  Large-scale astrophysical systems are non-extensive due to their long-range
force of gravity. Here we show an approach toward 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
count-in-cell method. This is applied to the data of CfA II South redshift
survey.
