Fickian yet non-Gaussian diffusion in an annealed heterogeneous environment

Fickian yet non-Gaussian diffusion is a ubiquitous phenomenon observed in various biological and soft matter systems. This anomalous dynamics is typically attributed to heterogeneous environments inducing spatiotemporal variations in the diffusivity of tracer particles. While previous studies have predominantly focused on systems exhibiting either spatial or temporal heterogeneity, this work bridges the gap by introducing a model based on an annealed extreme landscape to simultaneously account for both types of heterogeneities. Through a combination of computational analyses and analytical derivations, we investigate how the interplay of spatial and temporal heterogeneities in the energy landscape gives rise to Fickian yet non-Gaussian diffusion. Furthermore, we demonstrate that in the presence of temporal environmental fluctuations, the heterogeneous diffusion inevitably converges to classical Brownian motion via a homogenization process. We derive an analytical expression for the homogenization time as a function of key parameters governing the system's spatiotemporal heterogeneities. Additionally, we quantify particle-to-particle diffusion heterogeneity and examine the ergodic properties of this model, providing deeper insights into the dynamics of complex, heterogeneous systems.