David Jou†
Abstract: We present some conceptual reflections on time in the context of thermodynamics with internal variables or with internal fluxes with relaxation times of several different orders of magnitude. The com- bination between reversible and irreversible contributions to the dynamics depends on the observation timescale, and opens new aspects to the usual discussion on the contrast between reversibility and irreversibility. As an illustration of such situations, two different kinds of hierarchies of internal variables are presented. In one of them, all the variables are vectors following linear relaxational evolution equations, with their respective relaxation times following a potential law. In the other one, all the variables have a different tensorial order, in such a way that the variable of order i is the flux of the precedent variable of order i − 1, but all of them have the same relaxation time. Some mathematical and physical features of both hierarchies are examined.
Keywords: time, non-equilibrium thermodynamics, internal variables, extended irreversible thermodynamics.
MSC: 03D55, 70K70, 80A05, 80A20, 82C35, 82C40.
DOI 10.56082/annalsarscimath.2025.3.339
† david.jou.mirabent@gmail.com, Departament de Fisıca, Universitat Autonoma de Barcelona, 08193 Bellaterra, Catalonia, Spain; Institut d’Estudis Catalans, Carme 47, 08001 Barcelona, Catalonia, Spain
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 3, 2025
