Tsallis thermostatics as a statistical physics of random chains

Jizba, Petr; Korbel, Jan; Zatloukal, Vaclav

doi:10.1103/physreve.95.022103

Cited by 24 publications

(19 citation statements)

References 79 publications

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“…In passing, we mention that applications of Tsallis entropy have been widely considered in literature. Among the various systems that clarify the physical conditions under which Tsallis entropy and the associated statistics apply, we quote self-gravitating stellar systems [42,43], black holes [37], the cosmic background radiation [44,45], low-dimensional dissipative systems [38], solar neutrinos [46], polymer chains [47] and cosmological models [48,49].…”

Section: Introductionmentioning

confidence: 99%

Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

Luciano

Blasone

2021

Eur. Phys. J. C

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Flavor mixing of quantum fields was found to be responsible for the breakdown of the thermality of Unruh effect. Recently, this result was revisited in the context of nonextensive Tsallis thermostatistics, showing that the emergent vacuum condensate can still be featured as a thermal-like bath, provided that the underlying statistics is assumed to obey Tsallis prescription. This was analyzed explicitly for bosons. Here we extend this study to Dirac fermions and in particular to neutrinos. Working in the relativistic approximation, we provide an effective description of the modified Unruh spectrum in terms of the q-generalized Tsallis statistics, the q-entropic index being dependent on the mixing parameters $$\sin \theta $$ sin θ and $$\Delta m$$ Δ m . As opposed to bosons, we find $$q>1$$ q > 1 , which is indicative of the subadditivity regime of Tsallis entropy. An intuitive understanding of this result is discussed in relation to the nontrivial entangled structure exhibited by the quantum vacuum for mixed fields, combined with the Pauli exclusion principle.

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Section: Introductionmentioning

confidence: 99%

Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

Luciano

Blasone

2021

Eur. Phys. J. C

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“…The reason is that only these two cases provide a unique real MaxEnt distribution [34]. Thus, maximization under constraints is equal to maximization of Lagrange function which reads:…”

Section: Maxent Distributionmentioning

confidence: 99%

On statistical properties of Jizba–Arimitsu hybrid entropy

Çankaya

Korbel

2017

Physica A: Statistical Mechanics and its Applications

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Jizba-Arimitsu entropy (also called hybrid entropy) combines axiomatics of Rényi and Tsallis entropy. It has many common properties with them, on the other hand, some aspects as e.g., MaxEnt distributions, are completely different from the former two entropies. In this paper, we demonstrate the statistical properties of hybrid entropy, including the definition of hybrid entropy for continuous distributions, its relation to discrete entropy and calculation of hybrid entropy for some well-known distributions. Additionally, definition of hybrid divergence and its connection to Fisher metric is also discussed. Interestingly, the main properties of continuous hybrid entropy and hybrid divergence are completely different from measures based on Rényi and Tsallis entropy. This motivates us to introduce average hybrid entropy, which can be understood as an average between Tsallis and Rényi entropy

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“…One can mention, for instance, ecology, quantum information, the Heisenberg XY spin chain model, theoretical computer science, diffusion processes, several biological processes, high energy physics, etc. As a small sample, see for example, [1,2,3,4,5,6,7,8,9,10], [11,12,13,14,15,16,17,18,19,20,21,22].…”

Section: Introductionmentioning

confidence: 99%