Nonextensive effects on the relativistic nuclear equation of state

Abstract

The Walecka many-body field theory is investigated in the context of quantum nonextensive statistical mechanics, characterized by a dimensionless parameter q. In this paper, we consider nuclear matter described statistically by a power-law distribution which generalizes the standard Fermi-Dirac distribution (q = 1). We show that the scalar and vector meson fields become more intense due to the nonextensive effects (q = 1). From a numerical treatment, we also show that as the nonextensive parameter q increases, the nucleon effective mass diminishes and the equation of state becomes stiffer. Finally, the usual Maxwell construction seems not to be necessary for isotherms with temperatures in the range 14Mev < kBT < 20MeV.

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

“…This means than that, unlike in [22], we shall work on the quark rather than the hadronic level. Also, unlike in [22], we shall consider both the q > 1 and q < 1 cases.…”

“…This means than that, unlike in [22], we shall work on the quark rather than the hadronic level. Also, unlike in [22], we shall consider both the q > 1 and q < 1 cases. This will allow us to discuss the q-dependence of the chiral phase transition in dense quark matter, in particular the quark condensates and the effective quark masses.…”

“…Recently, q-statistics has been applied to the Walecka many-body field theory [21] (known as quantum hadrodynamics or QHD-I) [22]. It resulted, among other things, in the enhancement of the scalar and vector meson fields in nuclear matter, in diminishing of the nucleon effective mass and in hardening of the nuclear equation of state (only the q > 1 case was considered there).…”

Nonextensive critical effects in the NJL model

“…It means, that in our system, which contains both particles and antiparticles, both q and 2 − q occur (or, that one can encounter both q > 1 and q < 1 at the same time, and they both have physical meaning). This differentiates our q-NJL model from the model presented in [7]. Notice that for q → 1 one recovers the standard FD distribution, n(μ, T ).…”

“…Notice that for q → 1 one recovers the standard FD distribution, n(μ, T ). It is important to realize that for T → 0 one always gets n q (μ, T ) → n(μ, T ), irrespectively of the value of q [7]. This means that we can expect any nonextensive signature only for high enough temperatures [8].…”