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Thermodynamical properties of the Universe with dark energy

We have investigated the thermodynamical properties of the Universe with dark energy. Adopting the usual assumption in deriving the constant co-moving entropy density that the physical volume and the temperature are independent, we observed some strange thermodynamical behaviors. However, these strange behaviors disappeared if we consider the realistic situation that the physical volume and the temperature of the Universe are related. Based on the well known correspondence between the Friedmann equation and the first law of thermodynamics of the apparent horizon, we argued that the apparent horizon is the physical horizon in dealing with thermodynamics problems. We have concentrated on the volume of the Universe within the apparent horizon and considered that the Universe is in thermal equilibrium with the Hawking temperature on the apparent horizon. For dark energy with $w\ge -1$, the holographic principle and the generalized second law are always respected.