Editing Statistical mechanics (section)

== History ==
In 1738, Swiss physicist and mathematician [[Daniel Bernoulli]] published ''Hydrodynamica'' which laid the basis for the [[kinetic theory of gases]]. In this work, Bernoulli posited the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, that their impact on a surface causes the gas pressure that we feel, and that what we experience as [[heat]] is simply the kinetic energy of their motion.<ref name="uffink"/>

The founding of the field of statistical mechanics is generally credited to three physicists:
*[[Ludwig Boltzmann]], who developed the fundamental interpretation of [[entropy]] in terms of a collection of microstates
*[[James Clerk Maxwell]], who developed models of probability distribution of such states
*[[Josiah Willard Gibbs]], who coined the name of the field in 1884

In 1859, after reading a paper on the diffusion of molecules by [[Rudolf Clausius]], Scottish physicist [[James Clerk Maxwell]] formulated the [[Maxwell distribution]] of molecular velocities, which gave the proportion of molecules having a certain velocity in a specific range.<ref>See:
* Maxwell, J.C. (1860) [https://books.google.com/books?id=-YU7AQAAMAAJ&pg=PA19 "Illustrations of the dynamical theory of gases. Part I. On the motions and collisions of perfectly elastic spheres,"] ''Philosophical Magazine'', 4th series, '''19''' : 19–32. 
* Maxwell, J.C. (1860) [https://books.google.com/books?id=DIc7AQAAMAAJ&pg=PA21 "Illustrations of the dynamical theory of gases. Part II. On the process of diffusion of two or more kinds of moving particles among one another,"] ''Philosophical Magazine'', 4th series, '''20''' : 21–37.</ref> This was the first-ever statistical law in physics.<ref>{{cite book |last = Mahon |first = Basil |title=The Man Who Changed Everything – the Life of James Clerk Maxwell |location=Hoboken, NJ |publisher=Wiley |year=2003 |isbn=978-0-470-86171-4 |oclc=52358254}}</ref> Maxwell also gave the first mechanical argument that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium.<ref>{{cite journal | last = Gyenis | first = Balazs | doi = 10.1016/j.shpsb.2017.01.001 | title = Maxwell and the normal distribution: A colored story of probability, independence, and tendency towards equilibrium | journal = Studies in History and Philosophy of Modern Physics | volume = 57 | pages = 53–65 | year = 2017| arxiv = 1702.01411 | bibcode = 2017SHPMP..57...53G | s2cid = 38272381 }}</ref> Five years later, in 1864, [[Ludwig Boltzmann]], a young student in Vienna, came across Maxwell's paper and spent much of his life developing the subject further.

Statistical mechanics was initiated in the 1870s with the work of Boltzmann, much of which was collectively published in his 1896 ''Lectures on Gas Theory''.<ref>{{cite book |doi=10.1142/2012 |title=Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems |series=Series on Advances in Statistical Mechanics |date=2005 |volume=8 |bibcode=2005stst.book.....E |isbn=978-981-02-1382-4 |last1=Ebeling |first1=Werner |last2=Sokolov |first2=Igor M. }}</ref> Boltzmann's original papers on the statistical interpretation of thermodynamics, the [[H-theorem]], [[transport theory (statistical physics)|transport theory]], [[thermal equilibrium]], the [[equation of state]] of gases, and similar subjects, occupy about 2,000 pages in the proceedings of the Vienna Academy and other societies. Boltzmann introduced the concept of an equilibrium statistical ensemble and also investigated for the first time non-equilibrium statistical mechanics, with his [[H-theorem|''H''-theorem]].
[[File:Gibbs-Elementary principles in statistical mechanics.png|thumb|Cover of Gibbs' text on statistical mechanics]]
The term "statistical mechanics" was coined by the American mathematical physicist [[Josiah Willard Gibbs|J. Willard Gibbs]] in 1884.<ref>{{cite book |first1=J. W. |last1=Gibbs |date=1885 |title=On the Fundamental Formula of Statistical Mechanics, with Applications to Astronomy and Thermodynamics |oclc=702360353 }}</ref>  According to Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics, was first used by the Scottish physicist [[James Clerk Maxwell]] in 1871:
{{blockquote|text="In dealing with masses of matter, while we do not perceive the individual molecules, we are compelled to adopt what I have described as the statistical method of calculation, and to abandon the strict dynamical method, in which we follow every motion by the calculus."|author=J. Clerk Maxwell<ref>James Clerk Maxwell ,''Theory of Heat'' (London, England: Longmans, Green, and Co., 1871), [https://books.google.com/books?id=DqAAAAAAMAAJ&pg=PA309 p.&nbsp;309]</ref>}}
"Probabilistic mechanics" might today seem a more appropriate term, but "statistical mechanics" is firmly entrenched.<ref>{{cite book |title = The enigma of probability and physics |last=Mayants |first=Lazar |year=1984 |publisher=Springer |isbn=978-90-277-1674-3 |page=174 |url = https://books.google.com/books?id=zmwEfXUdBJ8C&pg=PA174 }}</ref> Shortly before his death, Gibbs published in 1902 ''[[Elementary Principles in Statistical Mechanics]]'', a book which formalized statistical mechanics as a fully general approach to address all mechanical systems—macroscopic or microscopic, gaseous or non-gaseous.<ref name="gibbs" /> Gibbs' methods were initially derived in the framework [[classical mechanics]], however they were of such generality that they were found to adapt easily to the later [[quantum mechanics]], and still form the foundation of statistical mechanics to this day.<ref name="tolman" />