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
∝
r
−α
with
0≤α/d≤1
). As a corollary, we recover a quite general expression for the classical principle of equipartition of energy for arbitrary q.