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We relate the information exchange between two stochastic systems to the nonequilibrium entropy production in the whole system. By deriving a general formula that decomposes the total entropy production into the thermodynamic and informational parts, we obtain nonequilibrium equalities such as the fluctuation theorem in the presence of information processing. Our results apply not only to situations under measurement and feedback control but also to those under multiple information exchanges between two systems, giving the fundamental energy cost for information processing and elucidating the thermodynamic and informational roles of a memory in information processing. We point out a dual relationship between measurement and feedback.
Sagawa et al. (Mon,) studied this question.