On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

Details On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

2008-05-23

arxiv.org/abs/0805.3652v2

Europhysics Letters 85 (2009) 60006

Physics

Condensed Matter

Statistical Mechanics

2 pages, 2 figures. Short version of the paper, accepted for publication in Europhysics Letters, (2009) in press

Scientific paper

10.1209/0295-5075/85/60006

In the present paper we refute the criticism advanced in a recent preprint by Figueiredo et al [1] about the possible application of the $q$-generalized Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model. We exhibit that, contrary to what is claimed by these authors and in accordance with our previous results, $q$-Gaussian-like curves are possible and real attractors for a certain class of initial conditions, namely the one which produces nontrivial longstanding quasi-stationary states before the arrival, only for finite size, to the thermal equilibrium.

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