Analytical Thermodynamics

TL;DR

This paper develops a theoretical framework connecting classical mechanics with nonequilibrium thermodynamics, deriving evolution equations from a variational principle for homogeneous systems with finite state variables.

Contribution

It introduces a novel approach to derive thermodynamic evolution equations using an augmented Lagrangian action, bridging mechanics and thermodynamics.

Findings

Free energy and entropy are independent functions away from equilibrium.

The theory applies to homogeneous systems with finite state variables.

Evolution equations are derived from a stationarity principle.

Abstract

This paper proposes a theory that bridges classical analytical mechanics and nonequilibrium thermodynamics. Its intent is to derive the evolution equations of a system from a stationarity principle for a suitably augmented Lagrangian action. This aim is attained for homogeneous systems, described by a finite number of state variables depending on time only. In particular, it is shown that away from equilibrium free energy and entropy are independent constitutive functions.