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All theories of matter, starting with the ancient Greek philosophers, can be classified as either continuous or discrete (i.e., particulate). This dichotomy is due to Aristotle. Aristotle held that matter was continuous: infinitely divisible. Aristotle believed that a vacuum was impossible (indeed, he claimed to prove this). Since a particulate theory ...

9

Stefano Bordoni's 2012 Taming Complexity (e-book from ResearchGate; review) is a good place to start.(Bordoni has a master's degree in physics and three PhDs, in the history of science, anthropology and epistemology of complexity, and philosophy.) Bordoni refers to Brush's 1986 The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in ...

7

No, he did not. Stokes could not have offered a problem of the distribution of velocities of gas particles for the simple reason that he never thought of fluids as consisting of particles. He was a typical 19-th century continualist, as a look at his works shows. After Bernoulli's derivation of the ideal gas law in 1738 kinetic theory was moribund until late ...

7

Community-wiki timeline of relevant literature: By year written, sources where $k$ is named after... Author |Dated |Published |Denoted|Called Boltzmann 1877 (e) –– S ein constanter Factor 1 Boltzmann• 1895.09 1896 (e) RM S für alle Gase gleiche Constante RM 2 Boltzmann• 1898.08 1898 (e) RM S –– ...

5

Bolzman was closer to the truth. On the modern state of this question, I recommend the classics: Ehrenfest, Paul; Ehrenfest, Tatiana The conceptual foundations of the statistical approach in mechanics. Translated from the German by Michael J. Moravcsik. With a foreword by M. Kac and G. E. Uhlenbeck. Reprint of the 1959 English edition. Dover Publications, ...

5

Finally found! This evening I was reading an article by Silver et al: Silver, H., N. E. Frankel, and B. W. Ninham. “A Class of Mean Field Models.” Journal of Mathematical Physics 13, no. 4 (April 1, 1972): 468–74. doi:10.1063/1.1666002, where you can find an explicit formula for the free energy of a class of mean field models (including XY model). The ...

4

The following two books are also very good resources about this topic ; the first one has a more historical approach. Carlo Cercignani, Ludwig Boltzmann. The man who trusted atoms. Oxford University Press, Oxford, 1998. xviii+329 pp. ISBN: 0-19-850154-4 Giovanni Gallavotti, Statistical mechanics. A short treatise. Texts and Monographs in Physics. Springer-...

4

Q: When did the name “Boltzmann constant” prevail, and how? In Herzfeld's review article from 1920 for the Encyklopädie der Mathematischen Wissenschaften the symbol $k$ is called Boltzmann's constant without further discussion, so this must have been common usage at that time. This implies that there is no connection with Boltzmann's tombstone, which is ...

4

One should remember the context of the time when Boltzmann wrote his 1877 paper. Weierstrass just created a rigorous version of mathematical analysis and probability theory was not even close to Kolmogorov's formalization. Kinetic theory of gases was highly controversial, with Mach and Ostwald rejecting it altogether. Boltzmann's earlier publication (1872) ...

3

Yes, it is a coincidence. The concept of fugacity (from the Latin for "fleetness, tendency to flee") was originally introduced by Gilbert Lewis in his 1901 paper "The Law of Physico-Chemical Change" for the pressure of an ideal gas which has the same chemical potential as a real gas. Lewis notated this with ψ, though these days the letter f is used. The ...

3

As far as I know, this model (well, the quantum version of it) was introduced in the following paper: Two soluble models of an antiferromagnetic chain, Elliott Lieb, Theodore Schultz and Daniel Mattis, Annals of Physics, Volume 16, Issue 3, December 1961, Pages 407--466. The paper can be found here. The model is introduced in Section II. Let us also ...

2

People often expect names and notations to have some deep meanings, or at least a story behind them, but in more cases than not all there is are some loose associations, if that, described as "historical reasons", which is a polite way of saying "just cuz". Gibbs introduced the names in Elementary Principles in Statistical Mechanics (1902), and he did not ...

2

@kimchi lover, gave the answer. The article: Brush, Stephen G. "Boltzmann's “Eta Theorem”: Where's the Evidence?." American Journal of Physics 35.9 (1967): 892-892. talks about the problem of the naming of the theorem. So initially Boltzmann used $E$ for entropy, but according to Sidney Chapman, S.H. Burbury changed the variable to $H$ (about 1890) and ...

1

The discovery was made in trying to explain the spectrum of black body radiation, using statistical mechanics. See Wikipedia articles on History of Bose-Einstein statistics and Ultraviolet catastrophe.

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Community-wiki timeline (continued, 1917–): After 1920, a vast majority of papers call $k$ Boltzmann’s constant. So (with few exceptions) mention is only made of sources calling it another name, plus some textbooks and reference books. Author |Dated |Published |Denoted|Called Millikan 1917.01 1917 k S the entropy constant ...

1

Much to my dismay, the first proof of a global solution to the Boltzmann equation was not published until 2010. The paper was: Gressman, P.T., and R.M. Strain "Global classical solutions of the Boltzmann equation with long-range interactions," Proc. Natl. Academy Sci. 107, pp. 5744-5749, 2010. Apparently, all previous proofs had been for local ...

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