Consistent thermodynamic treatment for a quark-mass density-dependent model

The ambiguities and inconsistencies in previous thermodynamic treatments for the quark-mass density-dependent model are addressed. A new treatment is suggested to obtain self-consistent results. A new independent variable of effective mass is introduced to make the traditional thermodynamic calculation with partial derivatives still practicable. The contribution from physical vacuum has been discussed. We find that the properties of strange quark matter given by the quark-mass density-dependent model are nearly the same as those obtained by the MIT bag model after considering the contribution of the physical vacuum. Besides the quark system, according to our argument, the new independent variable of effective mass should be taken seriously in any thermodynamically consistent treatment whenever the medium effect is represented in the mass term.