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We establish the fluctuation theorem in the presence of information exchangebetween a nonequilibrium system and other degrees of freedom such as anobserver and a feedback controller, where the amount of information exchange isadded to the entropy production. The resulting generalized second law sets thefundamental limit of energy dissipation and energy cost during the informationexchange. Our results apply not only to feedback-controlled processes but alsoto a much broader class of information exchanges, and provides a unifiedframework of nonequilibrium thermodynamics of measurement and feedback control.

Fluctuation Theorem with Information Exchange: Role of Correlations in Stochastic Thermodynamics