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Abstract. We present a nonextensive version of the QCD-based Nambu -JonaLasinio (NJL) model of a many-body field theory describing the behavior of strongly interacting matter. It is based on the nonextensive generalization of Boltzmann-Gibbs (BG) statistical mechanics used in the NJL model, which was taken in the form proposed by Tsallis characterized by a dimensionless nonextensivity parameter q (for q → 1 one recovers the usual BG case). This new phenomenological parameter accounts summarily for all possible effects resulting in a departure from the conditions required by application of the BG approach, and allows for a simple phenomenological check of the sensitivity of the usual NJL model to such effects (in particular to fluctuations of temperature and correlations in a system of quarks). As an example, we discuss the sensitivity of such a q-NJL model to the departures from the NJL form, both for q > 1 and q < 1 cases, for such observables as the temperature dependencies of chiral symmetry restoration, masses of π and σ mesons and characteristic features of spinodal decomposition.

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.

The possibility of a ferromagnetic transition in dense neutron matter is investigated using a simplified model of a pure hard core gas, with core radius c. Previous estimates of the density at which the ferromagnetic transition would occur are shown to be incorrect. The inclusion of terms cubic in kFc, in particular the P state interaction, leads to the conclusion that neutron matter in the liquid phase should not exhibit ferromagnetism. NUCLEAR STRUCTURE Ferromagnetism of dense hard-core neutron and nuclear matter.b, &0.(2) Now, both E(0) and E(1) may be expanded in x =k~c with the known result (see, e.g. , Ref. 6):There have been suggestions that neutron matter at a density pz, comparable to densities expected in neutron stars, may become ferromagnetic. '"'The estimates'" of p& were performed for a simplified model of a pure hard core neutron gas. A, possible ferromagnetic transition in a hard core fermion system has been suggested" for a long time and is important in the theory of magnetism in metals. 'In the present paper, we want to show that the previous estimates of p& were incorrect, and that it appears to be unlikely that neutron matter would exhibit ferromagnetism in the liquid phase. Our conclusion agrees with existing calculations of magnetic susceptibility of neutron matter, performed with realistic forces (see, e.g. , Ref. 7).We adopt the model of a pure hard core interaction of radius c for neutron matter for two reasons: (i) At high densities the short range repulsion is the decisive part of the interaction; (ii) the attraction between neutrons with a reasonable spin dependence is expected to increase the stability of the spin unpolarized state. We employ nonrelativistic quantum mechanics, and restrict ourselves to zero temperature. The energy per neutron E(a)/N depends on the spin excess parameter a =(N& -N&)/N and on the density p=kz'/3v'. kz is the Fermi momentum of spin unpolarized neutron matter. If we denote d = E(1)/N -E(0)/N, then the condition for the occurrence of ferromagnetism is, +-' , v 'x+ , ',n'(-ll -2 ln2)x'The factor 2' ' in (4) represents the increase in kinetic energy in the transition from the normal 0, =0 to the ferromagnetic a =1 state. Terms linear and quadratic in x and the part of the cubic term with the coefficient 0.0377 arise from interaction in the S state and do not appear in E(1), due to the Pauli principle. This is in accordance with the usual argument in favor of ferromagnetism: Although in the ferromagnetic transition the kinetic energy of the system increases, at high density this is more than balanced by the disappearance of the repulsive interaction. What has been overlooked in this argument is the interaction in the P state, which contributes the part of the cubic terms with the coefficients in the curly brackets. Now, by the same argument, the P state interaction acts in the opposite direction and, in fact, makes the ferromagnetic state less favorable. The function b(x) calculated with the help of expressions (3) and (4) is shown in Fig. 1. The curve curves ...

Recently the non-extensive approach has been used in a variety of ways to describe dense nuclear matter. They differ in the methods of introducing the appropriate non-extensive single particle distributions inside a relativistic many-body system, in particular when one has to deal both with particles and antiparticles, as in the case of quark matter exemplified in the NJL approach. I present and discuss in detail the physical consequences of the methods used so far, which should be recognized before any physical conclusions can be reached from the results presented.PACS: 21.65.+f 5.70 71.10