  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.
