Fickian Yet Non-Gaussian Diffusion in Complex - Yet Homogeneous - Fluids.

The discovery of Fickian yet non-Gaussian diffusion (FnGD), characterized by linear mean squared displacement (MSD) but non-Gaussian displacement statistics, has opened a new chapter in the study of complex diffusion, highlighting previously unexplored departures from Brownian motion. Identifying the physical origins of these deviations is essential for advancing our understanding of transport in biological systems, soft matter, and complex media. This goal has already been achieved for systems where the phenomenon originates from heterogeneities in the medium with characteristic length scales comparable to the size of the diffusing particles. Here we develop, to our knowledge, the first theoretical account of FnGD in complex but homogeneous fluids, where structural heterogeneities exist only at lengths far smaller than the probe and are therefore coarse-grained away. We show that in a medium treated as homogeneous, non-Gaussian propagators arise because the equilibrium velocity distribution is non-Maxwellian. This behavior can be accommodated within the classical Kubo fluctuation–dissipation framework if momentum transfer is driven by impulsive interactions represented as distributional time derivatives of compound Markov counting processes (rather than standard Wiener forcing). We obtain an analytic stationary velocity distribution, and we generalize the model to include dissipative impulsive interactions and two-phase kinetic effects associated with the adhesion of soft particles to a dispersed matrix.