Renormalization group approach to nonextensive statistical mechanics

We analyze thermal equilibrium of a simple classical Hamiltonian system wit hin the hypotheses of renormalizability and isotropy that essentially led M axwell to his ubiquitous Gaussian distribution of velocities. We show that the equilibrium-like power-law energy distribution emerging within nonexten sive statistical mechanics satisfies these hypotheses, in spite of nor bein g factorizable. A physically satisfactory renormalization group emerges in the (q, T-q) Space, where q and Tq are respectively the entropic index char acterizing nonextensivity, and an appropriate temperature. This scenario en ables the conjectural formulation of the one to be expected for d-dimension al systems involving long-range interactions (e.g., a classical two-body po tential alphar(-alpha) with 0 less than or equal to alpha /d less than or e qual to 1). As a corollary, we recover a quite general expression for the c lassical principle of equipartition of energy for arbitrary q. (C) 2001 Pub lished by Elsevier Science B.V.