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Open AccessArticle

Minimum Dissipation Principle in Nonlinear Transport

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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
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Royal Military School (RMS), Av. de la Renaissance 30, 1000 Brussels, Belgium
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High Energy Nuclear Physics Group, Institute of Modern Physics, Chinese Academy of Sciences, 730000 Lanzhou, China
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Department of Electrical Engineering and Information Technology (ETIT), Karlsruhe Institute of Technology (KIT), Campus South Engesserstrae 13, D-76131 Karlsruhe, Germany
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Ecole Polytechnique de Louvain (EPL), Université Catholique de Louvain (UCL), Rue Archimède, 1 bte L6.11.01, 1348 Louvain-la-Neuve, Belgium
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Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Entropy 2015, 17(11), 7567-7583; https://doi.org/10.3390/e17117567
Received: 6 September 2015 / Revised: 23 October 2015 / Accepted: 27 October 2015 / Published: 30 October 2015
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
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MDPI and ACS Style

Sonnino, G.; Evslin, J.; Sonnino, A. Minimum Dissipation Principle in Nonlinear Transport. Entropy 2015, 17, 7567-7583. https://doi.org/10.3390/e17117567

AMA Style

Sonnino G, Evslin J, Sonnino A. Minimum Dissipation Principle in Nonlinear Transport. Entropy. 2015; 17(11):7567-7583. https://doi.org/10.3390/e17117567

Chicago/Turabian Style

Sonnino, Giorgio; Evslin, Jarah; Sonnino, Alberto. 2015. "Minimum Dissipation Principle in Nonlinear Transport" Entropy 17, no. 11: 7567-7583. https://doi.org/10.3390/e17117567

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