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General achievable bound of extractable work under feedback control

A general achievable upper bound of extractable work under feedback control is given, where nonequilibrium equalities are generalized so as to be applicable to error-free measurements. The upper bound involves a term which arises from the part of the process whose information becomes unavailable and is related to the weight of the singular part of the reference probability measure. The obtained upper bound of extractable work is more stringent than the hitherto known one and sets a general achievable bound for a given feedback protocol. Guiding principles of designing the optimal protocol are also outlined. Examples are presented to illustrate our general results.