The problem of the phase oscillators chain kinetic simulation

One of the main problems of kinetic theory is the method of taking the correlations between intensively interacting particles into account on the BBGKY hierarchy truncation. This question becomes critical for the nonequilibrium processes in fluids and condensed matter. The classical multiplicative approximation which leads to the mean field approach often results in the qualitatively wrong behaviour of a system.
In this work the looped phase oscillators chain connected to the heat bath was studied. The interaction is limited to the nearest particles. Results for the direct numerical solution of the problem were compared to the outcome of simulations based on kinetic theory with different approximations. It is showed that Self-consistent moments approach provides acceptable values of the mean energy and the relaxation time for the certain interval of the temperatures.