IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v393y2014icp286-296.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113008327
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2013.09.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Zamora, Dario Javier & Tsallis, Constantino, 2022. "Probabilistic models with nonlocal correlations: Numerical evidence of q-Large Deviation Theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vignat, Christophe & Naudts, Jan, 2005. "Stability of families of probability distributions under reduction of the number of degrees of freedom," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 296-302.
    2. Atenas, Boris & Curilef, Sergio, 2021. "A statistical description for the Quasi-Stationary-States of the dipole-type Hamiltonian Mean Field Model based on a family of Vlasov solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    3. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    4. Priscila C A da Silva & Tiago V Rosembach & Anésia A Santos & Márcio S Rocha & Marcelo L Martins, 2014. "Normal and Tumoral Melanocytes Exhibit q-Gaussian Random Search Patterns," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-13, September.
    5. Naif Alotaibi & A. S. Al-Moisheer & Ibrahim Elbatal & Mansour Shrahili & Mohammed Elgarhy & Ehab M. Almetwally, 2023. "Half Logistic Inverted Nadarajah–Haghighi Distribution under Ranked Set Sampling with Applications," Mathematics, MDPI, vol. 11(7), pages 1, April.
    6. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    7. Deeb, Omar El, 2023. "Entropic spatial auto-correlation of voter uncertainty and voter transitions in parliamentary elections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    8. Zhenpeng Li & Xijin Tang & Zhenjie Hong, 2022. "Collective attention dynamic induced by novelty decay," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(8), pages 1-11, August.
    9. Ou, Congjie & Huang, Zhifu & Chen, Jincan & El Kaabouchi, A. & Nivanen, L. & Le Méhauté, A. & Wang, Qiuping A., 2009. "A basic problem in the correlations between statistics and thermodynamics," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2313-2318.
    10. 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.
    11. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    12. Ou, Congjie & Chen, Jincan & Wang, Qiuping A., 2006. "Temperature definition and fundamental thermodynamic relations in incomplete statistics," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 518-521.
    13. Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.
    14. Tsallis, Constantino & Borges, Ernesto P., 2023. "Time evolution of nonadditive entropies: The logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    15. Qiu, Hui-Bin & Liu, San-Qiu, 2018. "Nonlinear behavior of plasma: Connection with nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 486-491.
    16. Zozor, S. & Vignat, C., 2007. "On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 499-517.
    17. Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.
    18. Liu, Yanxiu & Xu, Cheng & Huang, Zhifu & Lin, Bihong, 2017. "The internal energy expression of a long-range interaction complex system and its statistical physical properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 423-427.
    19. Xie, Rongrong & Deng, Shengfeng & Deng, Weibing & Pato, Mauricio P., 2022. "Generalized Poisson ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    20. Dukkipati, Ambedkar & Bhatnagar, Shalabh & Murty, M. Narasimha, 2007. "On measure-theoretic aspects of nonextensive entropy functionals and corresponding maximum entropy prescriptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 758-774.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:393:y:2014:i:c:p:286-296. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.