PERTURBATION AND VARIATIONAL-METHODS IN NONEXTENSIVE TSALLIS STATISTICS

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is giv en here. In the case of the variational method, the Bogoliubov inequal ity is generalized in a very natural way following the Feynman proof f or the usual statistical mechanics. The inequality turns out to be for m invariant with respect to the entropic index q. The method is illust rated with a simple example in classical mechanics. The formalisms dev eloped here are expected to be useful in the discussion of nonextensiv e systems.