New look at an old principle: an alternative formulation of the theorem of minimum entropy production

Gyula Vincze,Andras Szasz

doi:10.24297/jap.v16i1.8516

Abstract

We formulate a direct generalization of the Prigogine’s principle of minimum entropy production, according to a new isoperimetric variation principle by classical non-equilibrium thermodynamics. We focus our attention on the possible mathematical forms of constitutive equations. Our results show that the Onsager’s reciprocity relations are consequences of the suggested variation principle. Furthermore, we show by the example of the thermo-diffusion such reciprocity relations for diffusion tensor, which are missing in Onsager’s theory. Our theorem applied to the non-linear constitutive equations indicates the existence of dissipation potential. We study the forms of general reciprocity with the dissipation potential. This consideration results in a weaker condition than Li-Gyarmati-Rysselberhe reciprocity has. Furthermore, in the case of electric conductivity in the magnetic field, our theorem shows the correct dependence of the Onsager’s kinetic coefficient by the axial vector of magnetic induction. We show in general that the evolution criterion of the global entropy production is a Lyapunov-function, and so the final stationer state is independent of the initial, time-independent boundary conditions.

Highlights

The first formulation of the minimum entropy production for the non-continuous system was firstly formulated by Prigogine [1], [2]
That a suggested modification of the principle of minimum entropy production has essential applications in the theory of constitutive laws of non-equilibrium thermodynamics, including reciprocal relations
We may regard the reciprocal relations as experimentally proven axioms, or we have to derive them on the direct phenomenological way

Summary

Introduction

The first formulation of the minimum entropy production for the non-continuous system was firstly formulated by Prigogine [1], [2] This theorem was generalized by introducing the order of stationarity by de Groot [3]. Gyarmati had proved [6] that a realistic generalization of Onsager’s principle of last dissipation of energy is equivalent to the above Glansdorff-Prigogine theorem These considerations feature again the dissipation potentials introduced by Rayleigh and Onsager. The theories mentioned above emphasize a strong correlation between the existence of minimum entropy production and the possible form of constitutive equations of dissipative forces and currents. In non-linear cases, such a generalized method does not exist to prove the potential behavior of the entropy production, (like for example to prove the higher-order Onsager’s relations). We investigate the constitutive equations with condition fix the extreme (more general stationer) behavior of the entropy production

Materials and Methods

T αj i xi

Conclusions