q-generalized Bose–Einstein condensation based on Tsallis entropy

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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“…The Tsallis form of the Fermi-Dirac and Bose-Einstein distributions as proposed in Refs. [30,31,32,33,34,35] is…”

Section: Speed Of Sound In a Physical Hadron Resonance Gasmentioning

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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“…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].…”

Section: Motivationmentioning

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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“…A significant amount of work has already been done to observe the effect of generalized Tsallis statistics on the phenomena of Bose-Einstein condensation [55,56,57,58]. Ou et alstudied the thermostatic properties of a q-generalized Bose system trapped in an n-dimensional harmonic oscillator potential [57] whereas Chen et alinvestigated q-generalized Bose-Einstein condensation based on Tsallis entropy [58].…”

Section: Specific Heat Variation and Be Condensationmentioning

confidence: 99%

“…Ou et alstudied the thermostatic properties of a q-generalized Bose system trapped in an n-dimensional harmonic oscillator potential [57] whereas Chen et alinvestigated q-generalized Bose-Einstein condensation based on Tsallis entropy [58]. Both of the above mentioned works deal with a Ddimensional q-generalized ideal boson system with the general energy spectrum…”

Section: Specific Heat Variation and Be Condensationmentioning

confidence: 99%

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An extensive study of Bose–Einstein condensation in liquid helium using Tsallis statistics

Guha

Das

2018

Physica A: Statistical Mechanics and its Applications

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Realistic scenario can be represented by general canonical ensemble way better than the ideal one, with proper parameter sets involved. We study the Bose-Einstein condensation phenomena of liquid helium within the framework of Tsallis statistics. With a comparatively high value of the deformation parameter q(∼ 1.4), the theoretically calculated value of the critical temperature(T c ) of the phase transition of liquid helium is found to agree with the experimentally determined value (T c = 2.17 K), although they differs from each other for q = 1 (undeformed scenario). This throws a light on the understanding of the phenomenon and connects temperature fluctuation(non-equilibrium conditions) with the interactions between atoms qualitatively. More interactions between atoms give rise to more non-equilibrium conditions which is as expected.

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q-generalized Bose–Einstein condensation based on Tsallis entropy

Cited by 38 publications

References 32 publications

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

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

Quark-gluon plasma connected to finite heat bath

An extensive study of Bose–Einstein condensation in liquid helium using Tsallis statistics

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