  Spontaneous persistent motions driven by active processes play a central role
to maintain the living cells far from equilibrium. In the majority of the
research works, the steady state dynamics of an active system has been
described in terms of an effective temperature. In the majority of the research
works, the steady state dynamics of an active system has been described in
terms of an effective temperature. By contrast, we have examined a prototype
model for diffusion in an activity-induced rugged energy landscape to describe
the slow dynamics of a tagged particle in a dense active environment. The
expression for the mean escape time from the active rugged energy landscape
holds only in the limit of low activity and the mean escape time from the
rugged energy landscape increases with activity. The precise form of the active
correlation will determine whether the mean escape time will depend on the
persistence time or not. The active rugged energy landscape approach also
allows an estimate of non-equilibrium effective diffusivity characterizing the
slow diffusive motion of the tagged particle due to activity. On the other
hand, in a dilute environment, high activity augments the diffusion of the
tagged particle. The enhanced diffusion can be attributed to an effective
temperature, higher than the ambient temperature and is used to calculate the
Kramers' mean escape time, which decreases with activity. Our results have
direct relevance to recent experiments on tagged particle diffusion in
condensed phases.
