Proof of Carathéodory's Local Theorem and Its Global Application to Thermostatics

Abstract

It is pointed out that Carathéodory's proof of his theorem on pfaffian forms, which was used in his axiomatic development of thermostatics, is not complete and does not make clear whether this result is valid locally or globally. This theorem is replaced by a more precise statement of a local nature, for which a proof is given. By tracing through Carathéodory's use of the concept of thermal equilibrium with respect to simple systems, it is shown how the existence of a global entropy and absolute temperature may be deduced from this local result.