Computing time scales from reaction coordinates by milestoning

An algorithm is presented to compute time scales of complex processes following predetermined milestones along a reaction coordinate. A non-Markovian hopping mechanism is assumed and constructed from underlying microscopic dynamics. General analytical analysis, a pedagogical example, and numerical solutions of the non-Markovian model are presented. No assumption is made in the theoretical derivation on the type of microscopic dynamics along the reaction coordinate. However, the detailed calculations are for Brownian dynamics in which the velocities are uncorrelated in time (but spatial memory remains).