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

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.