A geometric description of some thermodynamical systems

TL;DR

This paper demonstrates that almost cosymplectic structures provide a natural geometric framework for thermodynamical systems, enabling the application of geometric tools to analyze their evolution, symmetries, and discretizations.

Contribution

It introduces a geometric approach using almost cosymplectic structures to study thermodynamical systems, reproducing known equations through a new geometric perspective.

Findings

Reproduces thermodynamical evolution equations using geometric methods

Facilitates analysis of symmetries and reduction in thermodynamics

Enables geometric discretization of thermodynamical systems

Abstract

In this paper we show how almost cosymplectic structures are a natural framework to study thermodynamical systems. Indeed, we are able to obtain the same evolution equations obtained previously by Gay-Balmaz and Yoshimura (see Entropy, 21(8):39, 2019) using variational arguments. The proposed geometric description allows us to apply geometrical tools to discuss reduction by symmetries, the Hamilton-Jacobi equation or discretization of these systems.