Editing H-theorem (section)

{{short description|Thermodynamic theorem}}
{{DISPLAYTITLE:''H''-theorem}}
In classical [[statistical mechanics]], the ''' ''H''-theorem''', introduced by [[Ludwig Boltzmann]] in 1872, describes the tendency of the quantity ''H'' (defined below) to decrease in a nearly-[[ideal gas]] of molecules.<ref name=":0">L. Boltzmann, "[https://sites.google.com/site/articleshistoriques/theorie-cinetique/Boltzmann1872.pdf Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen] {{Webarchive|url=https://web.archive.org/web/20191017094637/https://sites.google.com/site/articleshistoriques/theorie-cinetique/Boltzmann1872.pdf |date=2019-10-17 }}." Sitzungsberichte Akademie der Wissenschaften 66 (1872): 275-370.
<br />English translation: {{Cite book | last1 = Boltzmann | first1 = L. | chapter = Further Studies on the Thermal Equilibrium of Gas Molecules | doi = 10.1142/9781848161337_0015 | title = The Kinetic Theory of Gases | series = History of Modern Physical Sciences | volume = 1 | pages = 262–349 | year = 2003 | isbn = 978-1-86094-347-8 | bibcode = 2003HMPS....1..262B }}</ref> As this quantity ''H'' was meant to represent the [[entropy]] of thermodynamics, the ''H''-theorem was an early demonstration of the power of [[statistical mechanics]] as it claimed to derive the [[second law of thermodynamics]]—a statement about fundamentally [[irreversible process]]es—from reversible microscopic mechanics. It is thought to prove [[Laws of thermodynamics|the second law of thermodynamics]],<ref>{{Cite journal|last1=Lesovik|first1=G. B.|last2=Lebedev|first2=A. V.|last3=Sadovskyy|first3=I. A.|last4=Suslov|first4=M. V.|last5=Vinokur|first5=V. M.|date=2016-09-12|title=H-theorem in quantum physics|journal=Scientific Reports|language=en|volume=6|pages=32815|doi=10.1038/srep32815|issn=2045-2322|pmc=5018848|pmid=27616571|arxiv=1407.4437|bibcode=2016NatSR...632815L}}</ref><ref>{{Cite news|url=http://www.popularmechanics.com/science/a23640/loophole-second-law-thermodynamics/|title=We May Have Found a Way to Cheat the Second Law of Thermodynamics|date=2016-10-31|newspaper=Popular Mechanics|access-date=2016-11-02}}</ref><ref>{{Cite news|url=https://www.theguardian.com/science/2013/dec/01/what-is-the-second-law-of-thermodynamics|title=What is the second law of thermodynamics?|last=Jha|first=Alok|date=2013-12-01|newspaper=The Guardian|language=en-GB|issn=0261-3077|access-date=2016-11-02}}</ref> albeit under the assumption of low-entropy initial conditions.<ref>Zeh, H. D., & Page, D. N. (1990). The physical basis of the direction of time. Springer-Verlag, New York</ref>

The ''H''-theorem is a natural consequence of the kinetic equation derived by Boltzmann that has come to be known as [[Boltzmann's equation]]. The ''H''-theorem has led to considerable discussion about its actual implications,<ref>Ehrenfest, Paul, & Ehrenfest, Tatiana (1959). The Conceptual Foundations of the Statistical Approach in Mechanics. New York: Dover.</ref> with major themes being:
* What is entropy? In what sense does Boltzmann's quantity ''H'' correspond to the thermodynamic entropy?
* Are the assumptions (especially the assumption of [[molecular chaos]]) behind Boltzmann's equation too strong? When are these assumptions violated?