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

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  • Cirto, Leonardo J.L.
  • Assis, Vladimir R.V.
  • Tsallis, Constantino

Abstract

We numerically study a one-dimensional system of N classical localized planar rotators coupled through interactions which decay with distance as 1/rα (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 Sq 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.

Suggested Citation

  • Cirto, Leonardo J.L. & Assis, Vladimir R.V. & Tsallis, Constantino, 2014. "Influence of the interaction range on the thermostatistics of a classical many-body system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 286-296.
    • Handle: RePEc:eee:phsmap:v:393:y:2014:i:c:p:286-296
    DOI: 10.1016/j.physa.2013.09.002
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    References listed on IDEAS

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    2. Alves, L.G.A. & Ribeiro, H.V. & Santos, M.A.F. & Mendes, R.S. & Lenzi, E.K., 2015. "Solutions for a q-generalized Schrödinger equation of entangled interacting particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 35-44.

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