The Concept of Probability in Statistical Mechanics

Abstract

Thermodynamics was first formulated to describe the thermal properties of matter and, although its scope has now been enlarged, its relationship with the other main theories of physics, general and special relativity, classical and quantum mechanics and elementary particle theory, is still rather uneasy. As Sklar remarks [1, p. 4], it “is surprising that there is any place at all in this picture for a discipline such as thermodynamics” . It could be argued that it was this perception, leading to the conclusion that there is indeed no room for thermodynamics, which was the driving force behind the development of statistical mechanics. Of course, if this point has any weight, it must be seen in the historic context of the late nineteenth century, when attitudes to atomic models were rather ambivalent [1, 2]. Writing in the introduction to his Lectures on Gas Theory about the decline of support for atomism in continental Europe, Boltzmann [3, p. 24] remarks (presumably, sadly) that “it has been concluded that the assumption that heat is motion of the smallest particles of matter will eventually be proved false and discarded”. The energeticist case is presented starkly by Mach:¹

¹Taken from Mach’s Popular Scientific Lectures (1894) and quoted in [2, p. 21].