Abstract
Large-scale astrophysical systems are non-extensive due to their long-range force of gravity. Here we show an approach towards the statistical mechanics of such self-gravitating systems (SGS). This is a generalization of the standard statistical mechanics based on the new definition of entropy; Tsallis statistical mechanics. Developing the composition of entropy and the generalized Euler relation, we investigate the galaxy distributions in the count-in-cell method. This is applied to the data of CfA II South redshift survey and we obtain the negative parameter q. This may represent the ubiquitous instability of SGS.
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