  We study a process of equilibration of holographic dark energy (HDE) with the
cosmic horizon around the dark-energy dominated epoch. This process is
characterized by a huge amount of information conveyed across the horizon,
filling thereby a large gap in entropy between the system on the brink of
experiencing a sudden collapse to a black hole and the black hole itself. At
the same time, even in the absence of interaction between dark matter and dark
energy, such a process marks a strong jump in the entanglement entropy,
measuring the quantum-mechanical correlations between the horizon and its
interior. Although the effective quantum field theory (QFT) with a peculiar
relationship between the UV and IR cutoffs, a framework underlying all HDE
models, may formally account for such a huge shift in the number of distinct
quantum states, we show that the scope of such a framework becomes tremendously
restricted, devoiding it virtually any application in other cosmological epochs
or particle-physics phenomena. The problem of negative entropies for the
non-phantom stuff is also discussed.
