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 ≠ 1 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 long-range interactions.
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Jiulin Du (2004) studied this question.
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