  The dynamics of a generic class of scalar active matter exhibiting a
diffusivity edge is studied in a confining potential where the amplitude is
governed by a time-dependent protocol. For such non-equilibrium systems, the
diffusion coefficient vanishes when the single-particle density field reaches a
critical threshold, inducing a condensation transition that is formally akin to
Bose-Einstein condensation. We show that this transition arises even for
systems that do not reach a steady state, leading to condensation in finite
time. Since the transition can be induced for a fixed effective temperature by
evolving the system, we effectively show that the temporal coordinate
constitutes an alternative control parameter to tune the transition
characteristics. For a constant-amplitude protocol, our generalised
thermodynamics reduces in the steady-state limit to earlier results. Lastly, we
show numerically that for periodic modulation of the potential amplitude, the
condensation transition is reentrant.
