IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v118y2019icp307-310.html
   My bibliography  Save this article

Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

Author

Listed:
  • Abreu, Everton M.C.
  • Ananias Neto, Jorge
  • Mendes, Albert C.R.
  • de Paula, Rodrigo M.

Abstract

In this letter we show that a possible connection between the LQG Immirzi parameter and the area of a punctured surface can emerge depending on the thermostatistics theory previously chosen. Starting from the Boltzmann–Gibbs entropy, the Immirzi parameter can be reobtained. Using the Kaniadakis statistics, which is an important non-Gaussian statistics, we derive a new relation between the Immirzi parameter, the kappa parameter and the area of a punctured surface. After that, we compare our result with the Immirzi parameter previously obtained in the literature within the context of Tsallis’ statistics. We demonstrate in an exact way that the LQG Immirzi parameter can also be used to compare both Kaniadakis and Tsallis statics.

Suggested Citation

  • Abreu, Everton M.C. & Ananias Neto, Jorge & Mendes, Albert C.R. & de Paula, Rodrigo M., 2019. "Loop quantum gravity Immirzi parameter and the Kaniadakis statistics," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 307-310.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:307-310
    DOI: 10.1016/j.chaos.2018.11.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918310373
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.11.033?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. Rajaonarison, Dominique & Bolduc, Denis & Jayet, Hubert, 2005. "The K-deformed multinomial logit model," Economics Letters, Elsevier, vol. 86(1), pages 13-20, January.
    2. Abreu, Everton M.C. & Neto, Jorge Ananias & Barboza Jr., Edesio M. & C. Nunes, Rafael, 2016. "Holographic considerations on non-gaussian statistics and gravothermal catastrophe," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 141-150.
    3. Bento, E.P. & Silva, J.R.P. & Silva, R., 2013. "Non-Gaussian statistics, Maxwellian derivation and stellar polytropes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 666-672.
    4. Kaniadakis, G. & Quarati, P. & Scarfone, A.M., 2002. "Kinetical foundations of non-conventional statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 76-83.
    5. Kaniadakis, G. & Scarfone, A.M., 2002. "A new one-parameter deformation of the exponential function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 69-75.
    6. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    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. da Silva, Sérgio Luiz E.F., 2021. "κ-generalised Gutenberg–Richter law and the self-similarity of earthquakes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

    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. 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.
    2. Rajaonarison, Dominique, 2008. "Deterministic heterogeneity in tastes and product differentiation in the K-logit model," Economics Letters, Elsevier, vol. 100(3), pages 396-398, September.
    3. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.
    4. 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).
    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. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2012. "A new model of income distribution: the κ-generalized distribution," Journal of Economics, Springer, vol. 105(1), pages 63-91, January.
    13. da Silva, Sérgio Luiz E.F., 2021. "κ-generalised Gutenberg–Richter law and the self-similarity of earthquakes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    14. 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.
    15. 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.
    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. F. Clementi & M. Gallegati & G. Kaniadakis, 2012. "A generalized statistical model for the size distribution of wealth," Papers 1209.4787, arXiv.org, revised Dec 2012.
    18. 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.
    19. Tsallis, Constantino & Borges, Ernesto P., 2023. "Time evolution of nonadditive entropies: The logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    20. 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.

    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:chsofr:v:118:y:2019:i:c:p:307-310. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.