Volume 71, Number 6, September 2005
|Page(s)||906 - 911|
|Published online||12 August 2005|
Non-extensive diffusion as nonlinear response
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles 1050 Bruxelles, Belgium
Corresponding authors: firstname.lastname@example.org email@example.com
Accepted: 18 July 2005
The porous-media equation has been proposed as a phenomenological “non-extensive” generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming nonlinear response, i.e. that the diffusive flux depends on gradients of a power of the concentration. The present equation distinguishes from the porous-media equation in that it describes generalized classical diffusion, i.e. with scaling, but with a generalized Einstein relation, and with power-law probability distributions typical of non-extensive statistical mechanics.
PACS: 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems / 05.60.-k – Transport processes / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
© EDP Sciences, 2005
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