Understanding diffusion in fluctuating hydrodynamic environments is crucial for molecular transport in biophysical systems. Diffusion enables nutrients and signaling molecules to move within cells, yet many systems exhibit anomalous behaviors—e.g., vesicles and organelles diffusing along or within membranes—that remain difficult to model. In nonequilibrium systems, anomalous diffusion is typically linked to spontaneously emerging spatial correlations, while in equilibrium, it is usually attributed to imposed heterogeneities such as confinement. The possibility that intrinsic spatial correlations in an equilibrium fluid could themselves generate anomalous transport has not been explored. Here, we investigate anomalous diffusion within the framework of fluctuating hydrodynamics, modeling the fluid through the incompressible Navier-Stokes equation augmented by a stochastic forcing first introduced by Landau and Lifshitz. When the forcing is spatially white, the model reproduces classic Brownian motion. By contrast, introducing spatial correlations while maintaining fluctuation-dissipation balance yields a fluid whose momentum diffusion is intrinsically nonlocal. We find that spatial correlations produce, for the first time to our knowledge, a non-trivial dependence of the mean-squared displacement (MSD) on the ratio of correlation length to particle radius. This leads to an emergent trapping phenomenon without physical potential wells: particles become intermittently confined within transient, correlation-induced traps, then hop between them before ultimately recovering normal diffusion. The underlying mechanism is a strong suppression of short-wavelength momentum diffusion, reminiscent of aging and slow dynamics in disordered media. At long times, momentum diffusion crosses over to the standard Laplacian, restoring Brownian motion.
Huang et al. (Sun,) studied this question.