Non-extensive statistical mechanics and black hole entropy from quantum geometry

Majhi, Abhishek

doi:10.1016/j.physletb.2017.10.043

Cited by 115 publications

(116 citation statements)

References 28 publications

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“…1. From these results we can see that using Kaniadakis statistics the values of γ are real and positive, confirming the results of [3] for Tsallis statistics in LQG. From Fig.…”

supporting

confidence: 84%

“…From Fig. 1 we can realize also that, in the case of a black hole described in LQG, since γ increases in magnitude as the coupling between the horizon and the bulk becomes stronger [3], analyzed from Kaniadakis formulation, the growth is slower than in Tsallis point of view.…”

mentioning

confidence: 79%

“…At the quantum level, we can say that γ corresponds to a quantization ambiguity of the theory. There is a real quantum theory for each positive and real γ [3]. It can be computed by counting the number of microstates in LQG.…”

mentioning

confidence: 99%

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Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

Abreu

Neto

Mendes

et al. 2019

Chaos, Solitons & Fractals

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In this letter we have shown 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 have derived a new relation between the Immirzi parameter, the kappa parameter and the area of a punctured surface. After that, we have compared our result with the Immirzi parameter previously obtained in the literature within the context of Tsallis' statistics. We have demonstrated in an exact way that the LQG Immirzi parameter can also be used to compare both Kaniadakis and Tsallis statics.

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“…1. From these results we can see that using Kaniadakis statistics the values of γ are real and positive, confirming the results of [3] for Tsallis statistics in LQG. From Fig.…”

supporting

confidence: 84%

mentioning

confidence: 79%

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Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

Abreu

Neto

Mendes

et al. 2019

Chaos, Solitons & Fractals

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“…In the recent work, using the concept of holography in the Tsallis entropy a new holographic dark energy models is appeared so-called the Tsallis holographic dark energy model(THDE) [39]. It is stated that by applying the Tsallis statics [41][42][43][44] to the system horizon the Bekenstein entropy can be achieved and leads to stable models [45]. The authors with choosing the Hubble horizon as IR cutoff studied different aspects of the THDE model without consideration of interaction between dark sectors [39].…”

Section: Introductionmentioning

confidence: 99%

Observational constraints on interacting Tsallis holographic dark energy model

Sadri

2019

Eur. Phys. J. C

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In this paper, we investigate a recent proposed model -so called the Tsallis holographic dark energy (THDE) model with consideration of the Hubble and the event future horizon as IR cutoffs. In this case, we consider the non-gravitational and phenomenological interaction between dark sectors. We fit the free parameters of the model using Pantheon Supernovae Type Ia data, Baryon Acoustic Oscillations, Cosmic Microwave Background, Gamma-Ray burst and the the local value of the Hubble constant. We examine the THDE model to check its compatibility with observational data using objective Information Criterion (IC). We find that the THDE models cannot be supported by observational data once the CDM is considered as the referring model. Therefore we re-examine the analysis with the standard holographic dark energy model (HDE) as another reference. Changing the CDM to main standard dark energy model (HDE), we observe the compatibility of the THDE models. Using the Alcock-Paczynski (AP) test we check the deviation of the model compared to CDM and HDE. Surveying the evolution of squared of sound speed v 2 s as an another test we check the stability of the interacting and non-interacting THDE models and we find that while the THDE model with the Hubble horizon as IR cutoff is unstable against the background perturbation, the future event horizon as IR cutoff show stability at the late time. In addition, using the modified version of the CAMB package, we observe the suppressing the CMB spectrum at small K-modes and large scale.Eur. Phys. J. C

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“…In the present paper, we focus on the axiomatic underpinning of pseudo-additive entropies that are currently being actively investigated in the context of non-equilibrium statistical physics and information theory (both classical and quantum) [1,2,15,16]. Among pseudo-additive entropies, we select and put under a deeper scrutiny a subclass of the so-called q-additive entropies.…”

Section: Introductionmentioning

confidence: 99%

On the Uniqueness Theorem for Pseudo-Additive Entropies

Jizba

Korbel

2017

Entropy

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Abstract:The aim of this paper is to show that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can be determined uniquely only when one fixes the prescription for handling conditional entropies. By using the concept of Kolmogorov-Nagumo quasi-linear means, we prove this with the help of Darótzy's mapping theorem. Our point is further illustrated with a number of explicit examples. Other salient issues, such as connections of conditional entropies with the de Finetti-Kolmogorov theorem for escort distributions and with Landsberg's classification of non-extensive thermodynamic systems are also briefly discussed.

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Non-extensive statistical mechanics and black hole entropy from quantum geometry

Cited by 115 publications

References 28 publications

Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

Observational constraints on interacting Tsallis holographic dark energy model

On the Uniqueness Theorem for Pseudo-Additive Entropies

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