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So far, feedback-driven systems have been discussed using (i) measurement andcontrol, (ii) a tape interacting with a system or (iii) by identifying animplicit Maxwell demon in steady state transport. We derive the correspondingsecond laws from one master fluctuation theorem and discuss their relationship.In particular, we show that both the entropy production involving mutualinformation between system and controller and the one involving a Shannonentropy difference of an information reservoir like a tape carry an extra termdifferent from the usual current times affinity. We thus generalize stochasticthermodynamics to the presence of an information reservoir.

Unifying Three Perspectives on Information Processing in Stochastic Thermodynamics