Nonextensive Nambu-Jona-Lasinio Model of QCD matter

Abstract

Abstract. We present a thermodynamical analysis of the nonextensive, QCD-based, Nambu-Jona-Lasinio (NJL) model of strongly interacting matter in the critical region. It is based on the nonextensive generalization of the Boltzmann-Gibbs (BG) statistical mechanics, used in the NJL model, to its nonextensive version. This can be introduced in different ways, depending on different possible choices of the form of the corresponding nonextensive entropies, which are all presented and discussed in detail. Unlike previous attempts, the present approach fulfils the basic requirements of thermodynamical consistency. The corresponding results are compared, discussed and confronted with previous findings.

Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

“…This is more illuminated in the phase diagrams of ( , ) plane correspondingly. The CEP (see Figure 4) reveals a clear variation with different nonextensive parameters of , namely, holding higher chemical potential but lower temperature with increasing, which agrees with [16,17]. As for the critical line in the diagram, as shown in Figure 4, -effects derive different trends of it on the first-order and crossover phase transitions, whose physical mechanism needs from us more attention and investigations next.…”

“…As for the critical endpoint (CEP), which is located between the two kinds of phase transition, larger occurs at higher chemical potential but lower temperature, which is also seen in the results of -NJL model [16,17]. This is because systems from fewer particles will encounter a larger value of , whose phase transition takes place with higher number density in turn.…”

“…Given the consistency of nonextensive generalizations with the initial BG approaches, we also list the results of = 1 which were investigated [15]. We close our researches with the comparisons to the nonextensive Nambu Jona-Lasinio model ( -NJL model) [16,17] of the critical endpoint (CEP), whose location is still the hot topic for experiments as well as its theoretical researches [3,5].…”

An example of the interplay of nonextensivity and dynamics in the description of QCD matter

“…The sensitivity of models of high-density matter to such an environment has been investigated for some time already (cf. the most recent works on nonextensive versions of the Walecka [9], Nambu-Jona-Lasinio [10] or other models [11][12][13], and references therein). In practice it consists in investigating the departure of values of some selected observables with increasing value of the parameter |q − 1| from their extensive values (obtained for q = 1).…”

“…In practice it consists in investigating the departure of values of some selected observables with increasing value of the parameter |q − 1| from their extensive values (obtained for q = 1). However, since in the all above mentioned models the interaction is defined by some form of a more or less complicated Lagrangian, this is not a simple task because particles considered acquire some dynamical masses which implicitly depend (usually in a very complicated manner) on the nonextensivity parameter q [10]. It would therefore be interesting and instructive to demonstrate the sensitivity of the calculational scheme used to the nonextensive environment in a more transparent way.…”