IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v340y2004i1p32-40.html
   My bibliography  Save this article

Generalized thermostatistics based on deformed exponential and logarithmic functions

Author

Listed:
  • Naudts, Jan

Abstract

The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function φ(x). It is shown that this assumption leads to an equilibrium distribution of the Boltzmann–Gibbs form with the exponential function replaced by a deformed exponential function. In this way one obtains a formalism of generalized thermostatistics introduced previously by the author. It is shown that Tsallis’ thermostatistics, with a slight modification, is the most obvious example of this formalism and corresponds with the choice φ(x)=xq.

Suggested Citation

  • Naudts, Jan, 2004. "Generalized thermostatistics based on deformed exponential and logarithmic functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 32-40.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:32-40
    DOI: 10.1016/j.physa.2004.03.074
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104003942
    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.2004.03.074?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. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.
    2. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    3. Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.
    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)

    Citations

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


    Cited by:

    1. Rosa, Wanderson & Weberszpil, José, 2018. "Dual conformable derivative: Definition, simple properties and perspectives for applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 137-141.
    2. Asgarani, Somayeh & Mirza, Behrouz, 2015. "Two-parameter entropies, Sk,r, and their dualities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 185-192.
    3. Naudts, Jan, 2006. "Parameter estimation in non-extensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 42-49.
    4. Suyari, Hiroki & Wada, Tatsuaki, 2008. "Multiplicative duality, q-triplet and (μ,ν,q)-relation derived from the one-to-one correspondence between the (μ,ν)-multinomial coefficient and Tsallis entropy Sq," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 71-83.
    5. Amblard, Pierre-Olivier & Vignat, Christophe, 2006. "A note on bounded entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 50-56.
    6. Suyari, Hiroki, 2006. "Mathematical structures derived from the q-multinomial coefficient in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 63-82.

    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. Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.
    2. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. 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.
    4. Tsallis, Constantino & Borges, Ernesto P., 2023. "Time evolution of nonadditive entropies: The logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
    6. Asgarani, Somayeh & Mirza, Behrouz, 2015. "Two-parameter entropies, Sk,r, and their dualities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 185-192.
    7. Suyari, Hiroki, 2006. "Mathematical structures derived from the q-multinomial coefficient in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 63-82.
    8. Amblard, Pierre-Olivier & Vignat, Christophe, 2006. "A note on bounded entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 50-56.
    9. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.
    10. 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.
    11. Bafghi, Seyed Mohammad Amin Tabatabaei & Kamalvand, Mohammad & Morsali, Ali & Bozorgmehr, Mohammad Reza, 2018. "Radial distribution function within the framework of the Tsallis statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 857-867.
    12. da Silva, Sérgio Luiz Eduardo Ferreira & dos Santos Lima, Gustavo Zampier & de Araújo, João Medeiros & Corso, Gilberto, 2021. "Extensive and nonextensive statistics in seismic inversion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    13. 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.
    14. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2010. "A model of personal income distribution with application to Italian data," Empirical Economics, Springer, vol. 39(2), pages 559-591, October.
    15. Yuri Biondi & Simone Righi, 2019. "Inequality, mobility and the financial accumulation process: a computational economic analysis," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 93-119, March.
    16. Masi, Marco, 2007. "On the extended Kolmogorov–Nagumo information-entropy theory, the q→1/q duality and its possible implications for a non-extensive two-dimensional Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 67-78.
    17. Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
    18. 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).
    19. Igor Lazov, 2019. "A Methodology for Revenue Analysis of Parking Lots," Networks and Spatial Economics, Springer, vol. 19(1), pages 177-198, March.
    20. Kalimeri, M. & Papadimitriou, C. & Balasis, G. & Eftaxias, K., 2008. "Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1161-1172.

    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:340:y:2004:i:1:p:32-40. 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.