Influence of the interaction range on the thermostatistics of a classical many-body system

2012/06/30 by Leonardo J. L. Cirto, Vladimir R. V. Assis, Constantino Tsallis · 1 citation
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physa.2013.09.002

published as Physica A: Statistical Mechanics and its Applications, Volume 393, 1 January 2014, Pages 286--296 · 15 pages, 13 figures

arxiv created 2013/11/04 · arxiv updated 2013/11/05

Abstract

We numerically study a one-dimensional system of N classical localized planar rotators coupled through interactions which decay with distance as 1/r^α (α≥ 0). The approach is a first principle one (i.e., based on Newton's law), and yields the probability distribution of momenta. For α large enough and N≫1 we observe, for longstanding states, the Maxwellian distribution, landmark of Boltzmann-Gibbs thermostatistics. But, for α small or comparable to unity, we observe instead robust fat-tailed distributions that are quite well fitted with q-Gaussians. These distributions extremize, under appropriate simple constraints, the nonadditive entropy S_q upon which nonextensive statistical mechanics is based. The whole scenario appears to be consistent with nonergodicity and with the thesis of the q-generalized Central Limit Theorem.

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