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