Some bounds upon the nonextensivity parameter using the approximate generalized distribution functions

Tirnakli, Uğur; Büyükkılıç, Fevzi; Demirhan, D.

doi:10.1016/s0375-9601(98)00378-8

Cited by 60 publications

(56 citation statements)

References 35 publications

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“…If we use the generalized statistics to describe the entropic measure of the whole system, the distribution function can not , in general, be reduced to a finite, closed, analytical expression [23][24][25][26][27][28]. For this reason we use generalized statistics to describe the entropies of the individual particles, rather than of the system as a whole 1 .…”

Section: (B) Generalized Statisticsmentioning

confidence: 99%

Generalized Statistics and the Formation of a Quark-Gluon Plasma

Teweldeberhan

Miller

Tegen

2003

Int. J. Mod. Phys. E

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The aim of this paper is to investigate the effect of a non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quarkgluon plasma (QGP). We suggest to account for the effects of the dominant part of the long-range interactions among the constituents in the QGP by a change in the statistics of the system in this phase, and we study the relevance of this statistics for the phase transition. The results show that small deviations (≈ 10%) from Boltzmann-Gibbs statistics in the QGP produce a noticeable change in the phase diagram, which can, in principle, be tested experimentally.1

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Section: (B) Generalized Statisticsmentioning

confidence: 99%

Generalized Statistics and the Formation of a Quark-Gluon Plasma

Teweldeberhan

Miller

Tegen

2003

Int. J. Mod. Phys. E

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“…One example is fully developed hydrodynamic turbulence [18]- [28], another one the statistical behaviour of particles produced in high energy e + e − collider experiments [29]- [31]. We will also deal with possible aspects of Tsallis statistics in the early universe [32]- [37], and in particular point out a connection with the fluctuations of the cosmic microwave background. In the last section we will show that (under certain assumptions on the orign of the temperature fluctuations) the e + e − scattering data may provide experimental evidence for the existence of compactified dimensions, as predicted by superstring theory.…”

Section: Introductionmentioning

confidence: 99%

Nonextensive methods in turbulence and particle physics

Beck¹

2002

Physica A: Statistical Mechanics and its Applications

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We describe some recent applications of Tsallis statistics in fully developed hydrodynamic turbulence and in high energy physics. For many of these applications nonextensive properties arise from spatial fluctuations of the temperature or the energy dissipation rate. The entropic index q is related to the relative magnitude of these fluctuations. We concentrate on a recently derived formula for the energy dependence of q that is experimentally verified by fits of cross sections in e + e − annihilation experiments. Evaluating this formula for much smaller energies E of the order of the recombination temperature, one obtains the correct order of magnitude of the fluctuations of the cosmic microwave background. Evaluating it for E → ∞, one obtains (under certain assumptions) possible evidence for the existence of 6 compactified dimensions, as predicted by superstring theory.

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“…These investigations are basically employed in the discussion of aspects related to nonextensive phenomena, such as, Lévy-type anomalous superdiffusion [5], Euler turbulence[6], self-gravitating systems and related themes [6,7,8,9,10], cosmic background radiation [11,12,13,14] [11,13,14] and in other many independent particle systems [27,28,29,30,31,32], but without a careful analysis of the validity of these methods. Thus, a detailed discussion of the (1 − q) expansion and the factorization approximation plays a special role in this scenario.…”

Section: I-introductionmentioning

confidence: 99%

Remarks on (1−q) expansion and factorization approximation in the Tsallis nonextensive statistical mechanics

Lenzi¹,

Mendes²,

Silva³

et al. 2001

Physics Letters A

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The validity of (1-q) expansion and factorization approximations are analysed in the framework of Tsallis statistics. We employ exact expressions for classical independent systems (harmonic oscillators) by considering the unnormalized and normalized constrainsts. We show that these approxiamtions can not be accurate in the analysis of systems with many degrees of freedom. I-IntroductionEver since the presentation by Tsallis[1, 2, 3] of a new possible generalization of the statistical mechanics (Tsallis statistics) based on the nonextensive entropy,a large number of investigations has been developed concerning this subject [4]. These investigations are basically employed in the discussion of aspects related to nonextensive phenomena, such as, Lévy-type anomalous superdiffusion [5], Euler turbulence[6], self-gravitating systems and related themes [6,7,8,9,10], cosmic background radiation [11,12,13,14] [11,13,14] and in other many independent particle systems [27,28,29,30,31,32], but without a careful analysis of the validity of these methods. Thus, a detailed discussion of the (1 − q) expansion and the factorization approximation plays a special role in this scenario. In this direction, Ref.[33] contains a discussion comparing these approximations in the context of the quantum gases. However, some important aspects of the comparison are still lacking, in particular the importance of the degrees of freedom N . This work is addressed to analyze how precise the (1−q) expansion and the factorization approximation are by considering N arbitrary. To perform this study it is convenient to consider a solvable model in order to carefully understand the degree of accuracy of these approximations. Furthermore, the chosen model must contain important features of other more realistic ones. This is just the case of a set of harmonic oscillators.In this direction, to analyze the (1 − q) expansion and the factorization approximation, we focus our discussion on the classical Tsallis statistics by considering N one dimesional harmonic oscillators, i. e., we employ the Hamiltonian H =

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Some bounds upon the nonextensivity parameter using the approximate generalized distribution functions

Cited by 60 publications

References 35 publications

Generalized Statistics and the Formation of a Quark-Gluon Plasma

Generalized Statistics and the Formation of a Quark-Gluon Plasma

Nonextensive methods in turbulence and particle physics

Remarks on (1−q) expansion and factorization approximation in the Tsallis nonextensive statistical mechanics

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