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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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    1. de Souza, AndréM.C. & Tsallis, Constantino, 1997. "Student's t- and r-distributions: Unified derivation from an entropic variational principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(1), pages 52-57.
    2. Upadhyaya, Arpita & Rieu, Jean-Paul & Glazier, James A. & Sawada, Yasuji, 2001. "Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(3), pages 549-558.
    3. Miritello, Giovanna & Pluchino, Alessandro & Rapisarda, Andrea, 2009. "Central limit behavior in the Kuramoto model at the “edge of chaos”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4818-4826.
    4. P.-H. Chavanis & A. Campa, 2010. "Inhomogeneous Tsallis distributions in the HMF model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 76(4), pages 581-611, August.
    5. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    6. V. Schwämmle & F. D. Nobre & C. Tsallis, 2008. "q-Gaussians in the porous-medium equation: stability and time evolution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(4), pages 537-546, December.
    7. Pluchino, Alessandro & Rapisarda, Andrea & Tsallis, Constantino, 2008. "A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3121-3128.
    8. Rego, Henio H.A & Lucena, Liacir S & da Silva, Luciano R & Tsallis, Constantino, 1999. "Crossover from extensive to nonextensive behavior driven by long-range d=1 bond percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 42-48.
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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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