Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities

TL;DR

This paper introduces a minimal model for diffusion with fluctuating diffusivity, explaining how non-Gaussian yet normal diffusive behavior arises and transitions to Gaussian at longer times, supported by simulations.

Contribution

It establishes a subordination framework linking diffusing diffusivities with superstatistical models, providing a unified understanding of Brownian yet non-Gaussian diffusion.

Findings

Equivalence of diffusing diffusivity with superstatistics at short times

Crossover from non-Gaussian to Gaussian distribution at longer times

Excellent agreement with simulations and numerical evaluations

Abstract

A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, that can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations.