The extended uncertainty principle inspires the Rényi entropy

Moradpour, H.; Corda, Christian; Ziaie, Amir Hadi; Ghaffari, S.

doi:10.1209/0295-5075/127/60006

Cited by 44 publications

(45 citation statements)

References 45 publications

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“…where Q, named Tsallis or non-extensive parameter, is an unknown free parameter (S T Q → S for Q → 1), and the last line is valid only for probability distributions meeting the P i = 1 W condition. The Q parameter may also be arisen from the quantum features of gravity [22,45]. Now, using Eq.…”

Section: Tsallis and Kaniadakis Entropies Of Black Holesmentioning

confidence: 99%

“…Generalized entropies have also been employed to study black holes [10][11][12][13][14][15][16] and also to build new holographic dark energy models [17][18][19]. Additionally, it has been shown that such entropies (i) can provide a theoretical basis for the MOND theory [20], (ii) affect the Jeans mass [21], (iii) may be motivated by a e-mail: hn.moradpour@maragheh.ac.ir (corresponding author) b e-mail: ah.ziaie@maragheh.ac.ir c e-mail: mkzangeneh@scu.ac.ir the quantum features of gravity [22,23], and even, (iv) may describe inflation without considering inflaton [24].…”

Section: Introductionmentioning

confidence: 99%

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Generalized entropies and corresponding holographic dark energy models

2020

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Using Tsallis statistics and its relation with Boltzmann entropy, the Tsallis entropy content of black holes is achieved, a result in full agreement with a recent study (Mejrhit and Ennadifi in Phys Lett B 794:24, 2019). In addition, employing Kaniadakis statistics and its relation with that of Tsallis, the Kaniadakis entropy of black holes is obtained. The Sharma-Mittal and Rényi entropy contents of black holes are also addressed by employing their relations with Tsallis entropy. Thereinafter, relying on the holographic dark energy hypothesis and the obtained entropies, two new holographic dark energy models are introduced and their implications on the dynamics of a flat FRW universe are studied when there is also a pressureless fluid in background. In our setup, the apparent horizon is considered as the IR cutoff, and there is not any mutual interaction between the cosmic fluids. The results indicate that the obtained cosmological models have (i) notable powers to describe the cosmic evolution from the matter-dominated era to the current accelerating universe, and (ii) suitable predictions for the universe age.

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Section: Tsallis and Kaniadakis Entropies Of Black Holesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized entropies and corresponding holographic dark energy models

2020

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“…Loop quantum gravity presents the spectrum of kinematic geometry operators such as the area operator and the volume operator [2]. It is a canonical quantification of general relativity within the framework of this formalism which leads to interesting applications of spin networks as the Hilbert space of the canonically quantized metric, the most fruitful implications that may arise from the application of LQG to BHs is to obtain a plausible explanation of BH thermodynamics based on non-extensive statistical mechanics taking into account strong gravitational couplings [3][4][5][6][7][8]. A comparative study of the results obtained with those based on Bekenstein-Hawking entropy shows the deep links between the entropy of BHs and their horizon surface, which clearly illustrates the underlying unity of the proposed cosmological models.…”

Section: Introductionmentioning

confidence: 99%

A semi-classical estimate for the q-parameter and decay time with Tsallis entropy of black holes in quantum geometry

Mejrhit

Hajji

2020

Eur. Phys. J. C

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In this letter, using the non-extensive entropy of Tsallis, we study some properties of the Schwarzschild black holes (BHs), based on the loop quantum gravity (LQG), some novel characteristics and results of the Schwarzschild BH can be obtained in Mejrhit and Ennadifi (Phys Lett B 794:45–49, 2019). Here we find that these findings are strikingly identical to ones obtained by Hawking and Page in anti-de Sitter space within the original of the Boltzmann entropy formula. By using the semi-classical estimate analysis on the energy at this minimum $$M_{min}$$ M min , an approximate relationship between the q and $$\gamma $$ γ parameters of BHs can be found, ($$q\approx \frac{\sqrt{3}\gamma }{\pi \ln 2}+1$$ q ≈ 3 γ π ln 2 + 1 ), which is remarkable approaching to q-parameters of cosmic ray spectra and quarks coalescing to hadrons in high energy.

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“…The quantum features of gravity [7,46] are also a source for the existence of Q parameter. Now, taking δ = 1 − Q and utilizing Equation (3) with Equation (5), one can find easily…”

Section: Tsallis and Kaniadakis Entropies Of Bhmentioning

confidence: 99%

Cosmic Consequences of Kaniadakis and Generalized Tsallis Holographic Dark Energy Models in the Fractal Universe

Jawad

Sultan

2021

Advances in High Energy Physics

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We investigate the recently proposed holographic dark energy models with the apparent horizon as the IR cutoff by assuming Kaniadakis and generalized Tsallis entropies in the fractal universe. The implications of these models are discussed for both the interacting ( Γ = 3 H b 2 ρ m ) and noninteracting ( b 2 = 0 ) cases through different cosmological parameters. Accelerated expansion of the universe is justified for both models through deceleration parameter q . In this way, the equation of state parameter ω d describes the phantom and quintessence phases of the universe. However, the coincidence parameter r ~ = Ω m / Ω d shows the dark energy- and dark matter-dominated eras for different values of parameters. It is also mentioned here that the squared speed of sound gives the stability of the model except for the interacting case of the generalized Tsallis holographic dark energy model. It is mentioned here that the current dark energy models at the apparent horizon give consistent results with recent observations.

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The extended uncertainty principle inspires the Rényi entropy

Cited by 44 publications

References 45 publications

Generalized entropies and corresponding holographic dark energy models

Generalized entropies and corresponding holographic dark energy models

A semi-classical estimate for the q-parameter and decay time with Tsallis entropy of black holes in quantum geometry

Cosmic Consequences of Kaniadakis and Generalized Tsallis Holographic Dark Energy Models in the Fractal Universe

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