  As we observe in the moon-earth system, tidal interactions in binary systems
can lead to angular momentum exchange. The presence of viscosity is generally
regarded as the condition for such transfer to happen. In this paper, we show
how the orbital evolution can cause a persistent torque between the binary
components, even for inviscid bodies. This preferentially occurs at the final
stage of coalescence of compact binaries, when the orbit shrinks successively
by gravitational waves and plunging on a timescale shorter than the viscous
timescale. The total orbital energy transferred to the secondary by this torque
is ~0.01 of its binding energy. We further show that this persistent torque
induces a differentially rotating quadrupole perturbation. Specializing to the
case of a secondary neutron star, we find that this non equilibrium state has
an associated free energy of 10^47-10^48 erg, just prior to coalescence. This
energy is likely stored in internal fluid motions, with a sizable amount of
differential rotation. By tapping this free energy reservoir, a preexisting
weak magnetic field could be amplified up to a strength of ~10^15 Gauss. Such a
dynamically driven tidal torque can thus recycle an old neutron star into a
highly magnetized neutron star, with possible observational consequences at
merger.
