  There have been two distinct formalisms of thermodynamics of information: One
is the measurement-feedback formalism, which concerns bipartite systems with
measurement and feedback processes, and the other is the information reservoir
formalism, which considers bit sequences as a thermodynamic fuel. In this
paper, we derive a second-law-like inequality by applying the
measurement-feedback formalism to information reservoirs, which provides a
stronger bound of extractable work than any other known inequality in the same
setup. In addition, we demonstrate that the Mandal-Jarzynski model, which is a
prominent model of the information reservoir formalism, is equivalent to a
model obtained by the contraction of a bipartite system with autonomous
measurement and feedback. Our results provide a unified view on the
measurement-feedback and the information-reservoir formalisms.
