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The collectivity in the simultaneous diffusion of many particles, i.e. theinterdependence of stochastic forces affecting different particles in the samesolution, is a largely overlooked phenomenon with no well-established theory.Recently, we have proposed a novel type of thermodynamically consistentLangevin dynamics driven by the Spatially Correlated Noise (SCN) that cancontribute to the understanding of this problem. This model draws a linkbetween the theory of effective interactions in binary colloidal mixtures andthe properties of SCN. In the current article we review this model from theperspective of collective diffusion and generalize it to the case of multiple($N>2$) particles. Since our theory of SCN-driven Langevin dynamics has certainissues that could not be resolved within its framework, in this article we alsoprovide another approach to the problem of collectivity. We discuss themulti-particle Mori-Zwanzig model, which is fully microscopically consistent.Indeed, we show that this model supplies many information, complementary to theSCN-based approach, e.g. it predicts the deterministic dynamics of the relativedistance between the particles, it provides the approximation fornon-equilibrium effective interactions and predicts the collective subdiffusionof tracers in group. These results provide the short-range, inertial limit ofthe earlier model and agree with its predictions under some general conditions.In this article we also review the origin of SCN and its consequences for thevariety of physical systems, with emphasis on the colloids.

Collectivity in diffusion of colloidal particles: from effective interactions to spatially correlated noise