  On-the-fly kinetic Monte Carlo (KMC) simulations are performed to investigate
slow relaxation of non-equilibrium systems. Point defects induced by 25 keV
cascades in $\alpha$-Fe are shown to lead to a characteristic time-evolution,
described by the \emph{replenish and relax} mechanism. Then, we produce an
atomistically-based assessment of models proposed to explain the slow
structural relaxation by focusing on the aggregation of 50 vacancies and 25
self-interstital atoms (SIA) in 10-lattice-parameter $\alpha$-Fe boxes, two
processes that are closely related to cascade annealing and exhibit similar
time signature. Four atomistic effects explain the timescales involved in the
evolution: defect concentration heterogeneities, concentration-enhanced
mobility, cluster-size dependent bond energies and defect-induced pressure.
These findings suggest that the two main classes of models to explain slow
structural relaxation, the Eyring model and the Gibbs model, both play a role
to limit the rate of relaxation of these simple point-defect systems.
