Liquid-gas phase transition in canonical and micro-canonical ensembles of strange hadronic matter

New calculus of the liquid-gas phase transition is developed for the strange hadronic matter in the relativistic mean-…eld model. Against the familiar geometrical construction of phase equilibrium we investigate canonical and micro-canonical ensembles. For the former the pressure and the chemical potentials are determined from de…nite values of baryon density, strangeness and temperature. We recover the convex minimized Helmholtz energy. Due to the …eld-dependent meson-nucleon coupling constants, the section of binodal surface has no critical point. The appearance of the retrograde condensation is also proved. For micro-canonical ensemble the temperature and the chemical potentials are determined from de…nite values of baryon density, strangeness and pressure. We recover the concave maximized entropy and the minimized Gibbs energy. The resultant caloric and boiling curves are analyzed. Because the derivatives of chemical potentials have discontinuities at transition points, we conclude against the preceding works that the phase transition is the …rst order. 1 Introduction The author has recently developed a new calculus [1,2] of the liquid-gas phase transition [3-6] in asymmetric nuclear matter against the geometrical construction used widely in the literature [7-11]. 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. In the geometrical construction the chemical potentials are determined for de…nite values of temperature, pressure and the asymmetry of nuclear matter. To the contrary, our calculus is applicable to canonical [1] and micro-canonical ensembles [2] of nuclear matter. The strange hadronic matter (SHM) [12-18] composed of nucleons and hyperons is another binary system in nuclear physics. It has two independent chemical potentials [15], the baryon and strangeness chemical potentials. The liquid-gas phase transition in 1 Liquid-gas phase transition in strange hadronic matter SHM has been also investigated [19-22] in terms of the geometrical construction. To the contrary, in the present paper we apply the calculus in Refs. [1] and [2] to the liquidgas phase transition in canonical and micro-canonical ensembles of SHM. We are based on the relativistic mean-…eld (RMF) model of SHM developed in Ref. [18]. The model has …eld-dependent meson-baryon coupling constants from a constituent quark picture of baryons. The hidden strange mesons and [12] are taken into account. 2 Maxwell construction of phase transition At …nite temperature T the thermodynamic potential per volume ~ =V of SHM is ~ = 1 2 m h i 2 1 2 m! h!0i 2 + 1 2 m h i 2 1 2 m h 0i 2