Thermodynamic systems as bosonic strings

TL;DR

This paper models thermodynamic systems using geometric principles, showing that their phase space and equilibrium states can be described by invariant metrics satisfying Nambu-Goto-like equations, linking thermodynamics with string theory concepts.

Contribution

It introduces a novel geometric framework for thermodynamics based on variational principles and string theory analogies, providing new solutions for thermodynamic systems.

Findings

Legendre invariant metrics describe ideal and van der Waals gases.

Equilibrium space volume elements are extremal, satisfying Nambu-Goto equations.

New solutions potentially representing specific thermodynamic systems are derived.

Abstract

We apply variational principles in the context of geometrothermodynamics. The thermodynamic phase space ${\cal T}$ and the space of equilibrium states ${\cal E}$ turn out to be described by Riemannian metrics which are invariant with respect to Legendre transformations and satisfy the differential equations following from the variation of a Nambu-Goto-like action. This implies that the volume element of ${\cal E}$ is an extremal and that ${\cal E}$ and ${\cal T}$ are related by an embedding harmonic map. We explore the physical meaning of geodesic curves in ${\cal E}$ as describing quasi-static processes that connect different equilibrium states. We present a Legendre invariant metric which is flat (curved) in the case of an ideal (van der Waals) gas and satisfies Nambu-Goto equations. The method is used to derive some new solutions which could represent particular thermodynamic systems.