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Classical and quantum entropic properties of holographic dark energy (HDE)are considered in view of the fact that its entropy is far more restrictivethan the entropy of a black hole of the same size. In cosmological settings (inwhich HDE is promoted to a plausible candidate for being the dark energy of theuniverse), HDE should be viewed as a combined state composed of the eventhorizon and the stuff inside the horizon. By any interaction of the subsystems,the horizon and the interior become entangled, raising thereby a possibilitythat their quantum correlations be responsible for the almost purity of thecombined state. Under this circumstances, the entanglement entropy is almostthe same for both subsystems, being also of the same order as the thermal(coarse grained) entropy of the interior or the horizon. In the context ofthermodynamics, however, only additive coarse grained entropies matter, so weuse these entropies to test the generalized second law (GSL) of gravitationalthermodynamics in this framework. While we find that the original Li's modelpasses the GSL test for a special choice of parameters, in a saturated modelwith the choice for the IR cutoff in the form of the Hubble parameter, the GSLalways breaks down.

Holographic dark energy: quantum correlations against thermodynamical description