Europhys. Lett.
Volume 71, Number 6, September 2005
Page(s) 906 - 911
Section General
Published online 12 August 2005
Europhys. Lett., 71 (6), pp. 906-911 (2005)
DOI: 10.1209/epl/i2005-10179-x

Non-extensive diffusion as nonlinear response

J. F. Lutsko and J. P. Boon

Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles 1050 Bruxelles, Belgium

received 10 May 2005; accepted in final form 18 July 2005
published online 12 August 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 $r/\sqrt Dt$ scaling, but with a generalized Einstein relation, and with power-law probability distributions typical of non-extensive statistical mechanics.

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