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In 1905 Boltzmann corresponded extensively with the Austro-German philosopher [[Franz Brentano]] with the hope of gaining a better mastery of philosophy, apparently, so that he could better refute its relevancy in science, but he became discouraged about this approach as well.

In 1905 Boltzmann corresponded extensively with the Austro-German philosopher [[Franz Brentano]] with the hope of gaining a better mastery of philosophy, apparently, so that he could better refute its relevancy in science, but he became discouraged about this approach as well.

1905年，玻尔兹曼与德-奥哲学家弗朗茨·布伦塔诺进行了广泛的通信，希望能更好地掌握哲学，显然，这样他就能更好地驳斥哲学在科学上的相关性，但他对这种方法也逐渐感到沮丧。

1905年，玻尔兹曼与德-奥哲学家弗朗茨·布伦塔诺  [[Franz Brentano]] 进行了广泛的通信，希望能更好地掌握哲学，显然，这样他就能更好地驳斥哲学在科学上的相关性，但他对这种方法也逐渐感到沮丧。

==物理学贡献==

==物理学贡献==

Boltzmann's most important scientific contributions were in [[kinetic theory of gases|kinetic theory]], including for motivating the [[Maxwell–Boltzmann distribution]] as a description of molecular speeds in a gas. [[Maxwell–Boltzmann statistics]] and the [[Boltzmann distribution]] remain central in the foundations of [[classical mechanics|classical]] statistical mechanics. They are also applicable to other [[phenomenon|phenomena]] that do not require [[Maxwell–Boltzmann statistics#Limits of applicability|quantum statistics]] and provide insight into the meaning of [[thermodynamic temperature|temperature]].

Boltzmann's most important scientific contributions were in [[kinetic theory of gases|kinetic theory]], including for motivating the [[Maxwell–Boltzmann distribution]] as a description of molecular speeds in a gas. [[Maxwell–Boltzmann statistics]] and the [[Boltzmann distribution]] remain central in the foundations of [[classical mechanics|classical]] statistical mechanics. They are also applicable to other [[phenomenon|phenomena]] that do not require [[Maxwell–Boltzmann statistics#Limits of applicability|quantum statistics]] and provide insight into the meaning of [[thermodynamic temperature|temperature]].

玻尔兹曼最重要的科学贡献是在动力学理论上，包括推动应用麦克斯韦-玻尔兹曼分布描述气体中分子的速度。直至今日，麦克斯韦-玻尔兹曼统计和玻尔兹曼分布仍然是经典统计力学基石之一。他们也适用于解释其他不需要量子统计的现象，另外提供关于温度内涵的洞见。

玻尔兹曼最重要的科学贡献是在动力学理论上，包括推动应用'''麦克斯韦-玻尔兹曼分布 [[Maxwell–Boltzmann distribution]]''' 描述气体中分子的速度。直至今日，'''麦克斯韦-玻尔兹曼统计 [[Maxwell–Boltzmann statistics]]''' 和'''玻尔兹曼分布 [[Boltzmann distribution]]''' 仍然是经典统计力学基石之一。他们也适用于解释其他不需要量子统计的现象，另外提供了关于温度内涵的洞见。

[[File:Boltzmanns-molecule.jpg|225px|thumb|right|Boltzmann's 1898 I₂ molecule diagram showing atomic "sensitive region" (α, β) overlap.

[[File:Boltzmanns-molecule.jpg|225px|thumb|right|Boltzmann's 1898 I₂ molecule diagram showing atomic "sensitive region" (α, β) overlap.

[[History of chemistry#The dispute about atomism|Most]] [[chemistry|chemists]], since the discoveries of [[John Dalton]] in 1808, and [[James Clerk Maxwell]] in Scotland and [[Josiah Willard Gibbs]] in the United States, shared Boltzmann's belief in [[atom]]s and [[molecule]]s, but much of the [[physics]] establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient [[Theory#Science|theoretical]] constructs. Only a couple of years after Boltzmann's death, [[Jean Baptiste Perrin|Perrin's]] studies of [[colloid]]al suspensions (1908–1909), based on [[Albert Einstein|Einstein's]] [[Albert Einstein#Thermodynamic fluctuations and statistical physics|theoretical studies]] of 1905, confirmed the values of [[Avogadro's number]] and [[Boltzmann constant|Boltzmann's constant]], convincing the world that the tiny particles [[Atomic theory#History|really exist]].

[[History of chemistry#The dispute about atomism|Most]] [[chemistry|chemists]], since the discoveries of [[John Dalton]] in 1808, and [[James Clerk Maxwell]] in Scotland and [[Josiah Willard Gibbs]] in the United States, shared Boltzmann's belief in [[atom]]s and [[molecule]]s, but much of the [[physics]] establishment did not share this belief until decades later. Boltzmann had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient [[Theory#Science|theoretical]] constructs. Only a couple of years after Boltzmann's death, [[Jean Baptiste Perrin|Perrin's]] studies of [[colloid]]al suspensions (1908–1909), based on [[Albert Einstein|Einstein's]] [[Albert Einstein#Thermodynamic fluctuations and statistical physics|theoretical studies]] of 1905, confirmed the values of [[Avogadro's number]] and [[Boltzmann constant|Boltzmann's constant]], convincing the world that the tiny particles [[Atomic theory#History|really exist]].

自1808年，约翰·道尔顿(John Dalton)提出原子理论以来、包括詹姆斯·克拉克·麦克斯韦（苏格兰）(James Clerk Maxwell)和乔赛亚·威拉德·吉布斯（美）(Josiah Willard Gibbs)在内，大多数化学家都认同玻尔兹曼对原子和分子的看法，但很多物理学家直到几十年后才认同这一观点。玻尔兹曼与当时著名的德国物理学杂志的编辑有长期的争执，后者拒绝让玻尔兹曼将原子和分子作为方便的理论结构之外的任何东西。玻尔兹曼去世几年后，佩兰基于爱因斯坦1905年的理论研究，对胶体悬浮液进行了研究(1908-1909)，证实了阿伏伽德罗数和玻尔兹曼常数的值，使世界相信微小粒子确实存在。

自1808年，约翰·道尔顿 John Dalton 提出原子理论以来、包括詹姆斯·克拉克·麦克斯韦James Clerk Maxwell（苏格兰）和乔赛亚·威拉德·吉布斯Josiah Willard Gibbs（美）在内，大多数化学家都认同玻尔兹曼对原子和分子的看法，但很多物理学家直到几十年后才认同这一观点。玻尔兹曼与当时著名的德国物理学杂志的编辑有长期的争执，后者拒绝让玻尔兹曼将原子和分子作为方便的理论结构之外的任何东西。玻尔兹曼去世几年后，佩兰 [[Jean Baptiste Perrin|Perrin]] 基于爱因斯坦 [[Albert Einstein|Einstein]] 1905年的理论研究，对胶体悬浮液进行了研究(1908-1909)，证实了阿伏伽德罗数 [[Avogadro's number]] 和玻尔兹曼常数的值，使世界相信微小粒子确实存在。

To quote [[Max Planck|Planck]], "The [[logarithm]]ic connection between [[entropy]] and [[probability]] was first stated by L. Boltzmann in his [[kinetic theory of gases]]".<ref>Max Planck, p. 119.</ref> This famous formula for entropy ''S'' is<ref>The concept of [[entropy]] was introduced by [[Rudolf Clausius]] in 1865. He was the first to enunciate the [[second law of thermodynamics]] by saying that "entropy always increases".</ref><ref>An alternative is the [[Information entropy#Formal definitions|information entropy]] definition introduced in 1948 by [[Claude Elwood Shannon|Claude Shannon]].[https://archive.is/20070503225307/http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html] It was intended for use in communication theory, but is applicable in all areas. It reduces to Boltzmann's expression when all the probabilities are equal, but can, of course, be used when they are not. Its virtue is that it yields immediate results without resorting to [[factorial]]s or [[Stirling's approximation]]. Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in [[H-theorem#Quantum mechanical H-theorem|Gibbs]] (see reference).</ref>

To quote [[Max Planck|Planck]], "The [[logarithm]]ic connection between [[entropy]] and [[probability]] was first stated by L. Boltzmann in his [[kinetic theory of gases]]".<ref>Max Planck, p. 119.</ref> This famous formula for entropy ''S'' is<ref>The concept of [[entropy]] was introduced by [[Rudolf Clausius]] in 1865. He was the first to enunciate the [[second law of thermodynamics]] by saying that "entropy always increases".</ref><ref>An alternative is the [[Information entropy#Formal definitions|information entropy]] definition introduced in 1948 by [[Claude Elwood Shannon|Claude Shannon]].[https://archive.is/20070503225307/http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html] It was intended for use in communication theory, but is applicable in all areas. It reduces to Boltzmann's expression when all the probabilities are equal, but can, of course, be used when they are not. Its virtue is that it yields immediate results without resorting to [[factorial]]s or [[Stirling's approximation]]. Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in [[H-theorem#Quantum mechanical H-theorem|Gibbs]] (see reference).</ref>