Upon application of both the general ensemble theory and basic thermodynamical principles, we derive in detail the thermodynamics of strange matter with density-dependent particle masses, which resolves the problem of inconsistencies in the thermodynamical properties of the earlier approaches. We then recalculate the properties of strange quark matter with this new thermodynamical treatment and our recently determined quark mass scaling, and find that the density behavior of the sound velocity is opposite to the previous finding, but consistent with one of our recent publications. The structure equations for strange stars are integrated with the presently obtained equation of state. We find that the mass-radius relation is similar to previous results except the maximum mass is smaller in our case if strange quark matter is absolutely stable.

The previous treatments for strange quark matter in the quark mass-density-dependent model have unreasonable vacuum limits. We provide a method to obtain the quark mass parametrizations and give a self-consistent thermodynamic treatment which includes the MIT bag model as an extreme. In this treatment, strange quark matter in bulk still has the possibility of absolute stability. However, the behavior of the sound velocity is opposite to previous findings.

The previous thermodynamic treatment for models with density and/or temperature dependent quark masses is shown to be inconsistent with the requirement of fundamental thermodynamics. We therefore study a fully self-consistent one according to the fundamental differential equation of thermodynamics. After obtaining a new quark mass scaling with the inclusion of both confinement and leading-order perturbative interactions, we investigate properties of strange quark matter in the fully consistent thermodynamic treatment. It is found that the equation of state become stiffer, and accordingly, the maximum mass of strange stars is as large as about 2 times the solar mass, if strange quark matter is absolutely or metastable.

Thermodynamic formulas for investigating systems with density- and/or temperature-dependent particle masses are generally derived from the fundamental derivation equality of thermodynamics. Various problems in the previous treatments are discussed and modified. Properties of strange quark matter in bulk and strangelets at both zero and finite temperature are then calculated based on the new thermodynamic formulas with a new quark mass scaling, which indicates that low-mass strangelets near β equilibrium are multiquark states with an antistrange quark, such as the pentaquark ($u^2{d}^2\overline{s}$) for baryon number 1 and the octaquark ($u^4{d}^3\overline{s}$) for dibaryon, etc.

We study the properties of strange quark matter in equilibrium with normal nuclear matter. Instead of using the conventional bag model in quark sector, we achieve the confinement by a density-dependent quark mass derived from in-medium chiral condensates. In nuclear matter, we adopt the equation of state from the Brueckner-Bethe-Goldstone approach with three-body forces. It is found that the mixed phase can occur, for a reasonable confinement parameter, near the normal nuclear saturation density and goes over to pure quark matter at about 5 times the saturation. The onset of mixed and quark phases is compatible with the observed class of low-mass neutron stars, but it hinders the occurrence of kaon condensation.

In this article, we study spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field $\mathit{E}$ and magnetic field $\mathit{B}$. We use a Nambu-Jona-Lasinio model with a local kernel interaction to compute the relevant quantities to describe chiral symmetry breaking at a finite temperature for a wide range of $E$ and $B$. We study the effect of this background on the inverse catalysis of chiral symmetry breaking for $E$ and $B$ of the same order of magnitude. We then focus on the effect of the equilibration of chiral density $n_5$, produced dynamically by an axial anomaly on the critical temperature. The equilibration of $n_5$, a consequence of chirality-flipping processes in the thermal bath, allows for the introduction of the chiral chemical potential ${\mu }_5$, which is computed self-consistently as a function of the temperature and field strength by coupling the number equation to the gap equation and solving the two within an expansion in $E/T^2$, $B/T^2$, and ${\mu }_5^2/T^2$. We find that even if chirality is produced and equilibrates within a relaxation time ${\tau }_M$, it does not change drastically the thermodynamics, with particular reference to the inverse catalysis induced by the external fields, as long as the average ${\mu }_5$ at equilibrium is not too large.