In mechanics, statistical mechanics is study of properties of matter in equilibrium, a subject derived from the kinetic theory interpretation of the laws of thermodynamics, applied generally to gases, albeit formulated from an a priori point of view, i.e. derived or reasoned from self-evident propositions. [1]

Etymology
In 1749, German scholar Gottfried Achenwall suggested that since ‘science’ dealt with the natural ‘states’ of society, it should be called statistik. [6]

In 1859, Scottish physicist James Maxwell obtained the normal distribution for molecular velocities in a gas (Maxwell-Boltzmann distribution), supposedly, taking his inspiration form Adolphe Quetelet’s curve for social statistics. [8]

There seems to be some inconsistency as to who coined the term "statistical mechanics". Some maintain that it was Maxwell in 1871 (Barri Gold) or 1878 (Werner Ebeling and Igor Sokolov). [2] Others maintain that it was American engineer Willard Gibbs who first used the term, either on his own, or citing Maxwell as having used it before him.

In 1884, Gibbs presented a paper, in Philadelphia to the American Association for the Advancement of Science, entitled “On the Fundamental Formula of Statistical Mechanics with Applications to Astronomy and Thermodynamics”, only a brief abstract of which survives. [7]

In 1892, Gibbs wrote English physicist John Strutt with characteristic modesty: [3]

“Just now I am trying to get ready for publication something on thermodynamics from the a priori point of view, or rather on 'statistical mechanics' . . . I do not know that I shall have anything particularly new in substance, but shall be contented if I can so choose my standpoint (as seems to me possible) as to get a simpler view of the subject.”

Supposedly, by the term a priori Gibbs meant related to or derived by reasoning from self-evident propositions. In any event, in 1902, Gibbs published Elementary Principles in Statistical Mechanics, which has since been called the "bible of statistical physics", which put statistical mechanics on a new and more general basis. [4]

Statistical thermodynamics
Treatises on statistical mechanics, as compared to statistical thermodynamics, according to Ralph Fowler and Edward Guggenheim, are nearly synonymous in content, albeit the former tend to contain considerable sections of purely physics or astrophysical interest, with many passages devoted entirely to mathematical details of proofs, with deliberate avoidance of the use of ordinary thermodynamic methods. [1]

Human thermodynamics
In 1952, English physicist C.G. Darwin, in his 1952 book The Next Million Years, argued that statistical mechanics could be used to study and predict human history, and that his would define the subject of human thermodynamics. In short, he argued that in order to logically predict human history, one would first need to define the person as a point molecule or human molecule and to model human social systems as "conservative dynamical systems" such that when human molecules collide there exists a conservative nature to the interaction and that both internal and external parameters must be accounted for in a statistical thermodynamic analysis of any human system. [5]

References
1. Fowler, Ralph and Guggenheim E.A. (1939). Statistical Thermodynamics: a version of Statistical Mechanics for students of Physics and Chemistry (pgs. vii-viii). The MacMillan Co. (1943 second edition).
2. (a) Ebeling, Werner and Sokolov, Igor M. (2005). Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems (ch. 1.2: On history of fundamentals of statistical thermodynamics, pgs. 3-12). World Scientific.
(b) Gold, Barri J. (2010). ThermoPoetics: Energy in Victorian Literature and Science (pg. 101). MIT Press.
3. Josiah Willard Gibbs (1829-1903) – AIP.org.
4. Gibbs, J. Willard (1901). Elementary Principles in Statistical Mechanics - Developed with Special Reference to the Rational Foundation of Thermodynamics. New York: Dover.
5. Darwin, Charles G. (1952). The Next Million Years (pg. 18). London: Rupert Hart-Davis.
6. Ball, Philip. (2004). Critical Mass - How One Thing Leads to Another (pg. 53). New York: Farrar, Straus and Giroux.
7. Klein, Martin J. (1990). “The Physics of J. Willard Gibbs in His Time” (pgs. 1-22), Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989 (pg. 12). American Mathematical Society.
8. (a) Wise, Norton M. (2002). “Time Discovered and Time Gendered in Victorian Science and Culture” (pg. 53), in: From Energy to Information: Representation in Science and Technology, Art, and Literature (editors: Bruce Clarke and Linda Henderson)) (39-58). Stanford University Press.
(b) Gold, Barri J. (2010). ThermoPoetics: Energy in Victorian Literature and Science (pg. 101). MIT Press.

Further reading
● Ma, Shang-Keng (1985). Statistical Mechanics. Philadelphia: World Scientific.

External links
Statistical mechanics – Wikipedia.