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We investigate the Friedmann-Robertson-Walker (FRW) universe (containing darkenergy) as a non-equilibrium (irreversible) thermodynamical system byconsidering the power-law correction to the horizon entropy. By takingpower-law entropy area law which appear in dealing with the entanglement ofquantum fields in and out the horizon, we determine the power-law entropycorrected apparent horizon of the FRW universe.

Non-equilibrium thermodynamics of dark energy on the power-law entropy corrected apparent horizon