The H-Theorem, Molecular Disorder and Probability: Perspectives from Boltzmann’s Lectures on Gas Theory

This paper examines Boltzmann’s responses to the Loschmidt reversibility objection to the H-theorem, as presented in his Lectures on Gas Theory. I describe and evaluate two distinct conceptions of the assumption of molecular disorder found in this work, and contrast these notions with the Stosszahlansatz, as well as with the predominant contemporary conception of molecular disorder. Both these conceptions are assessed with respect to the reversibility objection. Finally, I interpret Boltzmann as claiming that a state of molecular disorder serves as a necessary condition for the application of probabilistic arguments. This in turn offers a way to bridge the conceptual gap between the H-theorem and his combinatorial argument.