Optimal Finite-time Maxwell's Demons in Langevin Systems

In recent years, thermodynamics of information has been developed, enabling to quantify the fundamental costs for information processing of “Maxwell’s demon”. However, the minimal cost determined by the second law of thermodynamics is achieved only in the quasi-static limit, and the fundamental bound for finite-time information processing is yet to be established.

In this talk, we present the finite-time thermodynamic boud for information processing in Langevin systems. To this end, we provide a general framework to determine the tradeoff relation between the entropy productions of subsystems (i.e., the engine and the demon), and derive the minimal entropy productions of the subsystems based on optimal transport theory. While the obtained formulas are efficiently computable even for non-Gaussian distributions, we provide a concise and intuitive expression for the case of Gaussian distributions. As a key application of our theory, we demonstrate optimal Maxwell’s demons in finite time for both Gaussian and non-Gaussian (double-well) models.