Effects of active fluctuations on energetics of a colloidal particle: superdiffusion, dissipation and entropy production

We consider a colloidal particle immersed in an active bath and derive a Smoluchowski equation that governs the dynamics of colloidal particle. We address this as active Smoluchowski equation. Our analysis based on this active Smoluchowski equation shows a short time superdiffusive behavior that strongly depends on the activity. Our model also predicts a non-monotonic dependence of mean energy dissipation against time, a signature of activity-induced dynamics. By introducing a frequency-dependent effective temperature, we show that the mean rate of entropy production is time dependent unlike a thermal system. The prime reason for these anomalies is the absence of any fluctuation-dissipation theorem for the active noise. We also comment on how microscopic details of activity can reverse the trends for mean energy dissipation and mean rate of entropy production.