IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i1p103-110.html
   My bibliography  Save this article

Formulation of the Hellmann–Feynman theorem for the “second choice” version of Tsallis’ thermostatistics

Author

Listed:
  • Rastegin, Alexey E.

Abstract

An approach to formulating the Hellmann–Feynman theorem within the “second choice” formalism of non-extensive statistical mechanics is considered. For the state of thermal equilibrium, we derive a relation of Hellmann–Feynman type between the derivative of the non-extensive free energy with respect to the external parameter and the quantum statistical q-average of the derivative of the Hamilton operator. We also give a proper extension for an arbitrary observable commuting with the Hamiltonian. Some reasons for the usefulness of new formulas are discussed.

Suggested Citation

  • Rastegin, Alexey E., 2013. "Formulation of the Hellmann–Feynman theorem for the “second choice” version of Tsallis’ thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 103-110.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:103-110
    DOI: 10.1016/j.physa.2012.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112008035
    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.2012.08.010?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. R. K. Niven, 2009. "Combinatorial entropies and statistics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 49-63, July.
    2. Toral, Raúl & Salazar, Rafael, 2002. "Ensemble equivalence for non-extensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 52-57.
    3. Ferri, G.L. & Martínez, S. & Plastino, A., 2005. "The role of constraints in Tsallis' nonextensive treatment revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 205-220.
    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. 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.
    2. 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.
    3. 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).
    4. 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.
    5. Umpierrez, Haridas & Davis, Sergio, 2021. "Fluctuation theorems in q-canonical ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    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. Nishiyama, Tomohiro, 2019. "L^p-norm inequality using q-moment and its applications," OSF Preprints 7yzvj, Center for Open Science.
    17. 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.
    18. 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.
    19. 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.
    20. Oikonomou, Th., 2007. "Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 119-134.

    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:392:y:2013:i:1:p:103-110. 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.