  In this work, we revisit the thermodynamical self-consistency of the
quasiparticle model with the finite baryon chemical potential adjusted to
lattice QCD calculations. Here, we investigate the possibility that the
effective quasiparticle mass is also a function of its momentum, $k$, in
addition to temperature $T$ and chemical potential $\mu$. It is found that the
thermodynamic consistency can be expressed in terms of an integro-differential
equation concerning $k$, $T$, and $\mu$. We further discuss two special
solutions, both can be viewed as sufficient condition for the thermodynamical
consistency, while expressed in terms of a particle differential equation. The
first case is shown to be equivalent to those previously discussed by Peshier
et al. The second one, obtained through an ad hoc assumption, is an
intrinsically different solution where the particle mass is momentum dependent.
These equations can be solved by using boundary condition determined by the
lattice QCD data at vanishing baryon chemical potential. By numerical
calculations, we show that both solutions can reasonably reproduce the recent
lattice QCD results of the Wuppertal-Budapest and HotQCD Collaborations, and in
particular, those concerning finite baryon density. Possible implications are
discussed.
