Liouville geometry of classical thermodynamics

Abstract

In the contact-geometric formulation of classical thermodynamics distinction is made between the energy and entropy representation. This distinction can be resolved by taking homogeneous coordinates for the intensive variables. It results in a geometric formulation on the cotangent bundle of the manifold of extensive variables, where all geometric objects are homogeneous in the cotangent variables. The resulting geometry based on the Liouville form is studied in depth. Additional homogeneity with respect to the extensive variables, corresponding to the classical Gibbs-Duhem relation, is treated within the same geometric framework.