  We discuss the potential advantages of calculating the effective mass of
quasiparticles in the interacting electron liquid from the low-temperature free
energy vis-a-vis the conventional approach, in which the effective mass is
obtained from approximate calculations of the self-energy, or from a quantum
Monte Carlo evaluation of the energy of a variational "quasiparticle wave
function". While raw quantum Monte Carlo data are presently too sparse to allow
for an accurate determination of the effective mass, the values estimated by
this method are numerically close to the ones obtained in previous calculations
using diagrammatic many-body theory. In contrast to this, a recently published
parametrization of quantum Monte Carlo data for the free energy of the
homogeneous electron liquid yields effective masses that considerably deviate
from previous calculations and even change sign for low densities, reflecting
an unphysical negative entropy. We suggest that this anomaly is related to the
treatment of the exchange energy at finite temperature.
