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.