Microscopic dynamics underlying anomalous diffusion
The time-dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a nonlinear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A 222, 347 (1995)]. The scope of the present paper is twofold. First, we show that this distribution can be obtained also as a solution of the nonlinear porous media equation. Second, we prove that the time-dependent Tsallis distribution can be obtained also as a solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A 237, 229 (1997)] with coefficients depending on the velocity, which describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in the presence of multiplicative noise.
Kaniadakis
G
Istituto Nazionale per la Fisica della Materia, Unita del Politecnico di Torino, 10129 Torino, Italy and Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
Lapenta
G