On the kinetics of a many-body dissipative system placed in a random field

A kinetic equation for a dissipative system is obtained up to the second order in small potential interaction, small dissipative interaction and small correlation functions of an external random field. This work is an extension of the paper by Sliusarenko, Chechkin, and Slyusarenko (J. Math. Phys., 56, 043302, 2015) where the corresponding equation was obtained in the first order of smallness. For a simple case the evolution of a spatially uniform system is investigated. It is shown that the system reaches a steady state.