A Tsallisian Universe

Abbasi, Kavoos; Gharaati, Shirvan

doi:10.48550/arxiv.2006.01763

Cited by 3 publications

(4 citation statements)

References 52 publications

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“…Thus, it seems that the entropy of the black hole depends on the uncertainty principle relation and HUP is not, probably, allowed whenever Bekenstein entropy is not respected by the black hole. Recently, working in the Tsallis statistics framework, a new entropy has been obtained for black holes as follows [26][27][28]:…”

Section: Gaussianmentioning

confidence: 99%

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Tsallis uncertainty

Moradpour¹,

Ziaie²,

Corda³

2021

EPL

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It has been recently shown that the Bekenstein entropy bound is not respected by the systems satisfying modified forms of the Heisenberg uncertainty principle (HUP) including the generalized and extended uncertainty principles, or even their combinations. On the other hand, the use of generalized entropies, which differ from the Bekenstein entropy, in describing gravity and related topics indicates different equipartition expressions compared to the usual one. In that way, the mathematical form of an equipartition theorem can be related to the algebraic expression of a particular entropy, different from the standard Bekenstein entropy, initially chosen to describe the black hole event horizon, see Abreu E. M. C. et al., Mod. Phys. Lett. A, 35 (2020) 2050266. Motivated by these works, we address three new uncertainty principles leading to recently introduced generalized entropies. In addition, the corresponding energy-time uncertainty relations and Unruh temperatures are also calculated. As a result, it seems that systems described by generalized entropies, such as those of Tsallis, do not necessarily meet HUP and may satisfy modified forms of HUP.

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Section: Gaussianmentioning

confidence: 99%

“…in which q is the non-extensive parameter fixed by using other parts of physics or experiments [26][27][28][29][30], and Bekenstein entropy is recovered at the appropriate limit of q → 1, where the Gibbs statistics works [27]. This entropy has theoretically proper power to model the cosmic history in various setups [27,28].…”

Section: Gaussianmentioning

confidence: 99%

Tsallis uncertainty

Moradpour¹,

Ziaie²,

Corda³

2021

EPL

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show abstract

“…in which q is the non-extensive parameter fixed by using other parts of physics or experiments [21][22][23][24][25], and Bekenstein entropy is recovered at the appropriate limit of q → 1, where the Gibbs statistics works [22]. This entropy has theoretically proper power to model the cosmic history in various setups [22,23].…”

Section: Gaussian Extended Uncertainty Principle (Geup)mentioning

confidence: 99%

Tsallis uncertainty

Moradpour,

Ziaie,

Corda

2020

Preprint

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“…Investigations on the THDE model with Hubble horizon as IR cutoff in the higher derivative theory of gravity in [89], shows that it is not compatible with late time acceleration as it could not acquire the required value of the equation of state parameter. Due to the quantified non extensivity in Tsallis entropy, studies on modification of Friedmann equation and gravity theory, including emergence proposal of gravity [90,91,92,93,94,95] also flourish in this field. All these works were carried out considering the equation of state parameter of dark energy but as varying with the expansion of the universe.…”

Section: Introductionmentioning

confidence: 99%

Tsallis Holographic Dark Energy Reconsidered

Dheepika,

Mathew

2021

Preprint

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We consider the Interacting Tsallis Holographic Dark Energy (THDE) as dynamical vacuum, with the Granda-Oliveros (GO) scale as the infrared (IR) cutoff. To probe the evolution of the spatially flat Friedmann Lemaître Robertson Walker (FLRW) universe with dark energy and matter components, we analytically solved for the Hubble parameter, and the solution traces the evolutionary path from the prior decelerated to the late accelerated epoch. We used Pantheon Supernovae type Ia and Observational Hubble Data to constrain the free parameters of the model. The estimated values of the cosmological parameters were consistent with observational results. We analysed the behaviour of the model using the statefinder and ω e − ω e plane, and the model shows a quintessence behaviour in general and approach ΛCDM in the future. We performed a dynamical analysis of the model, concluding that the prior decelerated and late accelerated phases are unstable and stable equilibria, respectively. We also investigated the thermodynamical nature of the model and found that the horizon entropy is always an increasing function of time; the generalised second law remains valid in the dynamical vacuum treatment of the model.

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A Tsallisian Universe

Cited by 3 publications

References 52 publications

Tsallis uncertainty

Tsallis uncertainty

Tsallis uncertainty

Tsallis Holographic Dark Energy Reconsidered

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