Generalised Tsallis statistics in electron–positron collisions

Ürmössy, Károly; Barnaföldi, G. G.; Bı́ró, Tamás

doi:10.1016/j.physletb.2011.03.073

Cited by 76 publications

(92 citation statements)

References 49 publications

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“…(43) has the form of a microcanonical distribution in the one dimensional case, D = 1. In [79,80] it was shown that smearing this distribution over a Gamma-type multiplicity distribution results in a microcanonical generalization of the Tsallis distribution which fits the fragmentation functions measured in e + e − experiments with similar q(s) evolution to that presented in fig. 2.…”

Section: Energy Fluctuations -Heat Capacitysupporting

confidence: 53%

Consequences of temperature fluctuations in observables measured in high-energy collisions

2012

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Abstract.We review the consequences of intrinsic, nonstatistical temperature fluctuations as seen in observables measured in high-energy collisions. We do this from the point of view of nonextensive statistics and Tsallis distributions. Particular attention is paid to multiplicity fluctuations as a first consequence of temperature fluctuations, to the equivalence of temperature and volume fluctuations, to the generalized thermodynamic fluctuations relations allowing us to compare fluctuations observed in different parts of the phase space, and to the problem of the relation between Tsallis entropy and Tsallis distributions. We also discuss the possible influence of conservation laws on these distributions and provide some examples of how one can get them without considering temperature fluctuations.

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Section: Energy Fluctuations -Heat Capacitysupporting

confidence: 53%

Consequences of temperature fluctuations in observables measured in high-energy collisions

2012

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“…A respectable amount of papers applying this idea to one or the other area in physics appeared [14][15][16][17][18][19]. Since from this entropy the canonical energy distribution is power law tailed in place of the Boltzmann-Gibbs exponential, numerous high-energy distributions have been fitted using the Tsallis formula [12,[20][21][22][23][24][25][26][27][28]. Its independence from the thermostat and the thermodynamical foundation behind the use of such a formula are interesting questions.…”

Section: Motivationmentioning

confidence: 99%

“…We note that theoretically a really constant heat capacity, C 0 , stems from the equation of state eq. (22). The latter is a good ansatz for an effective equation of state of classical non-Abelian gauge field systems on the lattice [51] and represents the high-E limit of Planck's S (E) formula for thermal radiation.…”

Section: Applicationmentioning

confidence: 99%

Quark-gluon plasma connected to finite heat bath

2013

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Abstract. We derive entropy formulas for finite reservoir systems, S q , from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result interprets thermodynamically the subsystem temperature, T 1, and the index q in terms of the temperature, T , entropy, S, and heat capacity, C of the reservoir as T 1 = T exp(−S/C) and q = 1−1/C. In the infinite C limit, irrespective of the value of S, the Boltzmann-Gibbs approach is fully recovered. We apply this framework for the experimental determination of the original temperature of a finite thermostat, T , from the analysis of hadron spectra produced in high-energy collisions, by analyzing frequently considered simple models of the quark-gluon plasma. MotivationA nonlinear entropy formula has been suggested by Rényi long ago and been applied to several areas in physics [1][2][3][4][5][6][7]. Another formula, the Tsallis entropy, has more recently been promoted as the keystone for a generalized thermodynamics, treating correlated physical systems [8][9][10][11] with intrinsic, either statistical or dynamical fluctuations [12,13]. A respectable amount of papers applying this idea to one or the other area in physics appeared [14][15][16][17][18][19]. Since from this entropy the canonical energy distribution is power law tailed in place of the Boltzmann-Gibbs exponential, numerous high-energy distributions have been fitted using the Tsallis formula [12,[20][21][22][23][24][25][26][27][28]. Its independence from the thermostat and the thermodynamical foundation behind the use of such a formula are interesting questions. This is even true for such a simple system like the ideal gas in a generalized form [29], which can also provide power law distribution [30][31][32][33]. It has been recently proven that -considering in the traditional way-the thermodynamical and conditional probability of an ideal gas and its part, respectively, provide Rényi and Tsallis q-entropy formulas [34].In our earlier works we investigated some general mathematical properties of alternative entropy formulas via their pairwise composition rules, and established that a scaled repetition of an arbitrary composition rule leads to an associative asymptotic composition rule of large subsystems [35]. All such rules are uniquely defined by a strict monotonic function, their formal logarithm denoted by L (see eq. (3)). Recently we have also observed that -in a e-mail: Barnafoldi.Gergely@wigner.mta.hu connection to the zero-th law of thermodynamics-the factorizability condition on the common entropy maximum [36] allows only for such rules [37]. We seek in this paper for the thermodynamical meaning of the q parameter generalizing the classical entropy formula, valid for q = 1. Some q = 1 parameter were calculated theoretically [38][39][40]. Classical thermodynamical and statistical fundamentsThe total entropy is expressed by the Planck formula,withN i !, considering altogether N states in r classes and in each class N i indistinguish...

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“…In non-extensive statistics, the Tsallis parameter (q) is related to the temperature fluctuations [12] and therefore we estimate the speed of sound using Tsallis statistics in hadronic medium, and study it as a function of q, for systems undergoing small perturbations. Further, it has been observed that the transverse momentum spectra of the secondaries created in high energy p + p(p) [9,13,14,15,16,17,18,19], e + + e − collisions [20,21] are better described by the non-extensive Tsallis statistics [22]. In addition, non-extensive statistics with radial flow successfully describes the spectra at intermediate p T in heavy-ion collisions [23,24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Speed of sound in hadronic matter using non-extensive Tsallis statistics

Khuntia¹,

Sahoo²,

Garg³

et al. 2016

Eur. Phys. J. A

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Abstract. The speed of sound (cs) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark-gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems, which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a function of temperature for different q-values for a hadron resonance gas. We observe a similar mass cut-off behaviour in the nonextensive case for c 2 s by including heavier particles, as is observed in the case of a hadron resonance gas following equilibrium statistics. Also, we explicitly show that the temperature where the mass cut-off starts varies with the q-parameter which hints at a relation between the degree of non-equilibrium and the limiting temperature of the system. It is shown that for values of q above approximately 1.13 all criticality disappears in the speed of sound, i.e. the decrease in the value of the speed of sound, observed at lower values of q, disappears completely.

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Generalised Tsallis statistics in electron–positron collisions

Cited by 76 publications

References 49 publications

Consequences of temperature fluctuations in observables measured in high-energy collisions

Consequences of temperature fluctuations in observables measured in high-energy collisions

Quark-gluon plasma connected to finite heat bath

Speed of sound in hadronic matter using non-extensive Tsallis statistics

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