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本词条由栗子CUGB初步翻译{{short description| Austrian physicist and philosopher}}

本词条由栗子CUGB初步翻译{{short description| Austrian physicist and philosopher}}

{{See also|Boltzmann}}

{{See also|Boltzmann}}

 

{{Infobox scientist

{{Infobox scientist

| image = Boltzmann2.jpg

| image = Boltzmann2.jpg

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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>

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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" />

===Academic career===

===Academic career===

In 1894, Boltzmann succeeded his teacher [[Joseph Stefan]] as Professor of Theoretical Physics at the University of Vienna.

In 1894, Boltzmann succeeded his teacher [[Joseph Stefan]] as Professor of Theoretical Physics at the University of Vienna.

===Final years and death===

=== Final years and death===

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>

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" />

==Philosophy==

==Philosophy==

Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered [[pack of cards]] under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.)<ref>"[[Collier's Encyclopedia]]", Volume 19 Phyfe to Reni, "Physics", by David Park, p. 15</ref> The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary [[dice]], with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system ''must'' move to one of the more probable states.<ref>"Collier's Encyclopedia", Volume 22 Sylt to Uruguay, Thermodynamics, by Leo Peters, p. 275</ref> However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes{{Citation needed|date=January 2019}}, and since statistically the [[data]] tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.

Boltzmann accomplished the feat of showing that the second law of thermodynamics is only a statistical fact. The gradual disordering of energy is analogous to the disordering of an initially ordered [[pack of cards]] under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out. (This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.)<ref>"[[Collier's Encyclopedia]]", Volume 19 Phyfe to Reni, "Physics", by David Park, p. 15</ref> The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability. Consider two ordinary [[dice]], with both sixes face up. After the dice are shaken, the chance of finding these two sixes face up is small (1 in 36); thus one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable state to change to one that is more probable. With millions of dice, like the millions of atoms involved in thermodynamic calculations, the probability of their all being sixes becomes so vanishingly small that the system ''must'' move to one of the more probable states.<ref>"Collier's Encyclopedia", Volume 22 Sylt to Uruguay, Thermodynamics, by Leo Peters, p. 275</ref> However, mathematically the odds of all the dice results not being a pair sixes is also as hard as the ones of all of them being sixes{{Citation needed|date=January 2019}}, and since statistically the [[data]] tend to balance, one in every 36 pairs of dice will tend to be a pair of sixes, and the cards -when shuffled- will sometimes present a certain temporary sequence order even if in its whole the deck was disordered.

==Awards and honours==

== Awards and honours==

In 1885 he became a member of the Imperial [[Austrian Academy of Sciences]] and in 1887 he became the President of the [[University of Graz]]. He was elected a member of the [[Royal Swedish Academy of Sciences]] in 1888 and a [[List of Fellows of the Royal Society elected in 1899|Foreign Member of the Royal Society (ForMemRS) in 1899]].<ref name=frs>{{cite web|archiveurl=https://web.archive.org/web/20150316060617/https://royalsociety.org/about-us/fellowship/fellows/|archivedate=2015-03-16|url=https://royalsociety.org/about-us/fellowship/fellows/|publisher=[[Royal Society]]|location=London|title=Fellows of the Royal Society}}</ref> [[List of things named after Ludwig Boltzmann|Numerous things]] are named in his honour.

In 1885 he became a member of the Imperial [[Austrian Academy of Sciences]] and in 1887 he became the President of the [[University of Graz]]. He was elected a member of the [[Royal Swedish Academy of Sciences]] in 1888 and a [[List of Fellows of the Royal Society elected in 1899|Foreign Member of the Royal Society (ForMemRS) in 1899]].<ref name="frs">{{cite web|archiveurl=https://web.archive.org/web/20150316060617/https://royalsociety.org/about-us/fellowship/fellows/|archivedate=2015-03-16|url=https://royalsociety.org/about-us/fellowship/fellows/|publisher=[[Royal Society]]|location=London|title=Fellows of the Royal Society}}</ref> [[List of things named after Ludwig Boltzmann|Numerous things]] are named in his honour.

==See also==

==See also==

* [[Energetics]]

*[[Energetics]]

* [[Boltzmann brain]]

*[[Boltzmann brain]]

==References==

==References==

{{reflist|30em}}

{{reflist|30em}}

==Further reading==

== Further reading==

* Roman Sexl & John Blackmore (eds.), "Ludwig Boltzmann – Ausgewahlte Abhandlungen", (Ludwig Boltzmann Gesamtausgabe, Band 8), Vieweg, Braunschweig, 1982.

*Roman Sexl & John Blackmore (eds.), "Ludwig Boltzmann – Ausgewahlte Abhandlungen", (Ludwig Boltzmann Gesamtausgabe, Band 8), Vieweg, Braunschweig, 1982.

* John Blackmore (ed.), "Ludwig Boltzmann – His Later Life and Philosophy, 1900–1906, Book One: A Documentary History", Kluwer, 1995. {{ISBN|978-0-7923-3231-2}}

*John Blackmore (ed.), "Ludwig Boltzmann – His Later Life and Philosophy, 1900–1906, Book One: A Documentary History", Kluwer, 1995. {{ISBN|978-0-7923-3231-2}}

* John Blackmore, "Ludwig Boltzmann – His Later Life and Philosophy, 1900–1906, Book Two: The Philosopher", Kluwer, Dordrecht, Netherlands, 1995. {{ISBN|978-0-7923-3464-4}}

*John Blackmore, "Ludwig Boltzmann – His Later Life and Philosophy, 1900–1906, Book Two: The Philosopher", Kluwer, Dordrecht, Netherlands, 1995. {{ISBN|978-0-7923-3464-4}}

* John Blackmore (ed.), "Ludwig Boltzmann – Troubled Genius as Philosopher", in Synthese, Volume 119, Nos. 1 & 2, 1999, pp.&nbsp;1–232.

*John Blackmore (ed.), "Ludwig Boltzmann – Troubled Genius as Philosopher", in Synthese, Volume 119, Nos. 1 & 2, 1999, pp.&nbsp;1–232.

* {{cite book|last1=Blundell|first1=Stephen|last2=Blundell|first2=Katherine M.|title=Concepts in Thermal Physics|url=https://books.google.com/books?id=vuBHXwAACAAJ|year=2006|publisher=Oxford University Press|isbn=978-0-19-856769-1|page=29}}

*{{cite book|last1=Blundell|first1=Stephen|last2=Blundell|first2=Katherine M.|title=Concepts in Thermal Physics|url=https://books.google.com/books?id=vuBHXwAACAAJ|year=2006|publisher=Oxford University Press|isbn=978-0-19-856769-1|page=29}}

* Boltzmann, ''Ludwig Boltzmann – Leben und Briefe'', ed., Walter Hoeflechner, Akademische Druck- u. Verlagsanstalt. Graz, Oesterreich, 1994

*Boltzmann, ''Ludwig Boltzmann – Leben und Briefe'', ed., Walter Hoeflechner, Akademische Druck- u. Verlagsanstalt. Graz, Oesterreich, 1994

* Brush, Stephen G. (ed. & tr.), Boltzmann, ''Lectures on Gas Theory'', Berkeley, California: U. of California Press, 1964

*Brush, Stephen G. (ed. & tr.), Boltzmann, ''Lectures on Gas Theory'', Berkeley, California: U. of California Press, 1964

* Brush, Stephen G. (ed.), ''Kinetic Theory'', New York: Pergamon Press, 1965

*Brush, Stephen G. (ed.), ''Kinetic Theory'', New York: Pergamon Press, 1965

* {{cite book | last=Brush | first=Stephen G. | chapter=Boltzmann | editor=Charles Coulston Gillispie | title=Dictionary of Scientific Biography | chapter-url=https://archive.org/details/dictionaryofsci001gill | chapter-url-access=registration | publisher=Scribner | location=New York | year=1970 | isbn=978-0-684-16962-0 |series=}}

*{{cite book | last=Brush | first=Stephen G. | chapter=Boltzmann | editor=Charles Coulston Gillispie | title=Dictionary of Scientific Biography | chapter-url=https://archive.org/details/dictionaryofsci001gill | chapter-url-access=registration | publisher=Scribner | location=New York | year=1970 | isbn=978-0-684-16962-0 |series=}}

* {{cite book| last=Brush | first=Stephen G. | authorlink= | title=The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases | edition= | publisher=North-Holland | location=Amsterdam | year=1986 | isbn=978-0-7204-0370-1 | series=}}

*{{cite book| last=Brush | first=Stephen G. | authorlink= | title=The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases | edition= | publisher=North-Holland | location=Amsterdam | year=1986 | isbn=978-0-7204-0370-1 | series=}}

* {{cite book | last = Cercignani | first = Carlo | author-link = Carlo Cercignani | title = Ludwig Boltzmann: The Man Who Trusted Atoms | publisher = Oxford University Press | year = 1998 | isbn = 9780198501541 | url-access = registration | url = https://archive.org/details/ludwigboltzmannm0000cerc }}

*{{cite book | last = Cercignani | first = Carlo | author-link = Carlo Cercignani | title = Ludwig Boltzmann: The Man Who Trusted Atoms | publisher = Oxford University Press | year = 1998 | isbn = 9780198501541 | url-access = registration | url = https://archive.org/details/ludwigboltzmannm0000cerc }}

* {{Cite book |last=Darrigol |first = Olivier |title = Atoms, Mechanics, and Probability: Ludwig Boltzmann's Statistico-Mechanical |publisher = [[Oxford University Press]] |year = 2018 |url = https://books.google.com/books?id=APBIDwAAQBAJ&pg=PA376 |isbn = 978-0-19-881617-1}}

*{{Cite book |last=Darrigol |first = Olivier |title = Atoms, Mechanics, and Probability: Ludwig Boltzmann's Statistico-Mechanical |publisher = [[Oxford University Press]] |year = 2018 |url = https://books.google.com/books?id=APBIDwAAQBAJ&pg=PA376 |isbn = 978-0-19-881617-1}}

* [[Paul Ehrenfest|Ehrenfest, P.]] & [[Tatyana Afanasyeva|Ehrenfest, T.]] (1911) "Begriffliche Grundlagen der statistischen Auffassung in der Mechanik", in [[Klein's encyclopedia|''Encyklopädie der mathematischen Wissenschaften mit Einschluß ihrer Anwendungen'']] Band IV, 2. Teil ( F. Klein and C. Müller (eds.). Leipzig: Teubner, pp.&nbsp;3–90. Translated as ''The Conceptual Foundations of the Statistical Approach in Mechanics''. New York: Cornell University Press, 1959. {{ISBN|0-486-49504-3}}

*[[Paul Ehrenfest|Ehrenfest, P.]] & [[Tatyana Afanasyeva|Ehrenfest, T.]] (1911) "Begriffliche Grundlagen der statistischen Auffassung in der Mechanik", in [[Klein's encyclopedia|''Encyklopädie der mathematischen Wissenschaften mit Einschluß ihrer Anwendungen'']] Band IV, 2. Teil ( F. Klein and C. Müller (eds.). Leipzig: Teubner, pp.&nbsp;3–90. Translated as ''The Conceptual Foundations of the Statistical Approach in Mechanics''. New York: Cornell University Press, 1959. {{ISBN|0-486-49504-3}}

* {{cite journal | last=Everdell | first=William R | year=1988 | title=The Problem of Continuity and the Origins of Modernism: 1870–1913 | journal=History of European Ideas  | volume=9 | issue=5 | pages=531–552 | doi=10.1016/0191-6599(88)90001-0 }}

*{{cite journal | last=Everdell | first=William R | year=1988 | title=The Problem of Continuity and the Origins of Modernism: 1870–1913 | journal=History of European Ideas  | volume=9 | issue=5 | pages=531–552 | doi=10.1016/0191-6599(88)90001-0 }}

* {{cite book | last=Everdell | first=William R | year=1997 | title=The First Moderns | url=https://archive.org/details/firstmodernsprof00ever | url-access=registration | edition= | publisher=University of Chicago Press | location=Chicago }}

*{{cite book | last=Everdell | first=William R | year=1997 | title=The First Moderns | url=https://archive.org/details/firstmodernsprof00ever | url-access=registration | edition= | publisher=University of Chicago Press | location=Chicago }}

* {{cite book |last=Gibbs |first=Josiah Willard |authorlink=Josiah Willard Gibbs |title=Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics |year=1902 |publisher=Charles Scribner's Sons |location=New York|title-link=Elementary Principles in Statistical Mechanics }}

*{{cite book |last=Gibbs |first=Josiah Willard |authorlink=Josiah Willard Gibbs |title=Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics |year=1902 |publisher=Charles Scribner's Sons |location=New York|title-link=Elementary Principles in Statistical Mechanics }}

* {{cite book | last = Johnson | first = Eric | title = ''Anxiety and the Equation: Understanding Boltzmann's Entropy'' | publisher = The MIT Press | year = 2018 | isbn = 978-0-262-03861-4}}

*{{cite book | last = Johnson | first = Eric | title = ''Anxiety and the Equation: Understanding Boltzmann's Entropy'' | publisher = The MIT Press | year = 2018 | isbn = 978-0-262-03861-4}}

* {{cite book| last=Klein | first=Martin J. | chapter=The Development of Boltzmann's Statistical Ideas | editor=[[E.G.D. Cohen]] |editor2=W. Thirring | title=The Boltzmann Equation: Theory and Applications | url=https://archive.org/details/boltzmannequatio00schm | url-access=limited | publisher=Springer | location=Wien | year=1973 | isbn=978-0-387-81137-6 | pages=[https://archive.org/details/boltzmannequatio00schm/page/n65 53]–106 | series=Acta physica Austriaca Suppl. 10 }}

*{{cite book| last=Klein | first=Martin J. | chapter=The Development of Boltzmann's Statistical Ideas | editor=[[E.G.D. Cohen]] |editor2=W. Thirring | title=The Boltzmann Equation: Theory and Applications | url=https://archive.org/details/boltzmannequatio00schm | url-access=limited | publisher=Springer | location=Wien | year=1973 | isbn=978-0-387-81137-6 | pages=[https://archive.org/details/boltzmannequatio00schm/page/n65 53]–106 | series=Acta physica Austriaca Suppl. 10 }}

* {{cite book | last=Lindley | first=David | authorlink=David Lindley (Physicist) | title=Boltzmann's Atom: The Great Debate That Launched A Revolution In Physics | edition= | publisher=Free Press | location=New York | year=2001 | isbn=978-0-684-85186-0 | url=https://archive.org/details/isbn_9780684851860 }}

*{{cite book | last=Lindley | first=David | authorlink=David Lindley (Physicist) | title=Boltzmann's Atom: The Great Debate That Launched A Revolution In Physics | edition= | publisher=Free Press | location=New York | year=2001 | isbn=978-0-684-85186-0 | url=https://archive.org/details/isbn_9780684851860 }}

* {{cite journal | last=Lotka | first=A. J. | year=1922 | title=Contribution to the Energetics of Evolution | doi= 10.1073/pnas.8.6.147 | journal=Proc. Natl. Acad. Sci. U.S.A.  | volume=8 | issue=6 | pages=147–51 | pmid=16576642 | pmc=1085052 |bibcode = 1922PNAS....8..147L }}

*{{cite journal | last=Lotka | first=A. J. | year=1922 | title=Contribution to the Energetics of Evolution | doi= 10.1073/pnas.8.6.147 | journal=Proc. Natl. Acad. Sci. U.S.A.  | volume=8 | issue=6 | pages=147–51 | pmid=16576642 | pmc=1085052 |bibcode = 1922PNAS....8..147L }}

* {{cite book | last= Meyer| first=Stefan  | authorlink=Stefan Meyer (physicist) | title=Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage 20. Februar 1904  | url= https://archive.org/details/festschriftludw00meyegoog| publisher=J. A. Barth | year=1904  |language = German }}

*{{cite book | last= Meyer| first=Stefan  | authorlink=Stefan Meyer (physicist) | title=Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage 20. Februar 1904  | url= https://archive.org/details/festschriftludw00meyegoog| publisher=J. A. Barth | year=1904  |language = German }}

* {{cite book | last=Planck | first=Max | authorlink=Max Planck | title=The Theory of Heat Radiation | url=https://archive.org/details/theoryofheatradi00planrich | publisher=P. Blakiston Son & Co | year=1914}} English translation by Morton Masius of the 2nd ed. of ''Waermestrahlung''. Reprinted by Dover (1959) & (1991). {{ISBN|0-486-66811-8}}

*{{cite book | last=Planck | first=Max | authorlink=Max Planck | title=The Theory of Heat Radiation | url=https://archive.org/details/theoryofheatradi00planrich | publisher=P. Blakiston Son & Co | year=1914}} English translation by Morton Masius of the 2nd ed. of ''Waermestrahlung''. Reprinted by Dover (1959) & (1991). {{ISBN|0-486-66811-8}}

* {{cite book | last=Tolman | first=Richard C. | title=The Principles of Statistical Mechanics | publisher=Oxford University Press | year=1938}} Reprinted: Dover (1979). {{ISBN|0-486-63896-0}}

*{{cite book | last=Tolman | first=Richard C. | title=The Principles of Statistical Mechanics | publisher=Oxford University Press | year=1938}} Reprinted: Dover (1979). {{ISBN|0-486-63896-0}}

==External links==

==External links==

{{Sister project links|wikt=no|commons=Ludwig Boltzmann|b=no|n=no|q=Ludwig Boltzmann|s=Author:Ludwig Eduard Boltzmann|v=no|species=no|voy=no}}

{{Sister project links|wikt=no|commons=Ludwig Boltzmann|b=no|n=no|q=Ludwig Boltzmann|s=Author:Ludwig Eduard Boltzmann|v=no|species=no|voy=no}}

* {{cite encyclopedia | last=Uffink | first=Jos | title=Boltzmann's Work in Statistical Physics | year=2004 | url=http://plato.stanford.edu/entries/statphys-Boltzmann/ | accessdate=2007-06-11 | encyclopedia=[[Stanford Encyclopedia of Philosophy]]}}

*{{cite encyclopedia | last=Uffink | first=Jos | title=Boltzmann's Work in Statistical Physics | year=2004 | url=http://plato.stanford.edu/entries/statphys-Boltzmann/ | accessdate=2007-06-11 | encyclopedia=[[Stanford Encyclopedia of Philosophy]]}}

* {{MacTutor Biography|id=Boltzmann}}

*{{MacTutor Biography|id=Boltzmann}}

* [[Ruth Lewin Sime]], ''Lise Meitner: A Life in Physics'' [https://www.washingtonpost.com/wp-srv/style/longterm/books/chap1/lisemeitner.htm Chapter One: Girlhood in Vienna] gives [[Lise Meitner]]'s account of Boltzmann's teaching and career.

*[[Ruth Lewin Sime]], ''Lise Meitner: A Life in Physics'' [https://www.washingtonpost.com/wp-srv/style/longterm/books/chap1/lisemeitner.htm Chapter One: Girlhood in Vienna] gives [[Lise Meitner]]'s account of Boltzmann's teaching and career.

* Eftekhari, Ali, "[http://philsci-archive.pitt.edu/archive/00001717/02/Ludwig_Boltzmann.pdf Ludwig Boltzmann (1844–1906).]" Discusses Boltzmann's philosophical opinions, with numerous quotes.

*Eftekhari, Ali, "[http://philsci-archive.pitt.edu/archive/00001717/02/Ludwig_Boltzmann.pdf Ludwig Boltzmann (1844–1906).]" Discusses Boltzmann's philosophical opinions, with numerous quotes.

* {{cite arXiv | last = Rajasekar | first = S. |author2=Athavan, N. | title = Ludwig Edward Boltzmann | eprint = physics/0609047 | date = 2006-09-07 }}

*{{cite arXiv | last = Rajasekar | first = S. |author2=Athavan, N. | title = Ludwig Edward Boltzmann | eprint = physics/0609047 | date = 2006-09-07 }}

* {{MathGenealogy|13105}}

*{{MathGenealogy|13105}}

* {{ScienceWorldBiography |urlname=Boltzmann |title=Boltzmann, Ludwig (1844–1906)}}

*{{ScienceWorldBiography |urlname=Boltzmann |title=Boltzmann, Ludwig (1844–1906)}}

* {{Find a Grave|1518}}

*{{Find a Grave|1518}}

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[[Category:待整理页面]]