Minimum Dissipation Principle in Nonlinear Transport

Entropy

Giorgio Sonnino²  Jarah Evslin³  Alberto Sonnino¹ 

[1] Department of Electrical Engineering and Information Technology (ETIT), Karlsruhe Institute of Technology (KIT), Campus South Engesserstrae 13, D-76131 Karlsruhe, Germany; E-Mail:;Department of Theoretical Physics and Mathematics, Université Libre de Bruxelles (U.L.B.), Bvd du Triomphe, Campus Plaine C.P. 231, 1050 Brussels, Belgium;High Energy Nuclear Physics Group, Institute of Modern Physics, Chinese Academy of Sciences, 730000 Lanzhou, China; E-Mail:

关键词: nonequilibrium and irreversible thermodynamics;    transport processes;    nonequilibrium distribution function;   

DOI  :  10.3390/e17117567

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.