  Thermal properties of asymmetric nuclear matter, including the temperature
dependence of the symmetry energy, single-particle properties, and differential
isospin fractionation, are investigated with different neutron-proton effective
mass splittings using an improved isospin- and momentum-dependent interaction.
In this improved interaction, the momentum-dependence of the isoscalar
single-particle potential at saturation density is well fitted to that
extracted from optical model analyses of proton-nucleus scattering data up to
nucleon kinetic energy of 1 GeV, and the isovector properties, i.e., the slope
of the nuclear symmetry energy, the momentum-dependence of the symmetry
potential, and the symmetry energy at saturation density can be flexibly
adjusted via three parameters $x$, $y$, and $z$, respectively. Our results
indicate that the nucleon phase-space distribution in equilibrium, the
temperature dependence of the symmetry energy, and the differential isospin
fractionation can be significantly affected by the isospin splitting of nucleon
effective mass.
