Fokker-Planck approach to non-Gaussian normal diffusion: Hierarchical dynamics for diffusing diffusivity

TL;DR

This paper presents a theoretical framework based on the Fokker-Planck equation to model non-Gaussian normal diffusion with hierarchical dynamics, explaining phenomena like diffusing diffusivity in heterogeneous systems.

Contribution

It introduces a hierarchical Fokker-Planck model that captures the dynamics of fast and slow degrees of freedom in non-Gaussian diffusion.

Findings

Consistently describes diffusing diffusivity.

Derives three coupled equations for different time scales.

Applicable to heterogeneous systems exhibiting non-Gaussian diffusion.

Abstract

A theoretical framework is developed for the phenomenon of non-Gaussian normal diffusion that has experimentally been observed in several heterogeneous systems. From the Fokker-Planck equation with the dynamical structure with largely separated time scales, a set of three equations are derived for the fast degree of freedom, the slow degree of freedom and the coupling between these two hierarchies. It is shown that this approach consistently describes "diffusing diffusivity" and non-Gaussian normal diffusion.