Caveats of mean first-passage time methods applied to the crystallization transition: effects of non-Markovianity

Using the crystallization transition in a Lennard-Jones fluid as example, we show that mean first-passage time based methods may underestimate the reaction rates. We trace the reason of this deficiency back to the non-Markovian character of the dynamics caused by the projection to a poorly chosen reaction coordinate. The non-Markovianity of the dynamics becomes apparent in the behavior of the recurrence times.