Local equilibrium and the second law of thermodynamics for irreversible systems with thermodynamic inertia

TL;DR

This paper proposes a variational approach to irreversible thermodynamics for systems with inertia, reconciling local equilibrium assumptions with the second law by focusing on averaged entropy production in delayed response systems.

Contribution

It introduces a novel variational formulation that derives standard evolution equations and redefines the second law for systems with thermodynamic inertia and delayed response.

Findings

Standard equations derived from variational principle without violating local equilibrium

Second law interpreted as a consequence of variational formulation and local equilibrium

Entropy production should be considered as an average over heat wave periods in delayed systems

Abstract

Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper we address this question by suggesting a variational formulation of irreversible evolution of a system with non-zero thermodynamic inertia. We introduce the Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" systems. We show that the standard evolution equations, in particular the Maxwell-Cattaneo-Vernotte equation, can be derived from the variational procedure without going beyond the assumption of local equilibrium. We also argue, that the second law of thermodynamics should be understood as a consequence of the variational procedure and the property of local equilibrium. For systems with instantaneous response this leads to the standard requirement of the local instantaneous entropy production being always positive. However, if a system is characterized by delayed response, the formulation of the second law of thermodynamics should be altered. In particular, the quantity, which is always positive, is not the instantaneous entropy production, but the entropy production averaged over the period of the heat wave.