Optimal tuning of a confined Brownian information engine

A Brownian information engine is a device extracting a mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time $\tau$ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady state distribution for any $\tau$. We find that the extracted work per engine cycle is maximum when $\tau$ approaches infinity, while the power is maximum when $\tau$ approaches zero.