Symplectic structure of equilibrium thermodynamics

TL;DR

This paper introduces a symplectic geometric framework for equilibrium thermodynamics, revealing new structures and Hamiltonian descriptions of thermodynamic processes based on contact geometry and tangent bundle analysis.

Contribution

It presents a novel symplectic structure on the tangent bundle of the equilibrium space and interprets the equilibrium space as a Lagrange submanifold, enabling Hamiltonian formulations of thermodynamics.

Findings

Symplectic structure on tangent bundle derived from contact geometry.

Equilibrium space identified as a Lagrange submanifold.

Hamiltonians formulated for thermodynamic processes.

Abstract

The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a Lagrange submanifold of the corresponding tangent bundle, if the fundamental equation is known explicitly. As a consequence, Hamiltonians can be defined that describe thermodynamic processes.