How Feedback Impedes Relaxation in Active Baths

Abstract

An information engine extracts cyclic work from a bath by leveraging information through feedback. Recent studies have explored replacing thermal baths with active baths to enhance the bath's effective temperature. In this work, we investigate the relaxation dynamics of a one-dimensional Brownian particle confined in a harmonic potential and immersed in an active bath. Feedback is implemented by periodically shifting the potential minimum to align with the particle’s position. We compare baths with identical effective temperatures but varying fractions of active and thermal contributions. Our results reveal that increasing the active fraction slows relaxation, as the enhanced active component strengthens a conditioning mechanism that drives the particle away from equilibrium. However, the applied feedback disrupts this correlation, further delaying relaxation relative to purely thermal baths. To mitigate this effect, we introduce a proportional adjustment feedback method that leverages memory-assisted relaxation, significantly improving power output compared to conventional feedback strategies.