Minimum Dissipation Principle in Nonlinear Transport
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
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.
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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.
Sonnino G, Evslin J, Sonnino A. Minimum Dissipation Principle in Nonlinear Transport. Entropy. 2015; 17(11):7567-7583.
Sonnino, Giorgio; Evslin, Jarah; Sonnino, Alberto. 2015. "Minimum Dissipation Principle in Nonlinear Transport." Entropy 17, no. 11: 7567-7583.
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