# Statistical Mechanics and its Scope in the 19th Century

## By Hajime Inaba

### Kyoto University

Abstract:

To date, most of the research into the history of the kinetic theory of gases and of statistical mechanics has focused on probabilistic or statistical methods, the controversy on the existence of atoms, and the foundation of thermodynamics. Unlike these studies, this presentation examines the phenomena kinetic theory and statistical mechanics tried to explain during the 19th century, and reviews the framework and disciplinary identity of statistical mechanics during that period. My hypothesis is that statistical mechanics in the 19th century was a theory on chemical properties of matter that were explained in physical chemistry. The hypothesis will reveal the discontinuity between statistical mechanics in the 19th century and that in the 20th century, because the latter does not concentrate on physicochemical phenomena.

I support my hypothesis from two viewpoints: statistical mechanics and physical chemistry. First, I demonstrate that both Ludwig Boltzmann and Josiah Willard Gibbs tried to explain chemical phenomena, such as dissociation of gases, phase transition, and semipermeable membranes, with their statistical theories. This is evidenced by analyzing Boltzmann`s Lectures on Gas Theory (Vorlesungen über Gastheorie, 1896/98) and Gibbs`s Elementary Principles in Statistical Mechanics (1902).

Second, the development of physical chemistry in the same era also supports my hypothesis. Max Planck and Wilhelm Ostwald, the founders of physical chemistry, had succeeded in explaining chemical phenomena by employing thermodynamics. They criticized statistical mechanics as inadequate to explain chemical phenomena. They considered that the scope of statistical mechanics should include physicochemical phenomena.