An axiomatic approach to classical thermodynamics

Abstract

Carathéodory’s formulation of classical thermodynamics is cast into a mathematically rigorous form, in which such well-known results as the existence of entropy and of (positive) absolute temperature, the principle of increase of entropy and the positivity of isometric specific heats are shown to follow logically from a set of postulates closely related to the traditional laws of thermodynamics and more economical than those of the original formulation. The basic tools are differential geometry and topology, the latter being needed in order to eliminate those flaws in the old arguments that arise from the erroneous application of local results in a global context.