Non-extensive diffusion as nonlinear responseJ. 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 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