IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v340y2004i1p11-31.html
   My bibliography  Save this article

Entropy and equilibrium via games of complexity

Author

Listed:
  • Topsøe, Flemming

Abstract

It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy (q-entropy) and Kaniadakis entropy (κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.

Suggested Citation

  • Topsøe, Flemming, 2004. "Entropy and equilibrium via games of complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 11-31.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:11-31
    DOI: 10.1016/j.physa.2004.03.073
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104003930
    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.2004.03.073?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. Ferdinand Österreicher & Igor Vajda, 2003. "A new class of metric divergences on probability spaces and its applicability in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 639-653, September.
    2. D. Mittal, 1975. "On some functional equations concerning entropy, directed divergence and inaccuracy," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 22(1), pages 35-45, December.
    3. Souza, Andre M.C. & Tsallis, Constantino, 2004. "Stability analysis of the entropies for superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 132-138.
    4. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    5. B. Sharma & I. Taneja, 1975. "Entropy of type (α, β) and other generalized measures in information theory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 22(1), pages 205-215, December.
    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. Amari, Shun-ichi & Ohara, Atsumi & Matsuzoe, Hiroshi, 2012. "Geometry of deformed exponential families: Invariant, dually-flat and conformal geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4308-4319.

    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. Igor Lazov, 2016. "A methodology for information and capacity analysis of broadband wireless access systems," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 63(2), pages 127-139, October.
    2. Kaniadakis, Giorgio & Lissia, Marcello, 2004. "Editorial," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 1-1.
    3. Lazov, Petar & Lazov, Igor, 2014. "A general methodology for population analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 557-594.
    4. 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.
    5. 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.
    6. 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.
    7. Igor Lazov, 2019. "A Methodology for Revenue Analysis of Parking Lots," Networks and Spatial Economics, Springer, vol. 19(1), pages 177-198, March.
    8. Fabio Clementi & Mauro Gallegati, 2005. "Pareto's Law of Income Distribution: Evidence for Grermany, the United Kingdom, and the United States," Microeconomics 0505006, University Library of Munich, Germany.
    9. Karataieva, Tatiana & Koshmanenko, Volodymyr & Krawczyk, Małgorzata J. & Kułakowski, Krzysztof, 2019. "Mean field model of a game for power," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 535-547.
    10. Umpierrez, Haridas & Davis, Sergio, 2021. "Fluctuation theorems in q-canonical ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    11. Lucia, Umberto, 2010. "Maximum entropy generation and κ-exponential model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4558-4563.
    12. József Dombi & Ana Vranković Lacković & Jonatan Lerga, 2023. "A New Insight into Entropy Based on the Fuzzy Operators, Applied to Useful Information Extraction from Noisy Time-Frequency Distributions," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    13. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.
    14. Amelia Carolina Sparavigna, 2019. "Composition Operations of Generalized Entropies Applied to the Study of Numbers," International Journal of Sciences, Office ijSciences, vol. 8(04), pages 87-92, April.
    15. Sagron, Ruth & Pugatch, Rami, 2021. "Universal distribution of batch completion times and time-cost tradeoff in a production line with arbitrary buffer size," European Journal of Operational Research, Elsevier, vol. 293(3), pages 980-989.
    16. Ván, P., 2006. "Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 28-33.
    17. 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.
    18. Tsallis, Constantino & Borges, Ernesto P., 2023. "Time evolution of nonadditive entropies: The logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    19. Papastamoulis Panagiotis & Rattray Magnus, 2017. "Bayesian estimation of differential transcript usage from RNA-seq data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(5-6), pages 387-405, December.
    20. Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.

    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:11-31. 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.