更改

* [[''H''-定理]]

* [[''H''-定理]]

* [[麦克斯韦-玻尔兹曼分布]]

* [[麦克斯韦-玻尔兹曼分布]]

* [[斯特藩-玻尔兹曼常数]]

* [[斯特凡-玻尔兹曼常数]]

* [[斯特藩-玻尔兹曼定律]]

* [[斯特凡-玻尔兹曼定律]]

* [[麦克斯韦-玻尔兹曼统计]]

* [[麦克斯韦-玻尔兹曼统计]]

* [[玻尔兹曼因子]]

* [[玻尔兹曼因子]]

从1863年开始，玻尔兹曼在维也纳大学学习数学和物理。他于1866年获得博士学位，1869年获得venia legendi（任教资格）。波尔兹曼与物理研究所所长约瑟夫·斯特凡(Josef Stefan)密切合作。正是斯特凡把玻尔兹曼引入了麦克斯韦的研究。

从1863年开始，玻尔兹曼在维也纳大学学习数学和物理。他于1866年获得博士学位，1869年获得venia legendi（任教资格）。波尔兹曼与物理研究所所长约瑟夫·斯特凡(Josef Stefan)密切合作。正是斯特凡把玻尔兹曼引入了麦克斯韦的研究。

===学术生涯ademic career===

===学术生涯===

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.

1869年，25岁的玻尔兹曼经斯特凡的推荐，被任命为斯蒂里亚省格拉茨大学的数学物理正教授。1869年，他在海德堡与罗伯特·本森和里奥·柯尼斯堡一起工作数月，1871年在柏林与古斯塔夫·基尔霍夫和赫尔曼·冯·赫姆霍尔兹一起工作。1873年玻尔兹曼加入维也纳大学担任数学教授，直至1876年。

1869年，25岁的玻尔兹曼经斯特凡的推荐，被任命为斯蒂里亚省格拉茨大学的数学物理正教授。1869年，他在海德堡与罗伯特·本森和里奥·柯尼斯堡一起工作数月，1871年在柏林与古斯塔夫·基尔霍夫和赫尔曼·冯·赫姆霍尔兹一起工作。1873年玻尔兹曼加入维也纳大学担任数学教授，直至1876年。

[[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|链接=Special:FilePath/Boltzmann-grp.jpg]]

[[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

 

1887年，玻尔兹曼与他的合作者们在格拉茨（后排左起：能斯特，施特莱恩，阿伦尼乌斯，海耶克；前排左起：奥林格尔，埃廷斯豪森，玻尔兹曼，克莱门契奇，豪斯曼宁格）|链接=Special:FilePath/Boltzmann-grp.jpg]]

In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On July 17, 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881).<ref>https://www.boltzmann.com/ludwig-boltzmann/biography/</ref> Boltzmann went back to [[Graz]] to take up the chair of Experimental Physics. Among his students in Graz were [[Svante Arrhenius]] and [[Walther Nernst]].<ref name="springer">{{Cite journal |quote=Paul Ehrenfest (1880–1933) along with Nernst, Arrhenius, and Meitner must be considered among Boltzmann's most outstanding students. |last1=Jäger |first1=Gustav |last2=Nabl |first2=Josef |last3=Meyer |first3=Stephan |date=April 1999 |title=Three Assistants on Boltzmann |journal=Synthese |volume=119 |issue=1–2 |pages=69–84 |doi=10.1023/A:1005239104047|s2cid=30499879 }}</ref><ref name="huji">{{cite web |url=http://chem.ch.huji.ac.il/history/nernst.htm |title=Walther Hermann Nernst |quote=Walther Hermann Nernst visited lectures by Ludwig Boltzmann |archive-url=https://web.archive.org/web/20080612133921/http://chem.ch.huji.ac.il/history/nernst.htm |archive-date=2008-06-12 }}</ref> He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.

In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to audit lectures unofficially. Boltzmann supported her decision to appeal, which was successful. On July 17, 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and Else (1891); and a son, Arthur Ludwig (1881).<ref>https://www.boltzmann.com/ludwig-boltzmann/biography/</ref> Boltzmann went back to [[Graz]] to take up the chair of Experimental Physics. Among his students in Graz were [[Svante Arrhenius]] and [[Walther Nernst]].<ref name="springer">{{Cite journal |quote=Paul Ehrenfest (1880–1933) along with Nernst, Arrhenius, and Meitner must be considered among Boltzmann's most outstanding students. |last1=Jäger |first1=Gustav |last2=Nabl |first2=Josef |last3=Meyer |first3=Stephan |date=April 1999 |title=Three Assistants on Boltzmann |journal=Synthese |volume=119 |issue=1–2 |pages=69–84 |doi=10.1023/A:1005239104047|s2cid=30499879 }}</ref><ref name="huji">{{cite web |url=http://chem.ch.huji.ac.il/history/nernst.htm |title=Walther Hermann Nernst |quote=Walther Hermann Nernst visited lectures by Ludwig Boltzmann |archive-url=https://web.archive.org/web/20080612133921/http://chem.ch.huji.ac.il/history/nernst.htm |archive-date=2008-06-12 }}</ref> He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature.

1872年，远在女性可以被奥地利大学录取之前，他遇到了亨里埃特·冯·艾根特勒，这是一位有抱负的格拉茨数学和物理老师。然而她被拒绝旁听大学讲座。玻尔兹曼支持她上诉的决定，之后上诉成功。1876年7月17日，路德维希·玻尔兹曼与亨里埃特结婚；他们共育有三女一子：亨里埃特(1880年)、艾达(1884年)、爱尔莎(1891年)、亚瑟·路德维希(1881年)。玻尔兹曼回到格拉茨担任实验物理学的主席。他在格拉茨的学生中有斯凡特·阿伦尼乌斯和瓦尔特·能斯特。

1872年，远在女性可以被奥地利大学录取之前，他遇到了亨里埃特·冯·艾根特勒，这是一位有抱负的格拉茨数学和物理女教师。然而她被拒绝旁听大学讲座。玻尔兹曼支持她上诉的决定，之后上诉成功。1876年7月17日，路德维希·玻尔兹曼与亨里埃特结婚；他们共育有三女一子：亨里埃特(1880年)、艾达(1884年)、爱尔莎(1891年)、亚瑟·路德维希(1881年)。玻尔兹曼回到格拉茨担任实验物理学的主席。他在格拉茨的学生中有斯凡特·阿伦尼乌斯和瓦尔特·能斯特。

他在格拉茨度过了快乐的14年，正是在那里，他发展了他的自然界的统计概念。

他在格拉茨度过了快乐的14年，正是在那里，他发展了他的自然界的统计概念。

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" />

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>