Non-extensive diffusion as nonlinear response

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

Corresponding authors: jlutsko@ulb.ac.be jpboon@ulb.ac.be

Received: 10 May 2005
Accepted: 18 July 2005

Abstract

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.