Nonequilibrium Thermodynamics and Scale Invariance

Leonid M Martyushev,Vladimir Celezneff

doi:10.3390/e19030126

Abstract

A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces is proposed here. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It is shown here that such a modification not only makes it possible to deductively obtain the main results of classical linear nonequilibrium thermodynamics, but also provides evidence for a number of statements for a nonlinear case (the maximum entropy production principle, the macroscopic reversibility principle, and generalized reciprocity relations) that are under discussion in the literature.

Highlights

Classical nonequilibrium thermodynamics is an important field of modern physics that was developed for more than a century [1,2,3,4,5]
The basic concept of classical nonequilibrium thermodynamics is the local equilibrium concept, i.e., the assumption that a nonequilibrium system can be treated as a system consisting of a large number of macroscopic volume elements, where thermodynamic equilibrium is established in a time much smaller than that in the entire system
The proposed approach to the construction of local nonequilibrium thermodynamics replaces the concept of local equilibrium and assumptions of possible relations between fluxes and forces by the postulate of the scale invariance of such a relation

Summary

Introduction

Classical nonequilibrium thermodynamics is an important field of modern physics that was developed for more than a century [1,2,3,4,5]. The proportionality coefficient in this linear relation between the flux and thermodynamic force depends only on the equilibrium characteristics of the element under consideration This relation can be used, e.g., to determine the total steady-state heat flux jq,in in a rod with the length d and temperatures at the ends T1 and T2. 1 2 the heat flux is related to the temperature difference (thermodynamic force) through the quantities characterizing the rod as a whole This relation is obviously nonlocal in the space, it was obtained with the use of the relation based on the assumption of local equilibrium. We do not analyze relations existing in nonlocal systems [19], but study the most fundamental problems of the generalization of classical nonequilibrium thermodynamics and the determination of possible nonlinear local relations between fluxes and forces. The criticism of the results of this work in terms of the known properties of nonlocal systems, chemical systems (as in [10,13,20]), is incorrect

Foundations of the Theory

Consequences of the Theory

Conclusions