Brownian yet non-Gaussian diffusion in heterogeneous media: from superstatistics to homogenization

TL;DR

This paper explores conditions under which Brownian yet non-Gaussian diffusion occurs in heterogeneous media, highlighting that such behavior is unlikely in non-equilibrated systems but possible under equilibrium conditions, modeled via fluctuating diffusivity.

Contribution

It clarifies the circumstances for observing BnG diffusion, connecting heterogeneous media models with the diffusing diffusivity framework and emphasizing the role of initial conditions.

Findings

BnG diffusion is unlikely in non-equilibrated initial conditions.

Equilibrium conditions can lead to BnG behavior through fluctuating diffusivity.

The study links heterogeneous media models with the diffusing diffusivity paradigm.

Abstract

We discuss the situations under which Brownian yet non-Gaussian (BnG) diffusion can be observed in the model of a particle's motion in a random landscape of diffusion coefficients slowly varying in space. Our conclusion is that such behavior is extremely unlikely in the situations when the particles, introduced into the system at random at $t=0$, are observed from the preparation of the system on. However, it indeed may arise in the case when the diffusion (as described in Ito interpretation) is observed under equilibrated conditions. This paradigmatic situation can be translated into the model of the diffusion coefficient fluctuating in time along a trajectory, i.e. into a kind of the "diffusing diffusivity" model.