Bogolyubov generating functional method in statistical physics and “collective”-variables transform within grand canonical ensemble

Abstract

We show that the Bogolyubov generating functional method is a very efficient tool for studying distribution functions of both equilibrium and nonequilibrium states of classical many-particle dynamical systems. In some cases, the Bogolyubov generating functionals can be represented by means of infinite Ursell-Mayer diagram expansions, whose convergence holds under some additional constraints on the statistical system under consideration. The classical Bogolyubov idea to use the Wigner density operator transformation for studying nonequilibrium distribution functions is developed and a new analytic nonstationary solution to the classical Bogolyubov evolution functional equation is constructed.