IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v96y2023i1d10.1140_epjb_s10051-023-00481-7.html
   My bibliography  Save this article

Thermodynamic quantities of independent harmonic oscillators in microcanonical and canonical ensembles in the Tsallis statistics

Author

Listed:
  • Masamichi Ishihara

    (Koriyama Women’s University)

Abstract

We study the energy and the entropies of N independent harmonic oscillators in the microcanonical and the canonical ensembles in the Tsallis classical and the Tsallis quantum statistics of entropic parameter q, where N is the number of the oscillators and the value of q is larger than one. The energy and the entropies are represented with the physical temperature, and the well-known expressions are obtained for the energy and the Rényi entropy. The difference between the microcanonical and the canonical ensembles is the existence of the condition for N and q in the canonical ensemble: $$N(q-1)

Suggested Citation

  • Masamichi Ishihara, 2023. "Thermodynamic quantities of independent harmonic oscillators in microcanonical and canonical ensembles in the Tsallis statistics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-12, January.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:1:d:10.1140_epjb_s10051-023-00481-7
    DOI: 10.1140/epjb/s10051-023-00481-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/s10051-023-00481-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/s10051-023-00481-7?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. Masamichi Ishihara, 2022. "Thermodynamics of the independent harmonic oscillators with different frequencies in the Tsallis statistics in the high physical temperature approximation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(3), pages 1-10, March.
    2. Abe, Sumiyoshi, 2001. "Heat and entropy in nonextensive thermodynamics: transmutation from Tsallis theory to Rényi-entropy-based theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 417-423.
    3. Toral, Raúl, 2003. "On the definition of physical temperature and pressure for nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 209-212.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    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. Masamichi Ishihara, 2022. "Thermodynamics of the independent harmonic oscillators with different frequencies in the Tsallis statistics in the high physical temperature approximation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(3), pages 1-10, March.
    2. Ishihara, Masamichi, 2021. "Derivation of the density operator with quantum analysis for the generalized Gibbs ensemble in quantum statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    3. 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 1-32, April.
    4. 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).
    5. 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.
    6. Meyer-Gohde, Alexander, 2019. "Generalized entropy and model uncertainty," Journal of Economic Theory, Elsevier, vol. 183(C), pages 312-343.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Tsallis, Constantino & Borges, Ernesto P., 2023. "Time evolution of nonadditive entropies: The logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    12. 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.
    13. Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.
    14. 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.
    15. Xie, Rongrong & Deng, Shengfeng & Deng, Weibing & Pato, Mauricio P., 2022. "Generalized Poisson ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    16. 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.
    17. Nishiyama, Tomohiro, 2019. "L^p-norm inequality using q-moment and its applications," OSF Preprints 7yzvj, Center for Open Science.
    18. Takahashi, Taiki, 2009. "Tsallis’ non-extensive free energy as a subjective value of an uncertain reward," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 715-719.
    19. Potiguar, F.Q & Costa, U.M.S, 2003. "Fluctuation of energy in the generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 482-492.
    20. Ervin Kaminski Lenzi & Luiz Roberto Evangelista & Luciano Rodrigues da Silva, 2023. "Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches," Mathematics, MDPI, vol. 11(12), pages 1-15, June.

    More about this item

    Statistics

    Access and download statistics

    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:spr:eurphb:v:96:y:2023:i:1:d:10.1140_epjb_s10051-023-00481-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.