Nonextensive effects in the Nambu--Jona-Lasinio model of QCD

Abstract

We present a nonextensive version of the recently discussed QCD-based Nambu - Jona-Lasinio (NJL) model of many-body field theory describing behavior of strongly interacting matter. It is based on the nonextensive generalization of the Boltzmann-Gibbs (BG) statistical mechanics used in NJL model, which was taken in the form proposed by Tsallis and characterized by a dimensionless nonextensivity parameter q (for q -> 1 one recovers the usual BG case). This is a new phenomenological parameter of the model which accounts summarily for all possible (so far unspecified) effects leading to departure from the conditions required by the usual BG approach to be fully applicable. It turns out that temperature dependencies of chiral symmetry restoration, masses of pion and sigma meson and characteristic features of spinodal decomposition are sensitive to the departures from the usual BG case.

arXiv commentaccepted in J. Phys. G

References in corpus (45)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• NJL-model analysis of dense quark matter
• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• Constraints on the high-density nuclear equation of state from the phenomenology of compact stars and heavy-ion collisions
• Hadronization in the SU(3) Nambu-Jona-Lasinio Model
• Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
• Non-Extensive Approach to Quark Matter
• Power laws in elementary and heavy-ion collisions - A story of fluctuations and nonextensivity?
• Nonextensive models for earthquakes
• Nonadditive entropy: the concept and its use
• The nonextensive parameter and Tsallis distribution for self-gravitating systems
• Strange quark matter with dynamically generated quark masses
• Power-law tails from multiplicative noise
• Maximum entropy principle and power-law tailed distributions
• Non-extensive statistical effects in high-energy collisions
• Phase transition dynamics for baryon-dense matter
• Nonextensive hydrodynamics for relativistic heavy-ion collisions
• Thermodynamics and critical behavior in the Nambu-Jona-Lasinio model of QCD
• Non-extensive Boltzmann Equation and Hadronization
• The imprints of nonextensive statistical mechanics in high energy collisions
• Modified Hagedorn formula including temperature fluctuation - Estimation of temperatures at RHIC experiments -
• Negative heat capacity and non-extensive kinetic theory
• The QCD critical end point in the PNJL model
• On the Cut-Off Prescriptions Associated with Power-Law Generalized Thermostatistics
• Spinodal decomposition during the hadronization stage at RHIC?
• Pseudoscalars Mesons in Hot, Dense Matter
• Temperature of nonextensive system: Tsallis entropy as Clausius entropy
• Relativistic Entropy and Related Boltzmann Kinetics
• Nonextensive effects on the relativistic nuclear equation of state
• Hydrodynamical description of first-order phase transitions: Analytical treatment and numerical modeling
• Dynamical Correlations as Origin of Nonextensive Entropy
• Non-extensive statistics and the stellar polytrope index
• Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space
• Abstract composition rule for relativistic kinetic energy in the thermodynamical limit
• Dynamical Origin of Power Spectra
• Quark Droplets in the NJL Mean Field
• Generalized Statistics and the Formation a Quark-Gluon Plasma
• Nonextensive statistical effects on the relativistic nuclear equation of state
• Experimental determination of the non-extensive entropic parameter $q$
• Negative heat-capacity at phase-separations in microcanonical thermostatistics of macroscopic systems with either short or long-range interactions
• Classical Equilibrium Thermostatistics, "Sancta sanctorum of Statistical Mechanics", From Nuclei to Stars
• Nonextensive perfect hydrodynamics - a model of dissipative relativistic hydrodynamics?
• Nonextensive quantum method for itinerant-electron ferromagnetism: Fractorization approach
• Non-extensive equilibration in relativistic matter
• Negative specific heat in out-of-equilibrium nonextensive systems

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• Excitation Functions of Tsallis-like Parameters in High-Energy Nucleus-Nucleus Collisions
• Nonextensive statistical effects in the hadron to quark-gluon phase transition
• Nonextensive Nambu Jona-Lasinio model of QCD matter revisited
• The imprints of superstatistics in multiparticle production processes
• Nonextensive statistical effects and strangeness production in hot and dense nuclear matter
• Nonextensive Nuclear Liquid-Gas Phase Transition
• Equivalence of volume and temperature fluctuations in power-law ensembles
• Analyzing transverse momentum spectra by a new method in high-energy collisions
• Phase transition for the system of small volume in the ${\varphi }^4$ theory in the Tsallis nonextensive statistics
• Effects of the Tsallis distribution in the linear sigma model
• Chiral phase transitions in the linear sigma model in the Tsallis nonextensive statistics
• Momentum distribution and correlation for a free scalar field in the Tsallis nonextensive statistics based on density operator
• Non-extensive distributions for a relativistic Fermi Gas
• Generalized Nonlinear Proca Equation and its Free-Particle Solutions
• An energy independent scaling of transverse momentum spectra of direct (prompt) photons from two-body processes in high-energy proton-proton collisions
• Effects of the temperature and magnetic-field dependent coupling on the properties of QCD matter
• Nonextensive lattice gauge theories: algorithms and methods
• Momentum Distribution and Correlation due to mass difference caused by power-like distribution
• An NJL model analysis of a magnetised nonextensive QCD medium
• Dynamical nonextensivity or nonextensive dynamics?
• On the putative essential discreteness of q-generalized entropies
• Chiral phase transition in the linear sigma model within Hartree factorization in the Tsallis nonextensive statistics
• Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator
• Nonlinear statistical effects in relativistic mean field theory
• Effects of Tsallis distribution on parametric resonance in chiral phase transitions
• QCD phase transition at finite temperature and chemical potential with the non-extensive statistics
• Non-extensive Effects on the QCD Equation of State and Fluctuations of Conserved Charges within Polyakov Quark Meson Model