Nonextensive Quasiparticle Description of QCD Matter

Abstract

The dynamics of QCD matter is often described using effective mean field (MF) models based on Boltzmann-Gibbs (BG) extensive statistics. However, such matter is normally produced in small packets and in violent collisions where the usual conditions justifying the use of BG statistics are not fulfilled and the systems produced are not extensive. This can be accounted for either by enriching the original dynamics or by replacing the BG statistics by its nonextensive counterpart described by a nonextensivity parameter q = 1 (for q → 1 one returns to the extensive situation). In this work we investigate the interplay between the effects of dynamics and nonextensivity. Since the complexity of the nonextensive MF models prevents their simple visualization, we instead use some simple quasi-particle description of QCD matter in which the interaction is modelled phenomenologically by some effective fugacities, z. Embedding such a model in a nonextensive environment allows for a well-defined separation of the dynamics (represented by z) and the nonextensivity (represented by q) and a better understanding of their relationship.

Dynamical nonextensivity or nonextensive dynamics?

“…Because the corresponding changes in fugacities, δz q = z q =1 − z q=1 , for these values of q were also small, δz q < 1, the exact formulas practically coincided with a linear in (q − 1) approximation [1] (for clarity of presentation we suppress indices i = q, g):…”

“…To preserve thermodynamic consistency in the nonextensive environment, one has to use effective occupation numbers in the form of [n q (x)] q [1]. In all calculations one has always to ensure that the corresponding q-exponents are nonnegative and real valued, cf.…”

“…In all calculations one has always to ensure that the corresponding q-exponents are nonnegative and real valued, cf. [1] for details.…”

“…In [1,7] we have discussed in detail how the already known dynamics, represented by effective fugacities z i=q,g introduced in [12], is modified by immersing the system under consideration in some nonextensive environment characterized by the parameter q = 1. Fugacities z i=q,g were obtained from the results of lattice QCD simulations (which were treated as input data) by comparing the pressures of the gluons and quarks (expressed as functions of the fugacities) with the corresponding pressures obtained from the lattice calculations [12].…”

Nonlinear waves in a hot, viscous and non-extensive quark-gluon plasma

“…The interplay between the parameter q and the QCD dynamics has been studied in Refs. [45,46]. In relativistic nuclear collisions, the q is treated as a parameter to fit the transverse momentum spectra of hadrons, which can in principle vary from 0 to ∞.…”