2015/07/28 by K. S. Glavatskiy, Glavatskiy, K. S.
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Phase Equilibria and Thermodynamics #Statistical Mechanics (cond-mat.stat-mech) #Thermoelastic and Magnetoelastic Phenomena #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1507.07656
12 pages, 7 figures
arxiv created 2015/07/28 · openalex publication_date 2015/07/28 · arxiv updated 2015/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.