A consistent thermodynamic treatment for 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 the self-consistent results. A new independent variable of effective mass is introduced to make the traditional thermodynamic calculation with partial derivative still practicable. The contribution from physical vacuum has been discussed. We find that the properties of strange quark matter given by quark mass density-dependent model are nearly the same as those obtained by MIT bag model after considering the contribution of the physical vacuum.