Relativistic nuclear matter in generalized thermo-statistics

The generalized Fermi-Dirac thermo-statistics is developed for relativistic nuclear matter. We introduce the generalized thermodynamic potential using the q-deformed exponential and logarithm. The baryon density has a form of the qexpectation value. Then, we use the mapping of the non-extensive thermo-statistics onto the extensive one. Therefore, the Clausius extensive entropy and the physical intensive temperature are determined through the Gibbs thermodynamic relation. The power-law index is constrained into a region 1 < q < 4=3 and assumed to be density dependent. The pressure-density isotherms exhibit the liquid-gas phase transition. The calculated critical temperature agrees with the experimental value for …nite nuclei of intermediate masses. There is little di¤erence in the boiling temperatures from the standard and generalized thermo-statistics, although the latter improves the caloric curve of nuclear liquid. It is found that the cut-o¤ prescription by Teweldeberhan et al. for the generalized Fermi-Dirac distribution breaks the third-law of thermodynamics. 1 Introduction Now, the thermo-statistics generalized by power-law [1,2] has been acknowledged to be beyond the standard Boltzmann-Gibbs thermo-statistics and applicable to non-equilibrium systems, small systems, gravitational systems and others. (The comprehensive references are found in Ref. [3].) Although the theoretical origin [4] of the power-law is still an open problem, the generalized thermo-statistics is also useful [5-7] in nuclear physics. In the present paper we investigate warm nuclear matter in the relativistic mean-…eld (RMF) model [8] within the generalized thermo-statistics. Although there have been already similar works [9,10], our investigation is essentially di¤erent from them in the following respects. 1) We use the RMF model of …eld-dependent meson-nucleon coupling constants developed in Ref. [11]. The …eld-dependence is due to many-body correlation in dense nuclear medium. The correlation might lead to the power-law. 2) The baryon densities in Refs. [9,10] do not have the forms of q-expectation but the normal ones. 3) We introduce the physical intensive temperature and the conjugate extensive entropy [12-14] through the Gibbs thermodynamic relation. 1 Warm nuclear matter in generalized thermo-statistics of power-law 2 Generalized Fermi-Dirac thermo-statistics In the standard Fermi-Dirac thermo-statistics1, the thermodynamic potential per volume of nuclear matter in the RMF model [8] is = 1 2 m h i 2 1 2 m! h!0i 2 kBT Z dk (2 ) ln 1 + exp E (k) kBT : (1) We have neglected the e¤ect of anti-nucleon. M and E (k) = (k +M 2) are the e¤ective mass and the energy of nucleon in nuclear matter. The Boltzmann constant is kB. The spin-isospin degeneracy is = 4. The is de…ned using the chemical potential and the vector potential V of nucleon as