A fractal approach to entropy and distribution functions

Büyükkılıç, Fevzi; Demirham, Doǧan

doi:10.1016/0375-9601(93)91118-o

Cited by 151 publications

(126 citation statements)

References 9 publications

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“…where, for q > 1 considered there, 20) and x = β(E − µ). The q < 1 case was not considered in [22] whereas [18] advocated use of the usual Tsallis cut prescription in this case, i.e., to allow for a given q < 1 only for such values of (E, µ, β) for which [1 + (1 − q)x] ≥ 0.…”

Section: Formulation Of the Q-njlmentioning

confidence: 99%

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Nonextensive effects in the Nambu–Jona-Lasinio model of QCD

Rożynek¹,

Wilk²

2009

J. Phys. G: Nucl. Part. Phys.

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Abstract. We present a nonextensive version of the QCD-based Nambu -JonaLasinio (NJL) model of a many-body field theory describing the behavior of strongly interacting matter. It is based on the nonextensive generalization of Boltzmann-Gibbs (BG) statistical mechanics used in the NJL model, which was taken in the form proposed by Tsallis characterized by a dimensionless nonextensivity parameter q (for q → 1 one recovers the usual BG case). This new phenomenological parameter accounts summarily for all possible effects resulting in a departure from the conditions required by application of the BG approach, and allows for a simple phenomenological check of the sensitivity of the usual NJL model to such effects (in particular to fluctuations of temperature and correlations in a system of quarks). As an example, we discuss the sensitivity of such a q-NJL model to the departures from the NJL form, both for q > 1 and q < 1 cases, for such observables as the temperature dependencies of chiral symmetry restoration, masses of π and σ mesons and characteristic features of spinodal decomposition.

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Section: Formulation Of the Q-njlmentioning

confidence: 99%

“…As a result of application of the q-statistics, one gets a characteristic power-law distribution in energy-momentum [4] and specific q-versions of the Fermi-Dirac (FD) distribution [18,19] (see also [20,9]). …”

Section: Introductionmentioning

confidence: 99%

Nonextensive effects in the Nambu–Jona-Lasinio model of QCD

Rożynek¹,

Wilk²

2009

J. Phys. G: Nucl. Part. Phys.

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“…But this solution does not hold for the cases of q value very different from unity, as in the above mentioned examples of applications. Another way out is the factorization ap-proximation proposed in order to obtain the nonextensive Fermi-Dirac and Bose-Einstein distributions [12] which read…”

Section: Factorization Approximationmentioning

confidence: 99%

“…So one must be very careful in using nonextensive distribution for correlated subsystems within factorization approximation, especially in the case of the nonextensive quantum statistics derived on the basis of this approximation [12].…”

Section: Factorization Of the Joint Probabilitymentioning

confidence: 99%

Nonextensive distribution and factorization of the joint probability

Wang

Pezeril

Nivanen

et al. 2002

Chaos, Solitons & Fractals

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The problem of factorization of a nonextensive probability distribution is discussed. It is shown that the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the thermodynamic limit. In consequence, the factorization approximation should be employed carefully according to different systems. It is also shown that the zeroth law of thermodynamics can be established within the framework of the Incomplete Statistical Mechanics (ISM ).

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“…As mentioned direct generalization of the Havdra-Charvát or Tsallis entropy is given by n(x) = 1 e x 2−q ±1 [11,12]. The generalizations proposed here correspond to n I,I I = 1 g −1…”

Section: The Entropies Depending Only On the Probability Distributionmentioning

confidence: 92%

Generalized Entropies Depending Only on the Probability and Their Quantum Statistics

Obregón

Ortega-Cruz

2017

The 4th International Electronic Conference on Entropy and Its Applications

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Modified entropies have been extensively considered in the literature [1]. Among the most well known are the Rényi entropy [2] and the Havdra-Charv 'a [3] and Tsallis entropy [4,5]. All these depend on one or several parameters. By means of a modification to Superstatistics [6], one of the authors [7] has proposed generalized entropies that depend only on the probability [7,8]. There are three entropies: S I = k ∑

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A fractal approach to entropy and distribution functions

Cited by 151 publications

References 9 publications

Nonextensive effects in the Nambu–Jona-Lasinio model of QCD

Nonextensive effects in the Nambu–Jona-Lasinio model of QCD

Nonextensive distribution and factorization of the joint probability

Generalized Entropies Depending Only on the Probability and Their Quantum Statistics

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