Non-Gaussian statistics from the generalized uncertainty principle

Shababi, Homa; Ourabah, Kamel

doi:10.1140/epjp/s13360-020-00726-9

Cited by 44 publications

(40 citation statements)

References 60 publications

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“…In doing so, we come up with a nontrivial monotonic relation between the parameters β and q. We discuss our result compared to the correspondence found in [51]. We then extend our considerations to black hole thermodynamics.…”

Section: Introductionmentioning

confidence: 66%

“…In this context, we remark that a first effort to establish a connection between the Unruh effect in the GUP framework and non-Gaussian statistics has been made in [51]. There, the strategy was to explore how the prescription (1) enters into the phase space structure and modifies the elementary cell volume.…”

Section: S Q (A + B) = S Q (A) + S Q (B) + (1 − Q) S Q (A)s Q (B)mentioning

confidence: 99%

“…The concept was introduced as a basis for extending the traditional statistical mechanics and is formally identical to Havrda-Charvát structural α-entropy considered in the information theory [50]. On the other hand, the reverse problem of seeking for the statistics that emerges from the modification of the phase space cell volume implied by the GUP has been addressed in [51]. In particular, it has been shown that generalized statistics with a quadratic correction over Gaussian profile arise quite naturally if one assumes a change in the elementary cell volume as prescribed by the GUP (1), under the condition that the total phase space volume is kept invariant.…”

Section: Introductionmentioning

confidence: 99%

“…The correspondence between the two frameworks has been investigated concretely in the contexts of Unruh effect [52] and Jeans instability [53], proving that quadratic non-Gaussian statistics produce the same effects as the GUP (1) at the level of the modified Unruh temperature and Jeans mass, respectively. In turn, this allows establishing a link between the GUP parameter β and the index q that underlies the modified statistics [51].…”

Section: Introductionmentioning

confidence: 99%

“…For our purposes, we exploit the result of [59], where the Unruh effect has been studied in the context of quantum field theory with a quadratic GUP, obtaining a β-dependent expression for the particle spectrum of the vacuum condensate. It is important to stress that our approach is conceptually different from that in [51]. Indeed, the latter relies on the comparison between the GUP-and Tsallis-induced corrections at the level of the phase space cell volume and the ensuing effects on the energy/temperature relation.…”

Section: Introductionmentioning

confidence: 99%

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Tsallis statistics and generalized uncertainty principle

Luciano

2021

Eur. Phys. J. C

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It has been argued that non-Gaussian statistics provide a natural framework to investigate semiclassical effects in the context of Planck-scale deformations of the Heisenberg uncertainty relation. Here we substantiate this point by considering the Unruh effect as a specific playground. By working in the realm of quantum field theory, we reformulate the derivation of the modified Unruh effect from the generalized uncertainty principle (GUP) in the language of the nonextensive Tsallis thermostatistics. We find a nontrivial monotonic relation between the nonextensivity index q and the GUP deformation parameter $$\beta $$ β , which generalizes an earlier result obtained in quantum mechanics. We then extend our analysis to black hole thermodynamics. We preliminarily discuss our outcome in the broader context of an effective description of Planck-scale gravitational physics based on Tsallis theory.

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Section: Introductionmentioning

confidence: 66%

Section: S Q (A + B) = S Q (A) + S Q (B) + (1 − Q) S Q (A)s Q (B)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tsallis statistics and generalized uncertainty principle

Luciano

2021

Eur. Phys. J. C

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P − v criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics

Luciano,

Saridakis

2023

J. High Energ. Phys.

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Boltzmann entropy-based thermodynamics of charged anti-de Sitter (AdS) black holes has been shown to exhibit physically interesting features, such as P − V criticalities and van der Waals-like phase transitions. In this work we extend the study of these critical phenomena to Kaniadakis theory, which is a non-extensive generalization of the classical statistical mechanics incorporating relativity. By applying the typical framework of condensed-matter physics, we analyze the impact of Kaniadakis entropy onto the equation of state, the Gibbs free energy and the critical exponents of AdS black holes in the extended phase space. Additionally, we investigate the underlying micro-structure of black holes in Ruppeiner geometry, which reveals appreciable deviations of the nature of the particle interactions from the standard behavior. Our analysis opens up new perspectives on the understanding of black hole thermodynamics in a relativistic statistical framework, highlighting the role of non-extensive corrections in the AdS black holes/van der Waals fluids dual picture.

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Interacting Tsallis agegraphic dark energy in DGP braneworld cosmology

Mangoudehi

2022

Astrophys Space Sci

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Non-Gaussian statistics from the generalized uncertainty principle

Cited by 44 publications

References 60 publications

Tsallis statistics and generalized uncertainty principle

Tsallis statistics and generalized uncertainty principle

P − v criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics

Interacting Tsallis agegraphic dark energy in DGP braneworld cosmology

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