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Department of Theoretical Physics and Mathematics, Université Libre de Bruxelles U.L.B., Bvd du Triomphe, Campus Plaine C.P. 231, 1050 Brussels, Belgium


Royal Military School RMS, Av. de la Renaissance 30, 1000 Brussels, Belgium


High Energy Nuclear Physics Group, Institute of Modern Physics, Chinese Academy of Sciences, 730000 Lanzhou, China


Department of Electrical Engineering and Information Technology ETIT, Karlsruhe Institute of Technology KIT, Campus South Engesserstrae 13, D-76131 Karlsruhe, Germany


Ecole Polytechnique de Louvain EPL, Université Catholique de Louvain UCL, Rue Archimède, 1 bte L6.11.01, 1348 Louvain-la-Neuve, Belgium


Author to whom correspondence should be addressed.

Academic Editor: Kevin H. Knuth

Abstract We extend Onsager’s minimum dissipation principle to stationary states that are only subject to local equilibrium constraints, even when the transport coefficients depend on the thermodynamic forces. Crucial to this generalization is a decomposition of the thermodynamic forces into those that are held fixed by the boundary conditions and the subspace that is orthogonal with respect to the metric defined by the transport coefficients. We are then able to apply Onsager and Machlup’s proof to the second set of forces. As an example, we consider two-dimensional nonlinear diffusion coupled to two reservoirs at different temperatures. Our extension differs from that of Bertini et al. in that we assume microscopic irreversibility, and we allow a nonlinear dependence of the fluxes on the forces. View Full-Text

Keywords: nonequilibrium and irreversible thermodynamics; transport processes; nonequilibrium distribution function nonequilibrium and irreversible thermodynamics; transport processes; nonequilibrium distribution function

Author: Giorgio Sonnino 1,2,* , Jarah Evslin 3 and Alberto Sonnino 4,5



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