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We proposed the finite-time cycle model of a measurement-based quantum cooler, where the invasive measurement provides the power to drive the cooling cycle. Such a cooler may be regarded as an alternative thought experiment of Maxwell’s demon. The measurement-feedback information is capable of moving heat from the cold to hot bath without any work input and even making the maximum coefficient of performance larger than the Carnot limit. The causes that this seemingly paradoxical result does not violate the laws of thermodynamics can be clearly explained through the derivation of a generalized Clausius inequality including the mutual information.