Renormalization group approach to nonextensive statistical mechanics

Abstract

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.

4 pages, 3 ps figures

References in corpus (3)

• Measuring non-extensitivity parameters in a turbulent Couette-Taylor flow
• Non-extensive statistical mechanics and particle spectra in elementary interactions
• Long-range interacting rotators: connection with the mean--field approximation

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