Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

Abreu, Éverton M. C.; Neto, Jorge Ananias; Mendes, Albert C. R.; Paula, Rodrigo M. de

doi:10.1016/j.chaos.2018.11.033

Cited by 31 publications

(19 citation statements)

References 17 publications

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“…, and where the chemical potential μ can be fixed through normalization. Equivalently, Kaniadakis entropy can be expressed as [64][65][66][67][68][69][70][71]…”

Section: Kaniadakis Entropymentioning

confidence: 99%

Modified cosmology through Kaniadakis horizon entropy

2021

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We apply the gravity-thermodynamics conjecture, namely the first law of thermodynamics on the Universe horizon, but using the generalized Kaniadakis entropy instead of the standard Bekenstein–Hawking one. The former is a one-parameter generalization of the classical Boltzmann–Gibbs–Shannon entropy, arising from a coherent and self-consistent relativistic statistical theory. We obtain new modified cosmological scenarios, namely modified Friedmann equations, which contain new extra terms that constitute an effective dark energy sector depending on the single model Kaniadakis parameter K. We investigate the cosmological evolution, by extracting analytical expressions for the dark energy density and equation-of-state parameters and we show that the Universe exhibits the usual thermal history, with a transition redshift from deceleration to acceleration at around 0.6. Furthermore, depending on the value of K, the dark energy equation-of-state parameter deviates from $$\Lambda $$ Λ CDM cosmology at small redshifts, while lying always in the phantom regime, and at asymptotically large times the Universe always results in a dark-energy dominated, de Sitter phase. Finally, even in the case where we do not consider an explicit cosmological constant the resulting cosmology is very interesting and in agreement with the observed behavior.

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“…, and where the chemical potential μ can be fixed through normalization. Equivalently, Kaniadakis entropy can be expressed as [64][65][66][67][68][69][70][71]…”

Section: Kaniadakis Entropymentioning

confidence: 99%

Modified cosmology through Kaniadakis horizon entropy

2021

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“…For this reason, it has attracted the interest of many researchers over the last two decades who have studied its foundations and mathematical aspects [49][50][51][52][53][54][55][56][57][58], the underlying thermodynamics [59,60], and specific applications of the theory to various fields. A non-exhaustive list of applications includes those in quantum statistics [61][62][63][64], in quantum entanglement [65,66], in plasma physics [67][68][69][70][71][72][73], in nuclear fission [74][75][76][77], in astrophysics [78][79][80][81], in quantum gravity [82][83][84][85][86][87], in geomechanics [88,89], in genomics [90,91], in complex networks [92][93][94], in economy [95]…”

Section: A the κ-Deformed Exponential Functionmentioning

confidence: 99%

The κ-statistics approach to epidemiology

Kaniadakis

Baldi

Deisboeck

et al. 2020

Preprint

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A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced κ-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of κ-statistics in fitting empirical data. In this paper, we use κ-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived κ-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the κ-Weibull model has universal features.

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“…Recently there have been proposals of using q-deformed entropies (e.g. see [34,35,38]) in the context of LQG, owing to the interacting nature of the quantum field theory that describes the quantum degrees of freedom of an IH [36,37]. Introducing such a q-deformed definition of entropy and demanding the area law to follow, what one arrives at finally is the following relation:…”

Section: Proposal Of a New Scenariomentioning

confidence: 99%

Note on SU(2) isolated horizon

Majhi¹

2020

Class. Quantum Grav.

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We point out that the symplectic structure, written in terms of the Sen-Ashtekar-Immirzi-Barbero variables, of a spacetime admitting an isolated horizon as the inner boundary (SS in short), involves a positive constant parameter, say σ, if γ = ±i, where γ is the Barbero-Immirzi parameter. The parameter σ represents the rescaling freedom that defines the equivalence class of null generators of the isolated horizon. The validity of the laws of mechanics and the value of surface gravity associated with the isolated horizon does not depend on the choice of σ. The SS diverges for σ 2 = (1 + γ 2 ) −1 , implying that the SS is not compatible with the full symmetry of the isolated horizon. We offer some remarks on black hole entropy calculation, with real γ, considering the restriction σ 2 = (1 + γ 2 ) −1 . * Electronic address: abhishek.majhi@gmail.com 1 See [1] for the historical reasons behind this nomenclature.

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Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

Cited by 31 publications

References 17 publications

Modified cosmology through Kaniadakis horizon entropy

Modified cosmology through Kaniadakis horizon entropy

The κ-statistics approach to epidemiology

Note on SU(2) isolated horizon

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