Statistical Mechanics of Self Gravitating Systems

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1. Saddle poit method for the self gravitating/systems. Analyzing the self interacting systems, I evaluated the partition function by using the saddle point method. The 1-dim. phase transition is of second order, and the 3-dim. phase transition is of first order.2. Tsallis/Renyi statistical mechanics and the CfA-II-South data. The non-additivity turnd out to be the essence of the self gravitationg systems. Generalizing Euler relation in Tsallis statistical mechanics, I obtained negative parameter q,. which reflects the instability of the self gravitating systems.3. The origin of the fractal structure (negative specific heat an the cosmic expansion). Self gravitating particles constrained on a circle is investigated seeking for the origin of fractal structure. The negative specific heat, which comes from the short-distance singularity of the force, turned out to be the origin for the non-Gaussian velocity distributions.4. Multi-fractal analysis of Las Campanas galaxy redshift deta. From the 2-dim. Las Campanas data ; I extracted thev3-dim. information and concluded that the fractal distribution of galaxies continue upto several 10Mpc.5. Time sequence analysis of Gamma-ray hurts. I investigated the origin of the power-law structure in the power spectrum of the burst profile. The origin turned out to be the special form of the shots and not the self-similar structures of the burts.6. Statistical mechanics of the stable distributions. I found that the Tsallis distribution is a good approximation of the stable distributions, and the mathematically divergent dispersions include relevant information of the scale dependence.