Statistical Mechanics Of Gravitational Systems

The spirit beneath the surface of many astronomical phenomena is gravitation. In this paper we mainly discuss the statistical physics of gravitational systems. After some reviews of current investigation on gravitational systems with traditional Boltzman statistical mechanics and introduction of the generalized statistical mechanics of Tsallis, we study some gravitational systems in traditional and generalized approaches of statistical mechanics. Our main work is following: (1)A toy model of gravity in microcanonical ensemble is investigated according to generalized statistical mechanics which is more suitable to gravitating system because of its long range and non-extensive features. (2)The gravitational toy model in canonical ensemble is also studied under the regime of generalized statistical mechanics. We find that a region of negative specific heat describing the character of gravity also exists in canonical ensemble, which is remarkably distinguished from the result of traditional statistical mechanics that the specific heat must be positive in that ensemble, implying that the gravitating system may also be described by canonical one. (3)On basis of the result of equilibrium gravitating potential in a gravitational system, we explain the phenomenon of scale-free peculiar velocity in the universe by studying cosmic fluid equations. Furthermore, we reexamine the issue in the approach of generalized statistical mechanics. (4)The basic principle of maximal entropy is used to a cosmic gravitational system and we find that the observed result of two-point and three-point galaxy correlation functions in the universe is agree with an equilibrium assumption of mass distribution. A generalized statistical mechanics is also utilized to improve our result.