The action principle for equilibrium thermodynamics

TL;DR

This paper introduces an action principle framework for equilibrium thermodynamics, deriving conditions that ensure the path-independence of state functions through a variational approach.

Contribution

It formulates thermodynamic processes using an action principle and derives an integrability condition ensuring the path-independence of thermodynamic state functions.

Findings

Derivation of the Lagrangian 1-form closure relation

Establishment of a variational principle for thermodynamics

Clarification of conditions for path-independent thermodynamic functions

Abstract

The action principle is introduced to describe the thermodynamic processes of the state functions from the initial equilibrium state to the final equilibrium state. To capture the path-independent property of the state functions through the thermodynamic processes, one requires an integrability condition called the Lagrangian 1-form closure relation as a direct result of the least action principle with respect to the independent variables.