Maximum Path Information and Fokker-Planck Equation

TL;DR

This paper introduces a rigorous method to derive nonlinear Fokker-Planck equations for anomalous diffusion from a generalized least action principle, revealing dependencies on Tsallis entropy index and time.

Contribution

It provides a novel derivation of nonlinear Fokker-Planck equations from a generalized variational principle applicable to Markovian processes.

Findings

Derivation of two equivalent forms of the nonlinear FP equation

Diffusion constant depends on Tsallis q and time

Applicable to anomalous diffusion in irregular dynamics

Abstract

We present in this paper a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy) and the time t.