The Einstein–Ehrenfest system of $(0,M)$-type and asymptotical solutions of the multidimensional nonlinear Fokker–Planck–Kolmogorov equation

Semiclassical approximation formalism is developed for the multidimensional Fokker–Planck–Kolmogorov equation with non-local and nonlinear drift vector with respect to a small diffusion coefficient $D$, $D\to0$, in the class of trajectory concentrated functions. The Einstein–Ehrenfest system of $(0,M)$-type is obtained. A family of semiclassical solutions localized around a point driven by the Einstein–Ehrenfest system accurate to $O(D^{(M+1)/2})$ is found.