On the Formulation of Variational Principles of Irreversible Thermodynamics in Presence of a Magnetic Field

On the Formulation of Variational Principles of Irreversible Thermodynamics in Presence of a... Abstract We show that the matrix of coefficients in a set of linear phenomenological equations can be symmetrized also for systems with magnetic fields. This is due to a suitable choice of the spaces of thermodynamic forces and fluxes. Therefore the usual variational formulations of thermodynamics of irreversible processes also can be applied to systems with magnetic fields. In recent years several variational principles of thermodynamics of irreversible processes have been formulated [1--3]. None of these formulations take into account odd parameters such as the magnetic field. Therefore those principles only make use of the simple Onsager reciprocal relations (1) and in general of the linear phenomenological equations Ji = Lik Xk (2) between the components Ji of the fluxes and the components Xk of the forces. It should be noted that these variational principles remain valid in special non-linear cases [1--3]. As is well known [4] in the presence of a magnetic field B (1) must be replaced by the Onsager-Casimir reciprocal relations I*(B) = e l e k L k l ( - B ) , (3) where e{ -- ± 1 , depending on whether the component Xi of the forces is even or odd http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Non-Equilibrium Thermodynamics de Gruyter

On the Formulation of Variational Principles of Irreversible Thermodynamics in Presence of a Magnetic Field

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0340-0204
eISSN
1437-4358
DOI
10.1515/jnet.1976.1.1.61
Publisher site
See Article on Publisher Site

Abstract

Abstract We show that the matrix of coefficients in a set of linear phenomenological equations can be symmetrized also for systems with magnetic fields. This is due to a suitable choice of the spaces of thermodynamic forces and fluxes. Therefore the usual variational formulations of thermodynamics of irreversible processes also can be applied to systems with magnetic fields. In recent years several variational principles of thermodynamics of irreversible processes have been formulated [1--3]. None of these formulations take into account odd parameters such as the magnetic field. Therefore those principles only make use of the simple Onsager reciprocal relations (1) and in general of the linear phenomenological equations Ji = Lik Xk (2) between the components Ji of the fluxes and the components Xk of the forces. It should be noted that these variational principles remain valid in special non-linear cases [1--3]. As is well known [4] in the presence of a magnetic field B (1) must be replaced by the Onsager-Casimir reciprocal relations I*(B) = e l e k L k l ( - B ) , (3) where e{ -- ± 1 , depending on whether the component Xi of the forces is even or odd

Journal

Journal of Non-Equilibrium Thermodynamicsde Gruyter

Published: Jan 1, 1976

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