The concept is introduced of a generating functional. This enables one to find all the many-particle distribution functions by differentiation with respect to the functional argument. An equation is found for this functional which is equivalent to the equation for the density matrix of the system. It is shown that the steady-state solution of this equation, complemented by the principle of spatial correlation relaxation (the latter can be formulated simply in terms of the generating functional), is equivalent to the Gibbs distribution. An integral equation is found for the generating functional at the stage of evolution when the state of the system is described by a distribution function and a method of solving this equation as a series in powers of the density is developed.