We investigate thermodynamics of feedback processes driven by measurement. Regarding system and memory device as a composite system, mutual information as a measure of correlation between the two constituents contributes to the entropy of the composite system, which makes the generalized total entropy of the joint system and reservoir satisfy the second law of thermodynamics. We investigate the thermodynamics of the Szilard engine for an intermediate period before the completion of cycle. We show the second law to hold resolving the paradox of Maxwells demon independent of the period taken into account. We also investigate a feedback process to confine a particle excessively within a trap, which is operated by repetitions of feedback in a finite time interval. We derive the stability condition for multi-step feedback and find the condition for confinement below thermal fluctuation in the absence of feedback. The results are found to depend on interval between feedback steps and intensity of feedback protocol, which are expected to be important parameters in real experiments.
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