Optimal finite-time Maxwell's demons in Langevin systems

We identify the optimal protocols to achieve the minimum entropy production in finite-time information exchange processes in Langevin systems, on the basis of optimal transport theory. Our general results hold even for non-Gaussian cases, while we derive a concise expression of the minimum entropy production for Gaussian processes. In particular, we apply our results to Maxwell's demons that perform measurement and feedback, and demonstrate Gaussian and non-Gaussian models of optimal demons operating in finite time. Our results provide a general strategy for controlling Langevin systems, including colloidal particles and biomolecules, in a thermodynamically optimal manner beyond the quasistatic limit.