  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
clarify a dual relationship between measurement and feedback.
