Entropy of holographic dark energy and the generalized second law

In this paper we have considered holographic dark energy and studied its cosmology and thermodynamics. We have analyzed the generalized second law (GSL) of thermodynamics in a flat universe consisting of interacting dark energy and dark matter. We performed the analysis under both thermal equilibrium and nonequilibrium conditions. If the apparent horizon is taken as the boundary of the universe, we have shown that the rate of change of the total entropy of the universe is proportional to which in fact shows that the GSL is valid at the apparent horizon, irrespective of the sign of the deceleration parameter, . Hence, for any form of dark energy, the apparent horizon can be considered as a perfect thermodynamic boundary of the universe. We confirmed this conclusion by using the holographic dark energy model. When the event horizon is taken as the boundary, we found that the GSL is only partially satisfied. The analysis under nonequilibrium conditions revealed that the GSL is satisfied if the temperature of the dark energy is greater than the temperature of the dark matter.