Introductory note to 1906

pp. 562-593

in: Ernst Zermelo, Calculus of variations, applied mathematics, and physics/Variationsrechnung, angewandte mathematik und physik, Berlin, Springer, 2013

Abstract

The spirit of Zermelo's review 1906 of Gibbs 1902 becomes obvious from what Zermelo says in the preface to his German translation Gibbs 1905 of Gibbs 1902: "This is the first effort to develop rigorously and on a secure mathematical basis the statistical and probabilistic considerations in mechanics which are indispensable in various areas of physics, especially in the kinetic theory of gases. As such, this work is of paramount interest and of permanent value, even if not all the derivations by the author should turn out to be tenable. Which objections I have to make, from my side, in particular against the considerations in Chapter 12, in as far as these attribute to mechanical systems a tendency towards a state of statistical equilibrium, and on this basis, a complete analogy with thermodynamical systems, I intend to explicate on another occasion [namely in the review 1906]."