  The microcanonical partition function for self-gravitational system in three
dimensional case has been found. Used approach from the field theory of
statistical description of the system was tailored to gravitational interacting
particles with regard for an arbitrary spatially inhomogeneous particle
distribution. The entropy of self-gravitational system has been found from
extreme condition for the effective functional. For inhomogeneous distribution
particle (formation few cluster of finite size) the entropy are bigger as the
entropy homogeneous distribution of particles. The increasing of entropy of
self-gravitational system after formation cluster motive tendency to disperse.
