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Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

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  • 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
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    References listed on IDEAS

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    1. Rajaonarison, Dominique & Bolduc, Denis & Jayet, Hubert, 2005. "The K-deformed multinomial logit model," Economics Letters, Elsevier, vol. 86(1), pages 13-20, January.
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    5. 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.
    6. 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.
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    Cited by:

    1. Giuseppe Gaetano Luciano, 2024. "Kaniadakis entropy in extreme gravitational and cosmological environments: a review on the state-of-the-art and future prospects," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-13, June.
    2. 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).

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