Geometric Brownian information engine: Essentials for the best performance

We investigate a geometric Brownian information engine (GBIE) in the presence of an error-free feedback controller that transforms the information gathered on the state of Brownian particles entrapped in monolobal geometric confinement into extractable work. Outcomes of the information engine depend on the reference measurement distance xm, the feedback site xf, and the transverse force G. We determine the benchmarks for utilizing the available information in an output work and the optimum operating requisites for best achievable work. Transverse bias force (G) tunes the entropic contribution in the effective potential and hence the standard deviation (sigma) of the equilibrium marginal probability distribution. We recognize that the amount of extractable work reaches a global maximum when xf = 2xm with xm -0.6 sigma, irrespective of the extent of the entropic limitation. Because of the higher loss of information during the relaxation process, the best achievable work of a GBIE is lower in an entropic system. The feedback regulation also bears the unidirectional passage of particles. The average displacement increases with growing entropic control and is maximum when xm -0.81 sigma. Finally, we explore the efficacy of the information engine, a quantity that regulates the efficiency in utilizing the information acquired. With xf = 2xm, the maximum efficacy reduces with increasing entropic control and shows a crossover from 2 to 11/9. We discover that the condition for the best efficacy depends only on the confinement lengthscale along the feedback direction. The broader marginal probability distribution accredits the increased average displacement in a cycle and the lower efficacy in an entropy-dominated system.

Automated summary

We investigated a geometric Brownian information engine (GBIE) with an error-free feedback controller that converts information on trapped Brownian particles into extractable work. The outcomes depend on the reference measurement distance, feedback site, and transverse force. We determined the benchmarks for utilizing available information and the optimal operating requisites for best achievable work. The amount of extractable work is maximized when the feedback site is twice the reference measurement distance, regardless of the entropic limitation.