Measurement-feedback formalism meets information reservoirs

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.