Statistical-thermodynamical foundations of anomalous diffusion

Abstract

It is shown that Tsallis's generalized statistics provides a natural frame for the statistical-thermodynamical description of anomalous diffusion. Within this generalized theory, a maximum-entropy formalism makes it possible to derive a mathematical formulation for the mechanisms that underly Lévy-like superdiffusion, and for solving the nonlinear Fokker-Planck equation.