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Spontaneous persistent motions driven by active processes play a central roleto maintain the living cells far from equilibrium. In the majority of theresearch works, the steady state dynamics of an active system has beendescribed in terms of an effective temperature. In the majority of the researchworks, the steady state dynamics of an active system has been described interms of an effective temperature. By contrast, we have examined a prototypemodel for diffusion in an activity-induced rugged energy landscape to describethe slow dynamics of a tagged particle in a dense active environment. Theexpression for the mean escape time from the active rugged energy landscapeholds only in the limit of low activity and the mean escape time from therugged energy landscape increases with activity. The precise form of the activecorrelation will determine whether the mean escape time will depend on thepersistence time or not. The active rugged energy landscape approach alsoallows an estimate of non-equilibrium effective diffusivity characterizing theslow diffusive motion of the tagged particle due to activity. On the otherhand, in a dilute environment, high activity augments the diffusion of thetagged particle. The enhanced diffusion can be attributed to an effectivetemperature, higher than the ambient temperature and is used to calculate theKramers' mean escape time, which decreases with activity. Our results havedirect relevance to recent experiments on tagged particle diffusion incondensed phases.

Escape of a passive particle from activity-induced energy landscape: Emergence of slow and fast effective diffusion