[053] Non-extensive diffusion as nonlinear response

J. F. Lutsko and J. P. Boon, "Non-extensive diffusion as nonlinear response", EuroPhys. Lett., 71, 906 (2005) http://jimlutsko.github.io/files/Lutsko_EPL_2005.pdf


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.)