  The evolution of the phase-space density profile in dark matter (DM) halos is
investigated by means of constrained simulations, designed to control the
merging history of a given DM halo. Halos evolve through a series of quiescent
phases of a slow accretion intermitted by violent events of major mergers. In
the quiescent phases the density of the halo closely follows the NFW profile
and the phase-space density profile, Q(r), is given by the Taylor & Navarro
power law, r^{-beta}, where beta ~ 1.9 and stays remarkably stable over the
Hubble time. Expressing the phase-space density by the NFW parameters, Q(r)=Qs
(r/Rs)^{-beta}, the evolution of Q is determined by Qs. We have found that the
effective mass surface density within Rs, Sigma_s = rhos Rs, remains constant
throughout the evolution of a given DM halo along the main branch of its
merging tree. This invariance entails that Qs ~ Rs^{-5/2} and Q(r) ~
Sigma_s^{-1/2} Rs^{-5/2} (r/ Rs)^{-beta}. It follows that the phase-space
density remains constant, in the sense of Qs=const., in the quiescent phases
and it decreases as Rs^{-5/2} in the violent ones. The physical origin of the
NFW density profile and the phase-space density power law is still unknown.
Yet, the numerical experiments show that halos recover these relations after
the violent phases. The major mergers drive Rs to increase and Qs to decrease
discontinuously while keeping Qs Rs^{5/2} = const. The virial equilibrium in
the quiescent phases implies that a DM halos evolves along a sequence of NFW
profiles with constant energy per unit volume (i.e., pressure) within Rs.
