The intrinsic degree of freedom for quasiparticle in thermodynamics with medium effects

The thermodynamics with medium effects expressed by the temperature- and density-dependent effective mass of quasiparticle is studied. Series difficulties and many wrangles in references due to the extraordinary parameter dependence are addressed. A new independent intrinsic degree of freedom of quasiparticle $m^*$ in the equation of reversible process is introduced to clear the ambiguity. We prove all results are self-consistent.