Nuclear liquid-gas phase transition in generalized thermo-statistics

A new calculus of nuclear liquid-gas phase transition in the standard thermostatistics is applied to the generalized thermo-statistics. Because the phase equilibrium is de…ned in terms of intensive temperature and conjugate extensive entropy, we have to solve higher-order simultaneous nonlinear equations than those in the standard thermo-statistics. The features of phase transition are essentially the same as those in the standard thermo-statistics. The phase transition is the …rst order. There is no critical point in the section of binodal surface. The caloric curve reproduces the experimental data well. We however cannot …nd the retrograde condensation predicted in the standard thermo-statistics. The generalized thermo-statistics [1,2] is expected to be applicable to non-equilibrium systems and small systems. Because they are also produced in the multifragmentation reaction [3,4] of heavy ions, the generalized thermo-statistics recently attracts considerable attention [5-11] in nuclear physics. On the other hand, it is well known that [12,13] the asymmetric nuclear matter produced in heavy-ion reaction exhibits liquid-gas phase transition. It is therefore valuable to investigate nuclear liquid-gas phase transition in the generalized thermo-statistics. The asymmetric nuclear matter is a binary system that has two independent chemical potentials of proton and neutron. According to the Gibbs condition on phase equilibrium, both the chemical potentials in liquid and gaseous phases are equilibrated. Within the standard thermo-statistics, the geometrical construction [1419] is usually used to investigate nuclear liquid-gas mixed phase. To the contrary, Refs. [20,21] have recently developed another calculus, in which the two chemical potentials are calculated directly from the other intensive quantities of the system, temperature or pressure, baryon density and isospin asymmetry. In the present paper we extend the works [20,21] to the generalized thermo-statistics. Our formulation of warm nuclear matter is essentially based on Ref. [11], which investigates isospin symmetric matter in the generalized thermo-statistics. Its application to asymmetric matter is straightforward. Using the q-deformed exponential and logarithm expq(x) [ 1 + (1 q)x ] 1=(1 q) ; (1) 1 Nuclear liquid-gas phase transition in generalized thermo-statistics lnq(x) x q 1 1 q ; (2) the thermodynamic potential per volume is given by = 1 2 m h i 2 + 1 2 m h 3i 2 1 2 m! h!0i 2 1 2 m h 03i 2