Thermodynamic consistency of the q-deformed Fermi–Dirac distribution in nonextensive thermostatics

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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“…q (x) = ±(x ±(q−1) − 1)/(q − 1), then the q-deformed quantum distribution functions have the form [5,6] …”

Section: Introductionmentioning

confidence: 99%

Nonextensive thermodynamics with finite chemical potentials and protoneutron starss,

Megías

Menezes

Deppman

2014

EPJ Web of Conferences

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Abstract. We derive the nonextensive thermodynamics of an ideal quantum gas composed by bosons and/or fermions with finite chemical potentials. We find agreement with previous works when μ ≤ m, and some inconsistencies are corrected for fermions when μ > m. This formalism is then used to study the thermodynamical properties of hadronic systems based on a Hadron Resonance Gas approach. We apply this result to study the protoneutron star stability under several conditions.

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“…Referring to earlier work, in [58,59] the q-generalized Fermi-Dirac distribution have been discussed and in [60] a non-extensive quantum H-theorem has been studied. In the current work the quantum statistical factors in the momentum distribution of final state particles, introduced by Uehling and Uhlenbeck in semiclassical transport theory, have been carefully included while developing the q-generalized theory.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and relativistic kinetic theory for q-generalized Bose–Einstein and Fermi–Dirac systems

Mitra¹

2018

Eur. Phys. J. C

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The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of BoseEinstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the qmodified effective coupling are estimated for a quark-gluon system.

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Thermodynamic consistency of the q-deformed Fermi–Dirac distribution in nonextensive thermostatics

Cited by 70 publications

References 22 publications

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

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

Nonextensive thermodynamics with finite chemical potentials and protoneutron starss,

Thermodynamics and relativistic kinetic theory for q-generalized Bose–Einstein and Fermi–Dirac systems

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