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We develop a microscopic approach to the kinetic theory of many-particlesystems with dissipative and potential interactions in presence of activefluctuations. The approach is based on a generalization ofBogolyubov--Peletminsky reduced description method applied to the systems ofmany active particles. It is shown that the microscopic approach developedallows to construct the kinetic theory of two- and three-dimensional systems ofactive particles in presence of non-linear friction (dissipative interaction)and an external random field with active fluctuations. The kinetic equationsfor these systems in case of a weak interaction between the particles (bothpotential and dissipative) and low-intensity active fluctuations are obtained.We demonstrate particular cases in which the derived kinetic equations havesolutions that match the results known in the literature. It is shown that thedisplay of the head-tail asymmetry and self-propelling even in the case of alinear friction, is one of the consequences of the local nature of the activefluctuations.

Reduced description method in the kinetic theory of Brownian motion with active fluctuations