In this paper we have considered the holographic dark energy and studied it'scosmology and thermodynamics. We have analysed the generalized second law (GSL)of thermodynamics in a flat universe consists of interacting dark energy anddark matter. We did the analysis both under thermal equilibrium andnon-equilibrium conditions. If the apparent horizon is taken as the boundary ofthe universe, we have shown that the rate of change of the total entropy of theuniverse is proportional to $(1+q)^2,$ which in fact shows that the GSL isvalid at the apparent horizon irrespective of the sign of $q,$ the decelerationparameter. Hence for any form of dark energy the apparent horizon can beconsidered as a perfect thermodynamic boundary of the universe. We made aconfirmation of this conclusion by using the holographic dark energy. Whenevent horizon is taken as the boundary, we found that the GSL is only partiallysatisfied. The analysis under non-equilibrium conditions revealed that the GSLis satisfied if the dark energy temperature is greater than the temperature ofdark matter.
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