  The collectivity in the simultaneous diffusion of many particles, i.e. the
interdependence of stochastic forces affecting different particles in the same
solution, is a largely overlooked phenomenon with no well-established theory.
Recently, we have proposed a novel type of thermodynamically consistent
Langevin dynamics driven by the Spatially Correlated Noise (SCN) that can
contribute to the understanding of this problem. This model draws a link
between the theory of effective interactions in binary colloidal mixtures and
the properties of SCN. In the current article we review this model from the
perspective of collective diffusion and generalize it to the case of multiple
($N>2$) particles. Since our theory of SCN-driven Langevin dynamics has certain
issues that could not be resolved within its framework, in this article we also
provide another approach to the problem of collectivity. We discuss the
multi-particle Mori-Zwanzig model, which is fully microscopically consistent.
Indeed, we show that this model supplies many information, complementary to the
SCN-based approach, e.g. it predicts the deterministic dynamics of the relative
distance between the particles, it provides the approximation for
non-equilibrium effective interactions and predicts the collective subdiffusion
of tracers in group. These results provide the short-range, inertial limit of
the 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 the
variety of physical systems, with emphasis on the colloids.
