  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.
