Beta-approximation of the two-particle distribution function for the chains of phase oscillators

When constructing the BBGKY hierarchy for systems with strong local interaction (liquids, magnetic materials) the key problem is the issue of approximation of the two–particle distribution function. The traditional approximation of multiplicativity that leads to the theory of the mean field often gives qualitatively incorrect results.
In this paper, we consider a ring chain of phase oscillators with interaction only between the nearest neighbors, in a thermostat. On the basis of the analysis of the results of ab initio calculations, an approximation is constructed for the two-particle distribution function. It results in the one-particle Fokker–Planck equation with a self-consistent integral force. The results of the modeling based on the resulting equation are in a good agreement with the ab initio calculations.
The obtained results may be of great importance in the construction of selfconsistent models of systems with strong local interaction and temperature fluctuations.