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Statistical mechanics is one of the pillars of modern [[physics]]. It describes how macroscopic observations (such as [[temperature]] and [[pressure]]) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as [[heat capacity]]) to microscopic behavior, whereas, in [[classical thermodynamics]], the only available option would be to measure and tabulate such quantities for various materials.<ref name="gibbs">{{cite book |last=Gibbs |first=Josiah Willard |author-link=Josiah Willard Gibbs |title=Elementary Principles in Statistical Mechanics |year=1902 |publisher=[[Charles Scribner's Sons]] |location=New York |title-link=Elementary Principles in Statistical Mechanics }}</ref>

Statistical mechanics is one of the pillars of modern [[physics]]. It describes how macroscopic observations (such as [[temperature]] and [[pressure]]) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as [[heat capacity]]) to microscopic behavior, whereas, in [[classical thermodynamics]], the only available option would be to measure and tabulate such quantities for various materials.<ref name="gibbs">{{cite book |last=Gibbs |first=Josiah Willard |author-link=Josiah Willard Gibbs |title=Elementary Principles in Statistical Mechanics |year=1902 |publisher=[[Charles Scribner's Sons]] |location=New York |title-link=Elementary Principles in Statistical Mechanics }}</ref>

统计力学是现代物理学的支柱之一。它描述了宏观观察量(如温度和压力)如何与围绕平均值波动的微观参数相联系。它将热力学量(比如热容)与微观行为联系起来，而在经典热力学中，唯一可行的选择就是测量各种材料的热力学量，然后列成表格。

统计力学是现代物理学的支柱之一。它描述了宏观观察量(如温度和压力)如何与围绕平均值波动的微观参数相联系。它将热力学量(比如热容)与微观行为联系起来，而在经典热力学中，唯一可行的选择就是测量各种材料的热力学量，然后列成表格。<ref name="gibbs">{{cite book |last=Gibbs |first=Josiah Willard |author-link=Josiah Willard Gibbs |title=Elementary Principles in Statistical Mechanics |year=1902 |publisher=[[Charles Scribner's Sons]] |location=New York |title-link=Elementary Principles in Statistical Mechanics }}</ref>

==个人简介==

==个人简介==

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玻尔兹曼出生在维也纳郊区的埃尔德伯格。祖父从柏林搬到维也纳，是一名钟表制造商。父亲路德维希·格奥尔格·玻尔兹曼是一名税务官员，母亲卡塔琳娜·波恩芬德来自萨尔茨堡。他在父母家里接受了初等教育。高中时光在上奥地利的林茨度过。玻尔兹曼15岁时，他的父亲去世了。

玻尔兹曼出生在维也纳郊区的埃尔德伯格。祖父从柏林搬到维也纳，是一名钟表制造商。父亲路德维希·格奥尔格·玻尔兹曼是一名税务官员，母亲卡塔琳娜·波恩芬德来自萨尔茨堡。他在父母家里接受了初等教育。高中时光在上奥地利的林茨度过。玻尔兹曼15岁时，他的父亲去世了。</ref> Boltzmann attended high school in [[Linz]], [[Upper Austria]]. When Boltzmann was 15, his father died.<ref name="james2004">{{cite book

 

Starting in 1863, Boltzmann studied [[mathematics]] and [[physics]] at the [[University of Vienna]]. He received his doctorate in 1866 and his [[venia legendi]] in 1869. Boltzmann worked closely with [[Josef Stefan]], director of the institute of physics. It was Stefan who introduced Boltzmann to [[James Clerk Maxwell|Maxwell's]] work.<ref name="james2004" />

Starting in 1863, Boltzmann studied [[mathematics]] and [[physics]] at the [[University of Vienna]]. He received his doctorate in 1866 and his [[venia legendi]] in 1869. Boltzmann worked closely with [[Josef Stefan]], director of the institute of physics. It was Stefan who introduced Boltzmann to [[James Clerk Maxwell|Maxwell's]] work.<ref name="james2004" />

In 1869 at age 25, thanks to a letter of recommendation written by Stefan,<ref>{{cite journal |url=http://www.kvarkadabra.net/2001/12/ludwig-boltzmann/ |title=Ludwig Boltzmann in prva študentka fizike in matematike slovenskega rodu |language=Slovenian |trans-title=Ludwig Boltzmann and the First Student of Physics and Mathematics of Slovene Descent |date=December 2001 |last=Južnič |first=Stanislav |website=Kvarkadabra.net |issue=12 |accessdate=17 February 2012}}</ref> Boltzmann was appointed full Professor of [[Mathematical Physics]] at the [[University of Graz]] in the province of [[Styria]]. In 1869 he spent several months in [[Heidelberg]] working with [[Robert Bunsen]] and [[Leo Königsberger]] and in 1871 with [[Gustav Kirchhoff]] and [[Hermann von Helmholtz]] in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876.

In 1869 at age 25, thanks to a letter of recommendation written by Stefan,<ref>{{cite journal |url=http://www.kvarkadabra.net/2001/12/ludwig-boltzmann/ |title=Ludwig Boltzmann in prva študentka fizike in matematike slovenskega rodu |language=Slovenian |trans-title=Ludwig Boltzmann and the First Student of Physics and Mathematics of Slovene Descent |date=December 2001 |last=Južnič |first=Stanislav |website=Kvarkadabra.net |issue=12 |accessdate=17 February 2012}}</ref> Boltzmann was appointed full Professor of [[Mathematical Physics]] at the [[University of Graz]] in the province of [[Styria]]. In 1869 he spent several months in [[Heidelberg]] working with [[Robert Bunsen]] and [[Leo Königsberger]] and in 1871 with [[Gustav Kirchhoff]] and [[Hermann von Helmholtz]] in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876.

[[File:Boltzmann-grp.jpg|thumb|left|280px|Ludwig Boltzmann and co-workers in Graz, 1887: (standing, from the left) [[Walther Nernst|Nernst]], [[Heinrich Streintz|Streintz]], [[Svante Arrhenius|Arrhenius]], Hiecke, (sitting, from the left) Aulinger, [[Albert von Ettingshausen|Ettingshausen]], Boltzmann, [[Ignacij Klemenčič|Klemenčič]], Hausmanninger  

[[File:Boltzmann-grp.jpg|thumb|left|280px|Ludwig Boltzmann and co-workers in Graz, 1887: (standing, from the left) [[Walther Nernst|Nernst]], [[Heinrich Streintz|Streintz]], [[Svante Arrhenius|Arrhenius]], Hiecke, (sitting, from the left) Aulinger, [[Albert von Ettingshausen|Ettingshausen]], Boltzmann, [[Ignacij Klemenčič|Klemenčič]], Hausmanninger  

Boltzmann spent a great deal of effort in his final years defending his theories.<ref name="Carlo">Cercignani, Carlo (1998) Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford University Press. {{ISBN|9780198501541}}</ref> He did not get along with some of his colleagues in Vienna, particularly [[Ernst Mach]], who became a professor of philosophy and history of sciences in 1895. That same year [[Georg Helm]] and [[Wilhelm Ostwald]] presented their position on [[energetics]] at a meeting in [[Lübeck]]. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate.<ref>{{cite journal|author=Max Planck|title=Gegen die neure Energetik|journal=Annalen der Physik|volume=57|issue=1|year=1896|pages=72–78|doi=10.1002/andp.18962930107 |bibcode = 1896AnP...293...72P |url=https://zenodo.org/record/1423910}}</ref> In 1900, Boltzmann went to the [[University of Leipzig]], on the invitation of [[Wilhelm Ostwald]]. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when [[Gustav Heinrich Wiedemann]] died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902.<ref name="Carlo" /> In 1903, Boltzmann, together with [[Gustav von Escherich]] and [[Emil Müller (mathematician)|Emil Müller]], founded the [[Austrian Mathematical Society]]. His students included [[Karl Přibram]], [[Paul Ehrenfest]] and [[Lise Meitner]].<ref name="Carlo" />

Boltzmann spent a great deal of effort in his final years defending his theories.<ref name="Carlo">Cercignani, Carlo (1998) Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford University Press. {{ISBN|9780198501541}}</ref> He did not get along with some of his colleagues in Vienna, particularly [[Ernst Mach]], who became a professor of philosophy and history of sciences in 1895. That same year [[Georg Helm]] and [[Wilhelm Ostwald]] presented their position on [[energetics]] at a meeting in [[Lübeck]]. They saw energy, and not matter, as the chief component of the universe. Boltzmann's position carried the day among other physicists who supported his atomic theories in the debate.<ref>{{cite journal|author=Max Planck|title=Gegen die neure Energetik|journal=Annalen der Physik|volume=57|issue=1|year=1896|pages=72–78|doi=10.1002/andp.18962930107 |bibcode = 1896AnP...293...72P |url=https://zenodo.org/record/1423910}}</ref> In 1900, Boltzmann went to the [[University of Leipzig]], on the invitation of [[Wilhelm Ostwald]]. Ostwald offered Boltzmann the professorial chair in physics, which became vacant when [[Gustav Heinrich Wiedemann]] died. After Mach retired due to bad health, Boltzmann returned to Vienna in 1902.<ref name="Carlo" /> In 1903, Boltzmann, together with [[Gustav von Escherich]] and [[Emil Müller (mathematician)|Emil Müller]], founded the [[Austrian Mathematical Society]]. His students included [[Karl Přibram]], [[Paul Ehrenfest]] and [[Lise Meitner]].<ref name="Carlo" />

晚年的玻尔兹曼致力于维护自己所创立的理论。在维也纳，他和一些同事相处不很融洽，尤其是恩斯特·马赫(Ernst Mach，1895年成为哲学和科学史教授)。1895年，格奥尔格·赫尔姆（Georg Helm）和威廉·奥斯特瓦尔德（Wilhelm Ostwald）在吕贝克的一次会议上提出了他们关于能量学的观点。他们认为宇宙的主要组成部分是能量，而不是物质。会议辩论中玻尔兹曼的观点赢得了其他支持原子理论的物理学家的赞同。在威廉·奥斯特瓦尔德的邀请下，玻尔兹曼于1900年前往莱比锡大学，填补辞世的古斯塔夫·海因里希·维德曼留下的空缺，出任物理学首席教授。在马赫因健康原因退休以后，玻尔兹曼于1902年返回维也纳。1903年，玻尔兹曼与古斯塔夫·冯·埃舍里希、埃米尔·穆勒一同创立了奥地利数学学会。他的门生包括：卡尔·普里贝拉姆（经济学家），保罗·埃伦费斯特（理论物理学家），丽斯·迈特纳（物理学家，被爱因斯坦称为“德国居里夫人”）。

晚年的玻尔兹曼致力于维护自己所创立的理论。<ref name="Carlo">Cercignani, Carlo (1998) Ludwig Boltzmann: The Man Who Trusted Atoms. Oxford University Press. {{ISBN|9780198501541}}</ref>在维也纳，他和一些同事相处不很融洽，尤其是恩斯特·马赫(Ernst Mach，1895年成为哲学和科学史教授)。1895年，格奥尔格·赫尔姆（Georg Helm）和威廉·奥斯特瓦尔德（Wilhelm Ostwald）在吕贝克的一次会议上提出了他们关于能量学的观点。他们认为宇宙的主要组成部分是能量，而不是物质。会议辩论中玻尔兹曼的观点赢得了其他支持原子理论的物理学家的赞同。<ref>{{cite journal|author=Max Planck|title=Gegen die neure Energetik|journal=Annalen der Physik|volume=57|issue=1|year=1896|pages=72–78|doi=10.1002/andp.18962930107 |bibcode = 1896AnP...293...72P |url=https://zenodo.org/record/1423910}}</ref> 在威廉·奥斯特瓦尔德的邀请下，玻尔兹曼于1900年前往莱比锡大学，填补辞世的古斯塔夫·海因里希·维德曼留下的空缺，出任物理学首席教授。在马赫因健康原因退休以后，玻尔兹曼于1902年返回维也纳。<ref name="Carlo" /> 1903年，玻尔兹曼与古斯塔夫·冯·埃舍里希、埃米尔·穆勒一同创立了奥地利数学学会。他的门生包括：卡尔·普里贝拉姆（经济学家），保罗·埃伦费斯特（理论物理学家），丽斯·迈特纳（物理学家，被爱因斯坦称为“德国居里夫人”）。<ref name="Carlo" />

In Vienna, Boltzmann taught physics and also lectured on philosophy. Boltzmann's lectures on [[natural philosophy]] were very popular and received considerable attention. His first lecture was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann's philosophical lectures, the Emperor invited him for a reception at the Palace.<ref>The Boltzmann Equation: Theory and Applications, E.G.D. Cohen, W. Thirring, ed., Springer Science & Business Media, 2012</ref>

In Vienna, Boltzmann taught physics and also lectured on philosophy. Boltzmann's lectures on [[natural philosophy]] were very popular and received considerable attention. His first lecture was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann's philosophical lectures, the Emperor invited him for a reception at the Palace.<ref>The Boltzmann Equation: Theory and Applications, E.G.D. Cohen, W. Thirring, ed., Springer Science & Business Media, 2012</ref>

在维也纳大学，玻尔兹曼教授物理和哲学。他有关自然哲学的讲座颇受欢迎。开课当天，即使已经事先安排了最大的讲堂，现场依然是座无虚席，观者如山。讲座取得巨大成功，轰动全国，奥匈帝国皇帝也邀请玻尔兹曼入宫进行招待。

在维也纳大学，玻尔兹曼教授物理和哲学。他有关自然哲学的讲座颇受欢迎。开课当天，即使已经事先安排了最大的讲堂，现场依然是座无虚席，观者如山。讲座取得巨大成功，轰动全国，奥匈帝国皇帝也邀请玻尔兹曼入宫进行招待。<ref>The Boltzmann Equation: Theory and Applications, E.G.D. Cohen, W. Thirring, ed., Springer Science & Business Media, 2012</ref>

In 1906, Boltzmann's deteriorating mental condition forced him to resign his position, and his symptoms indicate he experienced what would today be diagnosed as [[bipolar disorder]].<ref name="Carlo" /><ref name="Paperpile">{{cite web | last = Nina Bausek and Stefan Washietl | title = Tragic deaths in science: Ludwig Boltzmann — a mind in disorder | publisher = [[Paperpile]] | date = February 13, 2018 | url = https://paperpile.com/blog/ludwig-boltzmann/  | accessdate = 2020-04-26 }}</ref> Four months later he died by suicide on September 5, 1906, by hanging himself while on vacation with his wife and daughter in [[Duino]], near [[Trieste]] (then Austria).<ref>"Eureka! Science's greatest thinkers and their key breakthroughs", Hazel Muir, p.152, {{ISBN|1780873255}}</ref><ref>{{cite book|last=Boltzmann|first=Ludwig|editor1-first=John T.|editor1-last=Blackmore|title=Ludwig Boltzmann: His Later Life and Philosophy, 1900-1906|chapter-url=https://books.google.com/books?id=apip-Jm9WuwC&pg=PA207 |volume=2|year=1995|publisher=Springer|isbn=978-0-7923-3464-4|pages=206–207|chapter=Conclusions}}</ref><ref>Upon Boltzmann's death, [[Friedrich Hasenöhrl|Friedrich ("Fritz") Hasenöhrl]] became his successor in the professorial chair of physics at Vienna.</ref><ref name="Paperpile" />

In 1906, Boltzmann's deteriorating mental condition forced him to resign his position, and his symptoms indicate he experienced what would today be diagnosed as [[bipolar disorder]].<ref name="Carlo" /><ref name="Paperpile">{{cite web | last = Nina Bausek and Stefan Washietl | title = Tragic deaths in science: Ludwig Boltzmann — a mind in disorder | publisher = [[Paperpile]] | date = February 13, 2018 | url = https://paperpile.com/blog/ludwig-boltzmann/  | accessdate = 2020-04-26 }}</ref> Four months later he died by suicide on September 5, 1906, by hanging himself while on vacation with his wife and daughter in [[Duino]], near [[Trieste]] (then Austria).<ref>"Eureka! Science's greatest thinkers and their key breakthroughs", Hazel Muir, p.152, {{ISBN|1780873255}}</ref><ref>{{cite book|last=Boltzmann|first=Ludwig|editor1-first=John T.|editor1-last=Blackmore|title=Ludwig Boltzmann: His Later Life and Philosophy, 1900-1906|chapter-url=https://books.google.com/books?id=apip-Jm9WuwC&pg=PA207 |volume=2|year=1995|publisher=Springer|isbn=978-0-7923-3464-4|pages=206–207|chapter=Conclusions}}</ref><ref>Upon Boltzmann's death, [[Friedrich Hasenöhrl|Friedrich ("Fritz") Hasenöhrl]] became his successor in the professorial chair of physics at Vienna.</ref><ref name="Paperpile" />

He is buried in the Viennese [[Zentralfriedhof]]. His tombstone bears the inscription of [[Boltzmann's entropy formula]]: <math>S = k \cdot \log W </math><ref name="Carlo" />

He is buried in the Viennese [[Zentralfriedhof]]. His tombstone bears the inscription of [[Boltzmann's entropy formula]]: <math>S = k \cdot \log W </math><ref name="Carlo" />