Linear nonequilibrium thermodynamics of reversible periodic processes and chemical oscillations

TL;DR

This paper develops a thermodynamic formalism for reversible periodic processes, demonstrating that isentropic oscillations can occur near equilibrium and applying it to mechanical and electrical systems, with potential extensions to chemical oscillations.

Contribution

It introduces a formalism incorporating antisymmetric coupling terms to describe isentropic oscillations in thermodynamic systems, extending Onsager's theory to include reversible periodic processes.

Findings

Isentropic oscillations are possible near equilibrium.

The formalism applies to mechanical and electrical oscillations.

Potential extension to chemical oscillations.

Abstract

Onsager's phenomenological equations successfully describe irreversible thermodynamic processes. They assume a symmetric coupling matrix between thermodynamic fluxes and forces. It is easily shown that the antisymmetric part of a coupling matrix does not contribute to dissipation. Therefore, entropy production is exclusively governed by the symmetric matrix even in the presence of antisymmetric terms. In this work we focus on the antisymmetric contributions which describe isentropic oscillations and well-defined equations of motion. The formalism contains variables that are equivalent to momenta, and coefficients that are analogous to an inertial mass. We apply this formalism to simple problems such as an oscillating piston and the oscillation in an electrical LC-circuit. We show that isentropic oscillations are possible even close to equilibrium in the linear limit and one does not require far-from equilibrium situations. One can extend this formalism to other pairs of variables, including chemical systems with oscillations. In isentropic thermodynamic systems all extensive and intensive variables including temperature can display oscillations reminiscent of adiabatic waves.