  The density of states of self-gravitational system diverges when the
particles are spread to infinity. Other problem based an inhomogeneous
distribution of particles,which motivate the gravitational interaction. In this
sense the statistical mechanics of self-gravitational system is essentially an
non-equilibrium problem. A new possible approach to statistical description of
self-gravitational system has been proposed. The approach based on
non-equilibrium statistical operator, which allow take into account
inhomogeneous distribution particle and temperature in self gravitational
system. The saddle point procedure, which used in the given method describes
the spatially inhomogeneous distribution in self gravitational system
accompanied by temperature changing.
