Thermodynamic optimization of finite-time feedback protocols for Markov jump systems

In recent advances in finite-time thermodynamics, the optimization of entropy production required for finite-time information processing is an important issue. In this work, we consider finite-time feedback processes in classical discrete systems described by Markov jump processes and derive achievable bounds on entropy production for feedback processes controlled by Maxwell's demons. The key ingredients of our approach are optimal transport theory and an achievable Fano's inequality, by which we optimize the Wasserstein distance over final distributions under fixed consumed information. Our study reveals the minimum entropy production required to consume a certain amount of information, and moreover, the optimal feedback protocol to achieve it. These results are expected to lead to design principles for information processing in various stochastic systems with discrete states.