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

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.