Statistical-thermodynamical foundations of anomalous diffusion

TL;DR

This paper demonstrates that Tsallis' generalized statistics offers a natural framework for describing anomalous diffusion, deriving mechanisms for Levy-like superdiffusion and solving related nonlinear equations.

Contribution

It introduces a maximum-entropy formalism within Tsallis' statistics to model anomalous diffusion and derive underlying mechanisms for Levy-like superdiffusion.

Findings

Provides a mathematical formulation for Levy-like superdiffusion

Derives mechanisms underlying anomalous diffusion

Solves the nonlinear Fokker-Planck equation using generalized statistics

Abstract

It is shown that Tsallis' 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 Levy-like superdiffusion, and for solving the nonlinear Fokker-Planck equation.