Thermodynamic properties and transport coefficients of QCD matter within the non-extensive Polyakov-Nambu-Jona-Lasinio model

Abstract

We present a non-extensive version of the Polyakov-Nambu-Jona-Lasinio model which is based on the non-extentive statistical mechanics. This new statistics is characterized by a dimensionless non-extensivity parameter $q$ that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs statistics (when $q\to 1$, it returns to the Boltzmann-Gibbs case). Using this q-Polyakov-Nambu-Jona-Lasinio model and including two different Polyakov-loop potentials, we discussed the influence of the parameter $q$ on chiral and deconfinement phase transition, various thermodynamic quantities and transport coefficients at finite temperature and zero quark chemical potential. We found that the Stefan-Boltzmann limit is actually related to the choice of statistics. For example, in the Tsallis statistics, the thermodynamic quantities $\frac{\epsilon }{T^4}$, $\frac{p}{T^4}$ and $\frac{s}{T^3}$ all increase with $q$, exceed their usual Stefan-Boltzmann limits and tend to a new $q$-related Tsallis limit at temperature high enough. Interestingly, however, due to a surprising cancellation, the high temperature limit of $c_s^2$ is still its SB limit $1/3$. In addition, we found some similarities between the non-extensive effect and the finite-size effect. For example, as $q$ increases (size decreases), the criticality of $\frac{c_v}{T^3}$ and $c_s^2$ gradually disappears. Besides, in order to better study the non-extensive effect, we defined a new susceptibility and calculated the response of thermodynamic quantities and transport coefficients to $q$. And found that their response patterns are different.

References in corpus (61)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral
• Chiral effective model with the Polyakov loop
• Phases of QCD: lattice thermodynamics and a field theoretical model
• From hadrons to quarks in neutron stars: a review
• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• The Phase Structure of the Polyakov--Quark-Meson Model
• Polyakov loop, diquarks and the two-flavour phase diagram
• Charged-particle multiplicities in pp interactions measured with the ATLAS detector at the LHC
• On the Strongly-Interacting Low-Viscosity Matter Created in Relativistic Nuclear Collisions
• Measurements of Strange Particle Production in $p+p$ Collisions at $\sqrt{s}$= 200 GeV
• Universal properties of bulk viscosity near the QCD phase transition
• Quark-Gluon Plasma as a Condensate of Z(3) Wilson Lines
• Transverse momentum and pseudorapidity distributions of charged hadrons in pp collisions at sqrt(s) = 0.9 and 2.36 TeV
• Production of pions, kaons and protons in pp collisions at $\sqrt{s}=900$ GeV with ALICE at the LHC
• Transport Coefficients of Hadronic Matter near $T_c$
• A nonextensive thermodynamical equilibrium approach in $e^{+}{e}^{-}\to hadrons$
• Quasi-Particle Theory of Shear and Bulk Viscosities of Hadronic Matter
• Susceptibilities and speed of sound from PNJL model
• Identified charged hadron production in p+p collisions at sqrt(s)=200 and 62.4 GeV
• Thermodynamics of (2+1)-flavor QCD: Confronting Models with Lattice Studies
• Systematic properties of the Tsallis Distribution: Energy Dependence of Parameters in High-Energy p-p Collisions
• Transport coefficients from the Nambu-Jona-Lasinio model for $SU(3{)}_f$
• Transport coefficients from the Nambu-Jona-Lasinio model for $SU(3{)}_f$
• Electrical Conductivity of Hot QCD Matter
• Description of High-Energy pp Collisions Using Tsallis Thermodynamics: Transverse Momentum and Rapidity Distributions
• Power-law tails from multiplicative noise
• Improved Polyakov-loop potential for effective models from functional calculations
• Exploring the QCD Phase Structure with Beam Energy Scan in Heavy-ion Collisions
• Origins of Bulk Viscosity at RHIC
• Entanglement between deconfinement transition and chiral symmetry restoration
• Nonextensive statistical effects in protoneutron stars
• Transport coefficients near chiral phase transition
• Phase diagram and critical properties within an effective model of QCD: the Nambu-Jona-Lasinio model coupled to the Polyakov loop
• Nonextensive hydrodynamics for relativistic heavy-ion collisions
• Thermodynamic Properties of Strongly Interacting Matter in a Finite Volume using the Polyakov-Nambu-Jona-Lasinio model
• Radial Flow in Non-Extensive Thermodynamics and Study of Particle Spectra at LHC in the Limit of Small $(q-1)$
• Transverse Momentum Distributions in proton - proton Collisions at LHC Energies and Tsallis Thermodynamics
• The K/pi ratio from condensed Polyakov loops
• Consequences of temperature fluctuations in observables measured in high energy collisions
• EMMI Rapid Reaction Task Force Meeting on 'Quark Matter in Compact Star'
• Estimating transport coefficients in hot and dense quark matter
• Transport coefficients in Polyakov quark meson coupling model: a relaxation time approximation
• Shear and Bulk Viscosities of Quark Matter from Quark-Meson Fluctuations in the Nambu--Jona-Lasinio model
• Formulation of transverse mass distributions in Au-Au collisions at 200 GeV/nucleon
• Shear viscosity due to the Landau damping from quark-pion interaction
• Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space
• The Wigner Solution and QCD Phase Transitions in a Modified PNJL Model
• Shear viscosity from Kubo formalism: NJL-model study
• Mesonic Excitations of QGP: Study with an Effective Model
• Non-extensive Statistics and Understanding Particle Production and Kinetic Freeze-out Process from $p_T$-spectra at 2.76 TeV
• Shear Viscosity and Phase Diagram from Polyakov$-$Nambu$-$Jona-Lasinio model
• Nonextensive Nambu Jona-Lasinio model of QCD matter revisited
• Dynamical Origin of Power Spectra
• Transport coefficients in a finite volume Polyakov--Nambu--Jona-Lasinio model
• Finite size effects in strongly interacting matter at zero chemical potential from Polyakov loop Nambu-Jona-Lasinio model in the light of lattice data
• Chiral phase transition in linear sigma model with non-extensive statistical mechanics
• Transport responses from rate of decay and scattering processes in the Nambu--Jona-Lasinio model
• Bulk viscosity of hot dense Quark matter in PNJL model
• Examining nonextensive statistics in relativistic heavy-ion collisions

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• Speed of sound in QCD matter
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