Renormalization group approach to nonextensive statistical mechanics

Details Renormalization group approach to nonextensive statistical mechanics Renormalization group approach to nonextensive statistical mechanics

2000-03-22

arxiv.org/abs/cond-mat/0003365v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 ps figures

Scientific paper

10.1016/S0375-9601(01)00372-3

We analyze a simple classical Hamiltonian system within the hypothesis of renormalizability and isotropy that essentially led Maxwell to his ubiquitous Gaussian distribution of velocities. We show that the equilibrium-like power-law energy distribution emerging within nonextensive statistical mechanics satisfies these hypothesis, in spite of not being factorizable. A physically satisfactory renormalization group emerges in the $(q, T_q)$ space, where q and $T_q$ respectively are the entropic index characterizing nonextensivity, and an appropriate temperature. This scenario enables the conjectural formulation of the one to be expected for d-dimensional systems involving long-range interactions (e.g., a classical two-body potential $\propto r^{-\alpha}$ with $0 \le \alpha/d \le 1$). As a corollary, we recover a quite general expression for the classical principle of equipartition of energy for arbitrary q.

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