New Look at an Old Principle: An Alternative Formulation of The Theorem of Minimum Entropy Production

  • Gyula Vincze Department of Biotechnics, St.Istvan University
  • Andras Szasz Department of Biotechnics, St.Istvan University
Keywords: General Reciprocal Relations, Minimum-Entropy-Production, Bertalanffy’s Equifinality

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.

Downloads

Download data is not yet available.

References

Prigogine I. Etude thermodynamique des processus irreversibles (Thesis), Dunod et Desoer, Paris, Liege 1947

Prigogine I. Thermodynamics of Irreversible processes, (John Wiley & Sons) 1954

De Groot SR. Thermodynamics of irreversible processes, North-Holland Publ. Co. Amsterdam 1951

Glansdorff P. & Prigogine I. Sur les Sur les propriétés différentielles de la production d'entropie, Physica, 1954 20, 773

Glansdorff P. & Prigogine I. Thermodynamic Theory of Structure, Stability and Fluctuations, John Wiley & Sons, London, New York 1971

Gyarmati I. Nonequilibrium Thermodynamics, Springer Verlag, Berlin, Göttingen Heidelberg 1970

Gyarmati I. Application of the Gyarmati principle to multicomponent nonisothermal and chemically reacting diffusional systems. Acta chim. Hung. 1971, 67, 303–320

Li JCM. Thermodynamics for nonequilibrium systems—principle of macroscopic separability and thermokinetic potential, J.Appl. Phys. 1962 33, 616-625

Gyarmati I. On the Wave Approach of Thermodynamics and some Problems of Non-Linear Theories. Journal of Non-Equilibrium Thermodynamics. 1977 2(4), 233–260

Rysselberghe, P. General reciprocity relation between the rates and affinities of simultaneous chemical reactions, J. Chem. Phys. 1962 36, 1329-1330

Vainberg MM. Variational Methods for the study of nonlinear operator Equations, Holden Day 1963

Onsager L. Reciprocal Relation in irreversible processes, I., Phys. Rev. 1931 37, 405-426,

Onsager L. Reciprocal Relation in irreversible processes, II., Phys. Rev. 1931 37, 2265–2279

Casimir HBG. On Onsager’s principle of microscopic reversibility, Rev. Mod. Phys. 1945 17, 343-356

Bertalanffy L. General System theory: Foundations, Development, Applications, George Braziller, New York 1968

Truesdell CA. Zu den Grundlagen der Mechanik und Thermodynamik, Physikalische Blitter. 1960 16, 512-517

Published
2019-11-16
How to Cite
Vincze, G., & Szasz, A. (2019). New Look at an Old Principle: An Alternative Formulation of The Theorem of Minimum Entropy Production. JOURNAL OF ADVANCES IN PHYSICS, 16(1), 508-517. https://doi.org/10.24297/jap.v16i1.8516
Section
Articles