  We use dissipationless N-body simulations to investigate the evolution of the
true coarse-grained phase-space density distribution f(x,v) in equal-mass
mergers between dark matter (DM) halos. The halo models are constructed with
various asymptotic power-law indices ranging from steep cusps to core-like
profiles and we employ the phase-space density estimator ``Enbid'' developed by
Sharma & Steinmetz to compute f(x,v). The adopted force resolution allows
robust phase-space density profile estimates in the inner ~1% of the virial
radii of the simulated systems. We confirm that mergers result in a decrease of
the coarse-grained phase-space density in accordance with expectations from
Mixing Theorems for collisionless systems. We demonstrate that binary mergers
between identical DM halos produce remnants that retain excellent memories of
the inner slopes and overall shapes of the phase-space density distribution of
their progenitors. The robustness of the phase-space density profiles holds for
a range of orbital energies, and a variety of encounter configurations
including sequences of several consecutive merger events, designed to mimic
hierarchical merging, and collisions occurring at different cosmological
epochs. If the progenitor halos are constructed with appreciably different
asymptotic power-law indices, we find that the inner slope and overall shape of
the phase-space density distribution of the remnant are substantially closer to
that of the initial system with the steepest central density cusp. These
results explicitly demonstrate that mixing is incomplete in equal-mass mergers
between DM halos, as it does not erase memory of the progenitor properties. Our
results also confirm the recent analytical predictions of Dehnen (2005)
regarding the preservation of merging self-gravitating central density cusps.
