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

2020/04/30 by Ya-Peng Zhao · 2 citations
Mathematics · Physics and Astronomy · #Boltzmann constant #Deconfinement #Dimensionless quantity #Fractional Differential Equations Solutions #High-Energy Particle Collisions Research #Limit (mathematics) #Mathematical physics #Mathematics #Order (exchange) #Phase transition #Physics #Statistical Mechanics and Entropy #Statistical physics #Thermodynamic limit #Thermodynamics #Tsallis statistics #hep-ph #nucl-th

paper · pdf · doi:10.1103/physrevd.101.096006

published as Phys. Rev. D 101, 096006 (2020)

arxiv created 2020/04/30 · openalex publication_date 2020/05/11 · openalex created_date 2020/05/13 · arxiv updated 2020/05/20 · openalex updated_date 2026/08/05

Abstract

We present a nonextensive version of the Polyakov--Nambu--Jona-Lasinio model which is based on the nonextensive statistical mechanics. This new statistics is characterized by a dimensionless nonextensivity parameter q that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs statistics (when q\ensuremath→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 (SB) limit is actually related to the choice of statistics. For example, in the Tsallis statistics, the thermodynamic quantities \frac\ensuremathεT⁴, \fracpT⁴, and \fracsT³ all increase with q, exceed their usual SB 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_s² is still its SB limit 1/3. In addition, we found some similarities between the nonextensive effect and the finite-size effect. For example, as q increases (size decreases), the criticality of \fracc_vT³ and c_s² gradually disappears. Besides, in order to better study the nonextensive 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.

Citations

• Susceptibilities and speed of sound from the Polyakov-Nambu-Jona-Lasinio model
• Transverse Momentum Distributions in proton - proton Collisions at LHC Energies and Tsallis Thermodynamics
• Chiral effective model with the Polyakov loop
• Shear viscosity and phase diagram from Polyakov–Nambu–Jona-Lasinio model
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Bulk viscosity of hot dense Quark matter in the PNJL model
• Universal properties of bulk viscosity near the QCD phase transition
• The Wigner solution and QCD phase transitions in a modified PNJL model
• Mesonic excitations of QGP: Study with an effective model
• Transport coefficients from the Nambu–Jona-Lasinio model for SU(3)<mml:mrow/>f
• Polyakov loop, diquarks, and the two-flavor phase diagram

Cited by

• QCD phase diagram and critical exponents within the nonextensive Polyakov-Nambu-Jona-Lasinio model
• Transport coefficients of strongly interacting quark-gluon plasma including elastic and inelastic scattering within the dynamical quasiparticle model