  Hydrodynamical simulations of neutron star cores, based on a two fluid
description in terms of a neutron-proton superfluid mixture, require the
knowledge of the Andreev-Bashkin entrainment matrix which relates the momentum
of one constituent to the currents of both constituents. This matrix is derived
for arbitrary nuclear asymmetry at zero temperature and in the limits of small
relative currents in the framework of the energy density functional theory. The
Skyrme energy density functional is considered as a particular case. General
analytic formulae for the entrainment parameters and various corresponding
effective masses are obtained. These formulae are applied to the liquid core of
a neutron star, composed of an homogeneous plasma of nucleons, electrons and
possibly muons in beta equilibrium.
