Phase transitions in geometrothermodynamics

TL;DR

This paper explores how the curvature of the equilibrium manifold in geometrothermodynamics signals phase transitions and measures thermodynamic interactions across various systems with different degrees of freedom.

Contribution

It demonstrates that thermodynamic curvature derived from Legendre invariant metrics can identify phase transitions and quantify interactions in diverse thermodynamic systems.

Findings

Thermodynamic curvature becomes singular at phase transition points.

The curvature effectively measures thermodynamic interactions.

The approach applies to systems with two and three degrees of freedom.

Abstract

Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic metrics for the equilibrium manifold whose curvature becomes singular at those points where phase transitions of first and second order occur. We conclude that the thermodynamic curvature of the equilibrium manifold, as defined in geometrothermodynamics, can be used as a measure of thermodynamic interaction in diverse systems with two and three thermodynamic degrees of freedom.