Liouville geometry of classical thermodynamics
arXiv:2102.05493 · doi:10.1016/j.geomphys.2021.104365
Abstract
In the contact-geometric formulation of classical thermodynamics distinction is made between the energy and entropy representation, which can be resolved by taking homogeneous coordinates for the intensive variables. This 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 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.
27 pages