Leonardo J. L. Cirto, Vladimir R. V. Assis, Constantino Tsallis
We numerically study a one-dimensional system of $N$ classical localized planar rotators coupled through interactions which decay with distance as $1/r^\alpha$ ($\alpha \ge 0$). The approach is a first principle one (i.e., based on Newton's law) which, through molecular dynamics, yields the probability distribution of angular momenta. For $\alpha$ large enough we observe, for longstanding states corresponding to $N \gg 1$ systems, the expected Maxwellian distribution. But, for $\alpha$ 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 $q$-generalized Central Limit Theorem. It confirms the more-than-centennial prediction by J.W. Gibbs that standard statistical mechanics are not applicable for long-range interactions (i.e., for $0 \le \alpha \le 1$) due to the divergence of the canonical partition function.
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http://arxiv.org/abs/1206.6133
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