Exact closed equation for reduced equilibrium distribution functions of the many-particle system

Abstract

An exact closed equation for s - particle equilibrium distribution function (s<N) of the system of N>>1 interacting particles is obtained. This integra-differential β - convolution equation (β=1/k_{B}T) follows from the Bloch equation for the canonical distribution function by applying the projection operator integrating off the coordinates of N-s irrelevant particles. The method of expansion of the obtained equation kernel in the particle density n is suggested. The solution to this equation in the linear in n approximation for the kernel is found.

arXiv comment11 pages