Eur. Phys. J. H 36, 353-378 (2011)
https://doi.org/10.1140/epjh/e2011-10048-5

Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann’s H-theorem (1868–1877)

¹ Max-Planck-Institut für Wissenschaftsgeschichte, Boltzmannstrasse 22, 14195 Berlin, Germany
² Fritz-Haber-Institut der Max Planck Gesellschaft, Theory Department, Faradayweg 4-6, 14195 Berlin, Germany

^a e-mail: mbadino@mpiwg-berlin.mpg.de

Received: 7 December 2010
Received in final form: 24 August 2011
Published online: 7 October 2011

Abstract

An intricate, long, and occasionally heated debate surrounds Boltzmann’s H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt’s 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann’s research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt’s challenge and Boltzmann’s response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.