  The properties of the nonextensive parameter q and the Tsallis distribution
for self-gravitating systems are studied. A mathematical expression of q is
deduced based on the generalized Boltzmann equation, the q-H theorem and the
generalized Maxwellian q-velocity distribution in the framework of Tsallis
statistics. We obtain a clear understanding of the physics of q different from
unity with regard to the temperature gradient and the gravitational potential
of the self-gravitating systems. It is suggested that the Tsallis statistics
could be statistics suitable for describing the nonequilibrium systems with
inhomogeneous temperature and the long-range interactions.
