Non-extensive galaxy distributions - Tsallis statistical mechanics

Large-scale astrophysical systems are non-extensive due to their long-range force of gravity. Here we show an approach towards the statistical mechani cs of such self-gravitating systems (SGS). This is a generalization of the standard statistical mechanics based on the new definition of entropy; Tsal lis statistical mechanics. Developing the composition of entropy and the ge neralized Euler relation, we investigate the galaxy distributions in the co unt-in-cell method. This is applied to the data of CfA Il South redshift su rvey and we obtain the negative parameter q. This may represent the ubiquit ous instability of SGS. (C) 2001 Elsevier Science Ltd. All rights reserved.