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.
The properties of two-flavor quark matter are investigated with a model which incorporates the confinement by density-dependent quark masses (CDDM). The results are compared with those in the conventional MIT bag model. It is found that the density behavior of quark matter in the two models are significantly different. Specially, the second derivative of the energy density can be negative in the CDDM while that in the bag model is always positive. This makes the velocity of sound very different in both models.
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