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Entropy of continuous Markov processes in local thermal equilibrium

Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata and Instituto de Investigaciones Físicas de Mar del Plata (Consejo Nacional de Investigaciones Científicas y Técnicas), Funes 3350, 7600 Mar del Plata, Argentina

Phys. Rev. E 79, 051123 – Published 22 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.051123

Abstract

The Boltzmann’s entropy of a continuous Markov process, in local thermal equilibrium, in contact with a reservoir at temperature $T$ , is analyzed. Assuming that the corresponding Fokker-Planck equation has constant coefficients and satisfies detailed balance, an equation for the entropy density is derived, from which it is possible to obtain expressions for the transport coefficients as functions of the diffusion matrix. Expressions for the entropy production terms of the system and of the combination of system plus reservoir are obtained. Known relations among transport coefficients are derived. The multicomponent case is also analyzed and the Prigogine theorem of minimum entropy production is derived in the context of reaction diffusion systems. The derivations presented in this paper are proposed as a framework for a deeper understanding of concepts used in nonequilibrium diffusion systems.

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Entropy of continuous Markov processes in local thermal equilibrium

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