Phase transitions in nonextensive spin systems

Botet, Robert; Płoszajczak, M.; González, Jorge A.

doi:10.1103/physreve.65.015103

Cited by 15 publications

(19 citation statements)

References 22 publications

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“…(1) and (2)). Note that the correct thermodynamic limit, (q − 1)N = const, for the Tsallis statistics has already been discussed in Botet et al [15,16]. In Abe [17], the thermodynamic limit for the Tsallis statistics is wrong because the limits N → ∞ and |z| → ∞ are not coordinated among themselves.…”

Section: Thermodynamics Of Microcanonical Ensemblementioning

confidence: 99%

Microcanonical ensemble extensive thermodynamics of Tsallis statistics

Parvan¹

2006

Physics Letters A

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The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution functions are derived by the thermodynamic method based upon the use of the fundamental equation of thermodynamics and the statistical definition of the functions of the state of the system. It is shown that if the entropic index ξ = 1/(q − 1) in the microcanonical ensemble is an extensive variable of the state of the system, then in the thermodynamic limitz = 1/(q − 1)N = const the principle of additivity and the zero law of thermodynamics are satisfied. In particular, the Tsallis entropy of the system is extensive and the temperature is intensive. Thus, the Tsallis statistics completely satisfies all the postulates of the equilibrium thermodynamics. Moreover, evaluation of the thermodynamic identities in the microcanonical ensemble is provided by the Euler theorem. The principle of additivity and the Euler theorem are explicitly proved by using the illustration of the classical microcanonical ideal gas in the thermodynamic limit.

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Section: Thermodynamics Of Microcanonical Ensemblementioning

confidence: 99%

Microcanonical ensemble extensive thermodynamics of Tsallis statistics

Parvan¹

2006

Physics Letters A

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“…The scaling properties of the variable z = 1/(q − 1) and their relations to the thermodynamic limit in the Tsallis statistics were found in Refs. [55,56]. In Refs.…”

Section: Introductionmentioning

confidence: 99%

“…(71), we obtain Eqs. (54) and (55) for the transverse momentum distribution of the Maxwell-Boltzmann statistics of particles in the Tsallis unnormalized statistics.…”

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confidence: 99%

Hadron transverse momentum distributions of the Tsallis normalized and unnormalized statistics

Parvan

Bhattacharyya

2020

Eur. Phys. J. A

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The exact analytical formulas for the transverse momentum distributions of the Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics of particles with nonzero mass in the framework of the Tsallis normalized and Tsallis unnormalized (also known as Tsallis-1 and Tsallis-2) statistics have been consistently derived. The final exact results were expressed in terms of the series expansions in the integral representation. The zeroth term approximation to both quantum and classical statistics of particles has been introduced. We have revealed that the phenomenological classical Tsallis distribution (widely used in high energy physics) is equal to the distribution of the Tsallis unnormalized statistics in the zeroth term approximation, but the phenomenological quantum Tsallis distributions (introduced by definition on the basis of the generalized entropy of the ideal gas) do not correspond to the distributions of the Tsallis statistics. We have found that in the ranges of the entropic parameter relevant to the processes of high-energy physics (q < 1 for Tsallis-1 and q > 1 for Tsallis-2) the Tsallis statistics is divergent. Therefore, to obtain physical results, we have regularized the Tsallis statistics by introducing an upper cut-off in the series expansion. The exact numerical results for the Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics of particles in the Tsallis normalized and unnormalized statistics have been obtained. We observed that the exact results of the Tsallis statistics strongly enhanced the production of high-pT hadrons in comparison with the usual phenomenological Tsallis distribution function at the same values of q. The q-duality of the Tsallis normalized and unnormalized statistics for the massive particles was studied.PACS. 13.85.-t Hadron-induced high-and super-high-energy interactions -13.85.Hd Inelastic scattering: many-particle final states -24.60.-k Statistical theory and fluctuations

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“…In [14,25], the author proved that the zeroth law of thermodynamics in the thermodynamic limit for the Tsallis statistics is satisfied only if the parameter z = 1/(q − 1) is an extensive variable of state. Notice that the consistent thermodynamic limit for the Tsallis statistics was firstly proposed in the particular case by Botet et al in [23,24].…”

Section: Introductionmentioning

confidence: 76%

Rényi statistics in equilibrium statistical mechanics

Parvan¹,

Bı́ró²

2010

Physics Letters A

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The Rényi statistics in the canonical and microcanonical ensembles is examined in the general case and in particular for the ideal gas. In the microcanonical ensemble the Rényi statistics is equivalent with the Boltzmann-Gibbs statistics. By the exact analytical results for the ideal gas, it is shown that in the canonical ensemble in the thermodynamic limit the Rényi statistics is also equivalent with the Boltzmann-Gibbs statistics. Furthermore it satisfies the requirements of the equilibrium thermodynamics, i.e. the thermodynamical potential of the statistical ensemble is a homogeneous function of degree 1 of its extensive variables of state. We conclude that the Rényi statistics duplicates the thermodynamical relations stemming from the Boltzmann-Gibbs statistics in the thermodynamical limit. PACS numbers: 05.; 21.65. Mn; 21.65.-f

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Phase transitions in nonextensive spin systems

Cited by 15 publications

References 22 publications

Microcanonical ensemble extensive thermodynamics of Tsallis statistics

Microcanonical ensemble extensive thermodynamics of Tsallis statistics

Hadron transverse momentum distributions of the Tsallis normalized and unnormalized statistics

Rényi statistics in equilibrium statistical mechanics

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