Curvature as a Measure of the Thermodynamic Interaction

TL;DR

This paper develops a geometric framework for thermodynamics using Riemannian contact geometry, demonstrating how curvature can quantify thermodynamic interactions across various models.

Contribution

It introduces invariant metrics on the phase manifold and systematically reviews the use of curvature as a measure of thermodynamic interaction.

Findings

Curvature serves as an indicator of thermodynamic interaction.

Invariant metrics are constructed for Legendre transformations.

The framework unifies various thermodynamic models through geometric methods.

Abstract

We present a systematic and consistent construction of geometrothermodynamics by using Riemannian contact geometry for the phase manifold and harmonic maps for the equilibrium manifold. We present several metrics for the phase manifold that are invariant with respect to Legendre transformations and induce thermodynamic metrics on the equilibrium manifold. We review all the known examples in which the curvature of the thermodynamic metrics can be used as a measure of the thermodynamic interaction.