Next Article in Journal
Choice Overload and Height Ranking of Menus in Partially-Ordered Sets
Next Article in Special Issue
The Bogdanov–Takens Normal Form: A Minimal Model for Single Neuron Dynamics
Previous Article in Journal
Entropy Generation of Desalination Powered by Variable Temperature Waste Heat
Article Menu

Export Article

Open AccessArticle
Entropy 2015, 17(11), 7567-7583; doi:10.3390/e17117567

Minimum Dissipation Principle in Nonlinear Transport

1
Department of Theoretical Physics and Mathematics, Université Libre de Bruxelles (U.L.B.), Bvd du Triomphe, Campus Plaine C.P. 231, 1050 Brussels, Belgium
2
Royal Military School (RMS), Av. de la Renaissance 30, 1000 Brussels, Belgium
3
High Energy Nuclear Physics Group, Institute of Modern Physics, Chinese Academy of Sciences, 730000 Lanzhou, China
4
Department of Electrical Engineering and Information Technology (ETIT), Karlsruhe Institute of Technology (KIT), Campus South Engesserstrae 13, D-76131 Karlsruhe, Germany
5
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
View Full-Text   |   Download PDF [258 KB, uploaded 3 November 2015]   |  

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
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Sonnino, G.; Evslin, J.; Sonnino, A. Minimum Dissipation Principle in Nonlinear Transport. Entropy 2015, 17, 7567-7583.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top