Deciphering Non-Gaussianity of Diffusion Based on the Evolution of Diffusivity

Abstract: Non-Gaussianity indicates complex dynamics related to extreme events or significant outliers. However, the correlation between non-Gaussianity and the dynamics of heterogeneous environments in anomalous diffusion remains uncertain. Inspired by a recent study by Alexandre et al. [Phys. Rev. Lett. 130, 077101 (2023)], we demonstrate that non-Gaussianity can be deciphered through the spatiotemporal evolution of heterogeneity-dependent diffusivity. Using diffusion experiments in a linear temperature field and Brownian dynamics simulations, we found that short- and long-time non-Gaussianity can be predicted based on diffusivity distribution. Non-Gaussianity variation is determined by an effective P\'eclet number (a ratio of the varying rate of diffusivity to the diffusivity of diffusivity), which clarifies whether the tail distribution expands or contracts. The tail is more Gaussian than exponential over long times, with exceptions significantly dependent on the diffusivity distribution. Our findings shed light on heterogeneity mapping in complex environments using non-Gaussian statistics.