Nonextensive diffusion as nonlinear response

Details Nonextensive diffusion as nonlinear response Nonextensive diffusion as nonlinear response

2005-05-09

arxiv.org/abs/cond-mat/0505216v1

Europhys. Lett., 71 (6), pp. 906-911 (2005)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1209/epl/i2005-10179-x

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 \emph{% generalized classical} diffusion, i.e. with $r/\sqrt Dt$ scaling, but with a generalized Einstein relation, and with power-law probability distributions typical of nonextensive statistical mechanics.

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