
Category:Statistical laws<br />
<br />
类别: 统计法<br />
<br />
<br />
<br />
Category:Rules of thumb<br />
<br />
类别: 经验法则<br />
<br />
{{authority control}}<br />
<br />
Category:Tails of probability distributions<br />
<br />
类别: 概率分布的尾部<br />
<br />
<br />
<br />
Category:Statistical principles<br />
<br />
类别: 统计原则<br />
<br />
[[Category:Statistical laws]]<br />
<br />
Category:Adages<br />
<br />
分类: 格言<br />
<br />
[[Category:Rules of thumb]]<br />
<br />
Category:Vilfredo Pareto<br />
<br />
类别: Vilfredo Pareto<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Pareto principle]]. Its edit history can be viewed at [[80/20原则/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>趣木木https://wiki.swarma.org/index.php?title=80/20%E5%8E%9F%E5%88%99&diff=1439580/20原则2020-09-26T07:32:43Z<p>趣木木：</p>
<hr />
<div>本词条由11初步翻译<br />
<br />
{{for|the optimal allocation of resources|Pareto efficiency}}<br />
{{为了资源的优化配置|帕累托效率}}<br />
<br />
{{short description|Statistical principle about ratio of effects to causes}}<br />
{{简述|关于效果与原因之比的统计原则}}<br />
<br />
[[File:Pareto principle applied to community fundraising.jpg|thumb|right|Pareto principle applied to community fundraising]]<br />
[[文件:应用于社区筹款的帕累托原则.jpg|thumb|right|应用于社区筹款的帕累托原则]]<br />
<br />
Pareto principle applied to community fundraising<br />
<br />
应用于社区筹款的帕累托原则<br />
<br />
The '''Pareto principle''' (also known as the '''80/20 rule''', the '''law of the vital few,''' or the '''principle of factor sparsity''')<ref>{{cite news|url=https://www.nytimes.com/2008/03/03/business/03juran.html|title=Joseph Juran, 103, Pioneer in Quality Control, Dies|last1=Bunkley|first1=Nick|date=March 3, 2008|work=New York Times|accessdate=25 January 2018|archiveurl=https://web.archive.org/web/20170906182706/http://www.nytimes.com/2008/03/03/business/03juran.html|archivedate=September 6, 2017}}</ref><ref>{{cite journal|last1=Box|first1=George E.P.|last2=Meyer|first2=R. Daniel|date=1986|title=An Analysis for Unreplicated Fractional Factorials|journal=Technometrics|volume=28|issue=1|pages=11–18|doi=10.1080/00401706.1986.10488093}}</ref> states that, for many events, roughly 80% of the effects come from 20% of the causes.<ref name="NYT">{{cite news|url=https://www.nytimes.com/2008/03/03/business/03juran.html|title=Joseph Juran, 103, Pioneer in Quality Control, Dies|last=Bunkley|first=Nick|date=March 3, 2008|work=[[The New York Times]]}}</ref> <br />
<br />
The Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes. <br />
<br />
'''<font color="#ff8000"> 帕累托原则</font>'''（又称80/20法则、至关重要的少数人法则或因素稀少原则）指出，对于许多事件，大约80%的影响来自20%的原因。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】注意专业名词后面需要添加大写开头的对应英文“帕累托原则 Pareto Principle” 下同<br />
<br />
<br />
[[Management consultant]] [[Joseph M. Juran]] suggested the principle and named it after Italian [[economist]] [[Vilfredo Pareto]], who noted the 80/20 connection while at the [[University of Lausanne]] in 1896. In his first work, ''Cours d'économie politique'', Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. The Pareto principle is only tangentially related to [[Pareto efficiency]]. Pareto developed both concepts in the context of the [[distribution of income]] and wealth among the population.<br />
<br />
Management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who noted the 80/20 connection while at the University of Lausanne in 1896. In his first work, Cours d'économie politique, Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population. The Pareto principle is only tangentially related to Pareto efficiency. Pareto developed both concepts in the context of the distribution of income and wealth among the population.<br />
<br />
管理顾问 Joseph M. Juran 提出了这个原则，并以意大利经济学家 Vilfredo Pareto 的名字命名，后者于1896年在洛桑大学指出了80/20的联系。帕雷托在他的第一部著作《政治经济学》中指出，意大利约80% 的土地为20% 的人口所拥有。帕雷托原则与帕累托最优的相关性不大。帕累托在人口的收入和财富分配的背景下发展出了这两个概念。<br />
<br />
<br />
<br />
Mathematically, the 80/20 rule is roughly followed by a [[power law]] distribution (also known as a [[Pareto distribution]]) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution.<ref>{{cite journal|url=https://arxiv.org/PS_cache/cond-mat/pdf/0412/0412004v3.pdf|title=Power laws, Pareto Distributions, and Zipf's law|journal=Contemporary Physics|volume=46|issue=5|pages=323–351|last=Newman|first=MEJ|access-date=10 April 2011|bibcode=2005ConPh..46..323N|year=2005|arxiv=cond-mat/0412004|doi=10.1080/00107510500052444|s2cid=202719165}}</ref> It is an axiom of business management that "80% of sales come from 20% of clients".<ref>{{Cite news|last=Marshall|first=Perry|url=https://www.entrepreneur.com/article/229294|title=The 80/20 Rule of Sales: How to Find Your Best Customers|date=2013-10-09|work=Entrepreneur|access-date=2018-01-05|language=en}}</ref><br />
<br />
Mathematically, the 80/20 rule is roughly followed by a power law distribution (also known as a Pareto distribution) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution. It is an axiom of business management that "80% of sales come from 20% of clients".<br />
<br />
在数学上，80/20原则对于一组特定的参数大致遵循'''<font color="#ff8000"> 幂律分布</font>'''(也称为'''<font color="#ff8000"> 帕累托分布</font>''') ，许多自然现象已经由试验证明呈现这样的分布。“80% 的销售额来自20% 的客户”是企业管理的一条公理。<br />
<br />
<br />
<br />
== In economics ==<br />
在经济学中<br />
<br />
<br />
<br />
The original observation was in connection with population and wealth. Pareto noticed that approximately 80% of Italy's land was owned by 20% of the population.<ref>{{citation|title=''Translation of'' Manuale di economia politica ("Manual of political economy") |first1=Vilfredo|last1=Pareto|first2=Alfred N.|last2=Page|publisher=A.M. Kelley|year=1971|isbn=978-0-678-00881-2|postscript=<!--none-->}}</ref> He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.<br />
<br />
The original observation was in connection with population and wealth. Pareto noticed that approximately 80% of Italy's land was owned by 20% of the population. He then carried out surveys on a variety of other countries and found to his surprise that a similar distribution applied.<br />
<br />
最初的观察结果与人口和财富有关。帕累托注意到，意大利约80% 的土地为20% 的人口所拥有。他随后对许多其他国家进行了调查，令他惊讶的是，类似的分布也同样适用。<br />
<br />
<br />
<br />
A chart that gave the inequality a very visible and comprehensible form, the so-called "champagne glass" effect,<ref>{{citation|first=Xabier|last=Gorostiaga|title=World has become a 'champagne glass' globalization will fill it fuller for a wealthy few|journal=National Catholic Reporter|date=January 27, 1995|postscript=<!--none-->}}</ref> was contained in the 1992 [[United Nations Development Programme|United Nations Development Program]] Report, which showed that distribution of global income is very uneven, with the richest 20% of the world's population controlling 82.7% of the world's income.<ref>{{citation|author=United Nations Development Program|title=1992 Human Development Report|year=1992|location=New York|publisher=Oxford University Press|postscript=<!--none-->}}</ref> Still, the [[Gini index]] of the world shows that nations have wealth distributions that vary greatly.<br />
<br />
A chart that gave the inequality a very visible and comprehensible form, the so-called "champagne glass" effect, was contained in the 1992 United Nations Development Program Report, which showed that distribution of global income is very uneven, with the richest 20% of the world's population controlling 82.7% of the world's income. Still, the Gini index of the world shows that nations have wealth distributions that vary greatly.<br />
<br />
1992年《联合国开发计划署报告》中的一张图表以非常明显和易懂的形式呈现了不平等，即所谓的 "香槟酒杯 "效应，该图表显示，全球收入分配非常不均衡，世界上最富有的20% 人口控制着82.7%的世界收入。不过，世界基尼系数显示，各国的财富分配差异很大。<br />
<br />
<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class = “ wikitable”<br />
<br />
|+ Distribution of world GDP, 1989<ref name="1992 Human Development Report, Chapter 3">{{citation|url=http://hdr.undp.org/en/reports/global/hdr1992/chapters/|title=Human Development Report 1992, Chapter 3|accessdate=2007-07-08|postscript=<!--none-->}}</ref><br />
<br />
|+ Distribution of world GDP, 1989<br />
<br />
| + 世界 GDP 分布，1989年<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! scope="col" | Quintile of population<br />
<br />
! scope="col" | Quintile of population<br />
<br />
!范围 = “ col” | 五分之一人口<br />
<br />
! scope="col" | Income<br />
<br />
! scope="col" | Income<br />
<br />
!范围 = “ col” | 收入<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Richest 20%<br />
<br />
| Richest 20%<br />
<br />
最富有的20% <br />
<br />
| 82.70%<br />
<br />
| 82.70%<br />
<br />
| 82.70%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Second 20%<br />
<br />
| Second 20%<br />
<br />
第二个20% <br />
<br />
| 11.75%<br />
<br />
| 11.75%<br />
<br />
| 11.75%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Third 20%<br />
<br />
| Third 20%<br />
<br />
第三20% <br />
<br />
| 2.30%<br />
<br />
| 2.30%<br />
<br />
| 2.30%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Fourth 20%<br />
<br />
| Fourth 20%<br />
<br />
第四个20% <br />
<br />
| 1.85%<br />
<br />
| 1.85%<br />
<br />
| 1.85%<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
| Poorest 20%<br />
<br />
| Poorest 20%<br />
<br />
最穷的20% <br />
<br />
| 1.40%<br />
<br />
| 1.40%<br />
<br />
| 1.40%<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
The Pareto principle also could be seen as applying to taxation. In the US, the top 20% of earners have paid roughly 80-90% of Federal income taxes in 2000 and 2006,<ref>Curtis Dubay (May 4, 2009) [https://www.heritage.org/poverty-and-inequality/report/the-rich-pay-more-taxes-top-20-percent-pay-record-share-income-taxes The Rich Pay More Taxes: Top 20 Percent Pay Record Share of Income Taxes], Heritage.org, accessed 12 April 2018</ref> and again in 2018.<ref>Laura Sanders (April 6, 2018) [https://www.wsj.com/articles/top-20-of-americans-will-pay-87-of-income-tax-1523007001 Top 20% of Americans Will Pay 87% of Income Tax], Wall Street Journal, accessed 12 April 2018</ref><br />
<br />
The Pareto principle also could be seen as applying to taxation. In the US, the top 20% of earners have paid roughly 80-90% of Federal income taxes in 2000 and 2006, and again in 2018.<br />
<br />
欧洲帕雷托法则也可以被视为适用于税收。在美国，收入最高的20%的人在2000年和2006年缴纳了大约80%-90%的联邦所得税，2018年又是如此。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】帕雷托法则 注意全文的专业名词统一性 是统一用原则还是法则<br />
<br />
<br />
However, it is important to note that while there have been associations of such with [[meritocracy]], the principle should not be confused with further reaching implications. As Alessandro Pluchino at the University of Catania in Italy points out, other attributes do not necessarily correlate. Using talent as an example, he and other researchers state, “The maximum success never coincides with the maximum talent, and vice-versa,” and that such factors are the result of chance.<ref>Emerging Technology from the arXiv (March 1, 2018) [https://www.technologyreview.com/s/610395/if-youre-so-smart-why-arent-you-rich-turns-out-its-just-chance/ If you’re so smart, why aren’t you rich? Turns out it’s just chance.], TechnologyReview.com, accessed 1 January 2019</ref><br />
<br />
However, it is important to note that while there have been associations of such with meritocracy, the principle should not be confused with further reaching implications. As Alessandro Pluchino at the University of Catania in Italy points out, other attributes do not necessarily correlate. Using talent as an example, he and other researchers state, “The maximum success never coincides with the maximum talent, and vice-versa,” and that such factors are the result of chance.<br />
<br />
然而，必须指出的是，虽然有这与精英管理体制有联系，但这一原则不应与进一步的影响混为一谈。正如意大利卡塔尼亚大学的 Alessandro Pluchino 指出的那样，其他属性并不一定相互关联。以天赋为例，他和其他研究人员指出，“最大的成功从来没有与最大的天赋相吻合，反之亦然”，这样的因素是偶然的结果。<br />
<br />
<br />
The physicist Victor Yakovenko of the [[University of Maryland, College Park]] and AC Silva analyzed income data from the US Internal Revenue Service from 1983 to 2001, and found that the income distribution among the upper class (1–3% of the population) follows Pareto's principle.<ref>{{Citation|last1=Yakovenko|first1=Victor M.|title=Two-class Structure of Income Distribution in the USA: Exponential Bulk and Power-law Tail|date=2005|work=Econophysics of Wealth Distributions: Econophys-Kolkata I|pages=15–23|editor-last=Chatterjee|editor-first=Arnab|series=New Economic Windows|publisher=Springer Milan|language=en|doi=10.1007/88-470-0389-x_2|isbn=978-88-470-0389-7|last2=Silva|first2=A. Christian|editor2-last=Yarlagadda|editor2-first=Sudhakar|editor3-last=Chakrabarti|editor3-first=Bikas K.}}</ref><br />
<br />
The physicist Victor Yakovenko of the University of Maryland, College Park and AC Silva analyzed income data from the US Internal Revenue Service from 1983 to 2001, and found that the income distribution among the upper class (1–3% of the population) follows Pareto's principle.<br />
<br />
马里兰大学学院帕克分校的物理学家Victor Yakovenko和AC Silva分析了美国国税局1983年到2001年的收入数据，发现上层阶级(占总人口的1-3%)的收入分配遵循帕累托原则。<br />
<br />
<br />
<br />
== In computing ==<br />
在计算领域<br />
<br />
In [[computer science]] the Pareto principle can be applied to [[optimization (computer science)|optimization]] efforts.<ref name=optimization>{{citation|first1=M.|last1=Gen|first2=R.|last2=Cheng|title=Genetic Algorithms and Engineering Optimization|location=New York|publisher=Wiley|year=2002|postscript=<!--none-->}}</ref> For example, [[Microsoft]] noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated.<ref>{{citation|url=http://www.crn.com/news/security/18821726/microsofts-ceo-80-20-rule-applies-to-bugs-not-just-features.htm|title=Microsoft's CEO: 80–20 Rule Applies To Bugs, Not Just Features|first=Paula|last=Rooney|date=October 3, 2002|publisher=ChannelWeb|postscript=<!--none-->}}</ref> [[Lowell Arthur]] expressed that "20 percent of the code has 80 percent of the errors. Find them, fix them!"<ref>Pressman, Roger S. (2010). Software Engineering: A Practitioner's Approach (7th ed.). Boston, Mass: McGraw-Hill, 2010. {{ISBN|978-0-07-337597-7}}.</ref> It was also discovered that in general the 80% of a certain piece of software can be written in 20% of the total allocated time. Conversely, the hardest 20% of the code takes 80% of the time. This factor is usually a part of [[COCOMO]] estimating for software coding.<br />
<br />
In computer science the Pareto principle can be applied to optimization efforts. For example, Microsoft noted that by fixing the top 20% of the most-reported bugs, 80% of the related errors and crashes in a given system would be eliminated. Lowell Arthur expressed that "20 percent of the code has 80 percent of the errors. Find them, fix them!" It was also discovered that in general the 80% of a certain piece of software can be written in 20% of the total allocated time. Conversely, the hardest 20% of the code takes 80% of the time. This factor is usually a part of COCOMO estimating for software coding.<br />
<br />
在计算机科学中，帕雷托原则可以应用于优化工作。例如，微软指出，通过修复前20%的报告最多的错误，可以消除给定系统中80%的相关错误和崩溃。Lowell Arthur表示“20% 的代码有80% 的错误。找到它们，修复它们!”人们还发现，一般来说，某个软件的80%可以在总分配时间的20%内编写完。相反，最难的20%的代码占用了80%的时间。这个因素通常是软件编码的COCOMO估算的一部分。<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）帕雷托原则 帕累托原则 80/20原则 全文注意名词的统一性 翻译完后一定一定通读 按照自审清单走一遍<br />
<br />
== In sports ==<br />
在体育领域<br />
<br />
It has been inferred that the Pareto principle applies to athletic training, where roughly 20% of the exercises and habits have 80% of the impact, and the trainee should not focus so much on a varied training.<ref>{{citation |url= http://speedendurance.com/2008/11/20/training-and-the-80-20-rule-of-paretos-principle/ |title=Training and the 80-20 rule of Pareto's Principle |date=21 November 2008 }}</ref> This does not necessarily mean that having a healthy diet or going to the gym are not important, but they are not as significant as the key activities. It is also important to note this 80/20 rule has yet to be scientifically tested in controlled studies of athletic training.<br />
<br />
It has been inferred that the Pareto principle applies to athletic training, where roughly 20% of the exercises and habits have 80% of the impact, and the trainee should not focus so much on a varied training. This does not necessarily mean that having a healthy diet or going to the gym are not important, but they are not as significant as the key activities. It is also important to note this 80/20 rule has yet to be scientifically tested in controlled studies of athletic training.<br />
<br />
据推测，帕雷托原则适用于运动训练，其中大约20%的训练和习惯有80%的影响，受训者不应该过多地注重多样化的训练。这并不一定意味着健康饮食或去健身房不重要，只是它们不如那些关键活动重要。另外需要注意的是，这个80/20原则还没有在运动训练的对照研究中得到科学验证。<br />
<br />
<br />
<br />
In [[baseball]], the Pareto principle has been perceived in [[Wins Above Replacement]] (an attempt to combine multiple statistics to determine a player's overall importance to a team). "15% of all the players last year produced 85% of the total wins with the other 85% of the players creating 15% of the wins. The Pareto principle holds up pretty soundly when it is applied to baseball."<ref>Jeff Zimmerman (Jun 4, 2010). [https://www.beyondtheboxscore.com/2010/6/4/1501048/applying-the-parento-principle-80 Applying the Pareto Principle (80-20 Rule) to Baseball], BeyondTheBoxScore.com, accessed 12 April 2018</ref><br />
<br />
In baseball, the Pareto principle has been perceived in Wins Above Replacement (an attempt to combine multiple statistics to determine a player's overall importance to a team). "15% of all the players last year produced 85% of the total wins with the other 85% of the players creating 15% of the wins. The Pareto principle holds up pretty soundly when it is applied to baseball."<br />
<br />
在棒球比赛中，帕雷托原则已经在Wins Above Replacement(试图结合多种统计数据来确定一个球员对一个球队的整体重要性)中被认识到。“去年15%的球员创造了85%的总胜利，其他85%的球员创造了15%的胜利。帕雷托原则在棒球比赛中得到了充分体现。”<br />
<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】“中被认识到” 避免被动语态<br />
<br />
== Occupational health and safety ==<br />
职业健康和安全<br />
<br />
[[Occupational health and safety]] professionals use the Pareto principle to underline the importance of hazard prioritization. Assuming 20% of the hazards account for 80% of the injuries, and by categorizing hazards, safety professionals can target those 20% of the hazards that cause 80% of the injuries or accidents. Alternatively, if hazards are addressed in random order, a safety professional is more likely to fix one of the 80% of hazards that account only for some fraction of the remaining 20% of injuries.<ref>{{cite book |last=Woodcock |first=Kathryn |title=Safety Evaluation Techniques |year=2010 |publisher= Ryerson University |location= Toronto, ON |pages=86 |url= http://www.ryerson.ca/woodcock/}}</ref><br />
<br />
Occupational health and safety professionals use the Pareto principle to underline the importance of hazard prioritization. Assuming 20% of the hazards account for 80% of the injuries, and by categorizing hazards, safety professionals can target those 20% of the hazards that cause 80% of the injuries or accidents. Alternatively, if hazards are addressed in random order, a safety professional is more likely to fix one of the 80% of hazards that account only for some fraction of the remaining 20% of injuries.<br />
<br />
职业健康和安全方面的专业人士使用帕雷托原则来强调危害优先级的重要性。假设20% 的危险占伤害的80% ，通过对危险进行分类，安全专业人员可以有针对性地解决造成80%伤害或事故的那20%的危害。或者，如果危害按随机顺序处理，安全专业人员更有可能解决那80%的危害中的一个，而这个危害只占其余20%伤害的某一部分。<br />
<br />
<br />
<br />
Aside from ensuring efficient accident prevention practices, the Pareto principle also ensures hazards are addressed in an economical order, because the technique ensures the utilized resources are best used to prevent the most accidents.<ref name=USCG001>{{cite web|title=Introduction to Risk-based Decision-Making |url= http://www.uscg.mil/hq/cg5/cg5211/docs/RBDM_Files/PDF/RBDM_Guidelines/Volume%202/Volume%202-Chapter%206.pdf |work=USCG Safety Program |publisher= United States Coast Guard |accessdate= 14 January 2012}}</ref><br />
<br />
Aside from ensuring efficient accident prevention practices, the Pareto principle also ensures hazards are addressed in an economical order, because the technique ensures the utilized resources are best used to prevent the most accidents.<br />
<br />
除了确保有效的事故预防措施，帕雷托法则安全管理局原则还能确保以经济的顺序处理危险，因为该技术能确保所利用的资源被最好地用于预防最多的事故。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】“帕雷托法则安全管理局原则”此处是否没有经过人工翻译？<br />
<br />
== Other applications ==<br />
其他应用<br />
<br />
In engineering control theory, such as for electromechanical energy converters, the 80/20 principle applies to optimization efforts.<ref name=optimization/><br />
<br />
In engineering control theory, such as for electromechanical energy converters, the 80/20 principle applies to optimization efforts.<br />
<br />
在工程控制理论中，如对于机电式能量转换器，80/20原则适用于优化工作。<br />
<br />
<br />
<br />
The law of the few can be also seen in betting, where it is said that with 20% effort you can match the accuracy of 80% of the bettors.<ref>{{citation|title=The Pareto Principle of Prediction|url=https://www.pinnacle.com/en/betting-articles/betting-strategy/the-pareto-principle-of-prediction}}</ref><br />
<br />
In the systems science discipline, Joshua M. Epstein and Robert Axtell created an agent-based simulation model called Sugarscape, from a decentralized modeling approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 principle became emergent in their results, which suggests the principle is a collective consequence of these individual rules.<br />
<br />
在系统科学领域，Joshua M. Epstein和Robert Axtell从分散建模方法出发，基于为经济中的每个代理人定义的个人行为规则创建了创建了一个名为Sugarscape的基于代理的仿真模型。财富分配原则和帕累托80/20原则在其结果中突现，这表明这一原则是这些个体规则的集体结果。<br />
--[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）【翻译反馈】“创建了创建了一个” 下次需要认真细心<br />
<br />
<br />
In the systems science discipline, [[Joshua M. Epstein]] and [[Robert Axtell]] created an [[Agent-based social simulation|agent-based simulation]] model called [[Sugarscape]], from a [[Decentralised system|decentralized modeling]] approach, based on individual behavior rules defined for each agent in the economy. Wealth distribution and Pareto's 80/20 principle became emergent in their results, which suggests the principle is a collective consequence of these individual rules.<ref>{{Citation|last1=Epstein|first1=Joshua|title=Growing Artificial Societies: Social Science from the Bottom-Up|url=https://books.google.com/books?id=xXvelSs2caQC|page=208|year=1996|postscript=<!--none-->|publisher=[[MIT Press]]|isbn=0-262-55025-3|last2=Axtell|first2=Robert}}<br />
<br />
The Pareto principle has many applications in quality control. It is the basis for the Pareto chart, one of the key tools used in total quality control and Six Sigma techniques. The Pareto principle serves as a baseline for ABC-analysis and XYZ-analysis, widely used in logistics and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.<br />
<br />
帕雷托原则在质量控制方面有很多应用。它是帕累托图的基础，帕累托图是用于全面质量控制和六西格玛技术的关键工具之一。帕雷托原则分析作为ABC分析法和XYZ分析法的基准，广泛应用于物流和采购，目的是优化库存以及保存和补充库存的成本。<br />
<br />
</ref><br />
<br />
<br />
<br />
In health care in the United States, in one instance 20% of patients have been found to use 80% of health care resources.<br />
<br />
在美国的医疗服务中，一个事例发现20%的病人使用了80%的医疗资源。<br />
<br />
The Pareto principle has many applications in quality control.<ref>{{Cite book|url=https://books.google.com/books?id=QtVmCgAAQBAJ&pg=PA8&lpg=PA8&dq=The+Pareto+principle+has+many+applications+in+quality+control#v=onepage|title=The Pareto Principle for Business Management: Expand your business with the 80/20 rule|last=50MINUTES.COM|date=2015-08-17|publisher=50 Minutes|isbn=9782806265869|language=en}}</ref> It is the basis for the [[Pareto chart]], one of the key tools used in [[total quality management|total quality control]] and [[Six Sigma]] techniques. The Pareto principle serves as a baseline for [[time management#abc analysis|ABC-analysis]] and XYZ-analysis, widely used in [[logistics]] and procurement for the purpose of optimizing stock of goods, as well as costs of keeping and replenishing that stock.<ref>{{harvtxt|Rushton|Oxley|Croucher|2000}}, pp. 107–108.</ref><br />
<br />
<br />
<br />
Some cases of super-spreading conform to the 20/80 rule, where approximately 20% of infected individuals are responsible for 80% of transmissions, although super-spreading can still be said to occur when super-spreaders account for a higher or lower percentage of transmissions. In epidemics with super-spreading, the majority of individuals infect relatively few secondary contacts.<br />
<br />
一些超级传播病例符合20/80原则，其中大约20%的感染者要为80%的传播负责，尽管当超级传播者占传播的比例较高或较低时，仍然可以说发生了超级传播。在超级传播的流行病中，大多数个体感染的二次接触者相对较少。<br />
<br />
In health care in the United States, in one instance 20% of patients have been found to use 80% of health care resources.<ref>[http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html Myrl Weinberg: In health-care reform, the 20-80 solution | Contributors | projo.com | The Providence Journal<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20090802002952/http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|date=2009-08-02}}</ref><ref>{{cite web|url=http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|archiveurl=https://archive.today/20090802002952/http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html|url-status=dead|title=Myrl Weinberg: In health-care reform, the 20-80 solution - Contributo…|date=2 August 2009|archivedate=2 August 2009|website=archive.li}}</ref><ref>{{cite web |last1=Sawyer and Claxton |first1=Bradley and Gary |title=How do health expenditures vary across the population? |url=https://www.healthsystemtracker.org/chart-collection/health-expenditures-vary-across-population/#item-discussion-of-health-spending-often-focus-on-averages-but-a-small-share-of-the-population-incurs-most-of-the-cost_2016 |website=Peterson-Kaiser Health System Tracker |publisher=Peterson Center on Healthcare and the Kaiser Family Foundation |accessdate=13 March 2019}}</ref><br />
<br />
<br />
<br />
The Dunedin Study has found 80% of crimes are committed by 20% of criminals. This statistic has been used to support both stop-and-frisk policies and broken windows policing, as catching those criminals committing minor crimes will supposedly net many criminals wanted for (or who would normally commit) larger ones.<br />
<br />
达尼丁研究发现80%的犯罪是20%的罪犯所为。这一统计数据被用来支持拦截搜查政策和破窗执法，因为抓获那些犯有轻罪的罪犯，可能会让许多想犯(或通常会犯)重罪的通缉犯落网。<br />
<br />
Some cases of [[Super-spreader|super-spreading]] conform to the 20/80 rule,<ref>{{cite journal|last1=Galvani|first1=Alison P.|last2=May|first2=Robert M.|year=2005|title=Epidemiology: Dimensions of superspreading|url=|journal=Nature|volume=438|issue=7066|pages=293–295|doi=10.1038/438293a|pmid=16292292|bibcode=2005Natur.438..293G|pmc=7095140}}</ref> where approximately 20% of infected individuals are responsible for 80% of transmissions, although super-spreading can still be said to occur when super-spreaders account for a higher or lower percentage of transmissions.<ref name="Lloyd-Smith JO 2005">{{cite journal|last1=Lloyd-Smith|first1=JO|last2=Schreiber|first2=SJ|last3=Kopp|first3=PE|last4=Getz|first4=WM|year=2005|title=Superspreading and the effect of individual variation on disease emergence|url=|journal=Nature|volume=438|issue=7066|pages=355–359|doi=10.1038/nature04153|pmid=16292310|bibcode=2005Natur.438..355L|pmc=7094981}}</ref> In [[epidemic]]s with super-spreading, the majority of individuals infect relatively few [[contact tracing|secondary contacts]].<br />
<br />
<br />
<br />
Many video rental shops reported in 1988 that 80% of revenue came from 20% of videotapes. A video-chain executive discussed the "Gone with the Wind syndrome", however, in which every store had to offer classics like Gone with the Wind, Casablanca, or The African Queen to appear to have a large inventory, even if customers very rarely rented them.<br />
<br />
1988年，许多录像带出租店报告说，80%的收入来自20%的录像带。然而，一家视频连锁店的高管谈到了“乱世佳人综合症”，即每家商店都必须提供《飘》、《卡萨布兰卡》或《非洲女王号》等经典影片，以显得其库存庞大，即使顾客很少租用这些影片。<br />
<br />
The [[Dunedin Multidisciplinary Health and Development Study|Dunedin Study]] has found 80% of crimes are committed by 20% of criminals.<ref>{{Citation|last=Nicola|first=Davis|title='High social cost' adults can be predicted from as young as three, says study|url=https://www.theguardian.com/science/2016/dec/12/high-social-cost-adults-can-be