Thermodynamic Optimization of Finite-Time Feedback Processes

Elucidating the fundamental energy cost for information processing is one of the central topics in stochastic thermodynamics and the fundamental bound on the energy cost has been established in recent decades. However, since the bound can be achieved only in the quasi-static limit, the energy cost for information processing achieved in finite time has yet to be fully clarified.

In this talk, we will present an achievable bound on energy cost for consuming information through finite-time feedback on Markov jump processes. We will also show the explicit optimal protocol to achieve the bound. Our approach is based on two mathematical tools; one is a tight Fano’s inequality, by which we can optimize the final state under fixed consumed information, and the other is optimal transport theory, which enables us to identify the explicit protocol to achieve the obtained bound. We will also demonstrate the numerical results for the coupled two-level systems, which is experimentally feasible by using the brownian particles. Our results would serve as a design principle of finite-time feedback processes in stochastic systems.