Committors, first-passage times, fluxes, Markov states, milestones, and all that

Milestoning on a one-dimensional potential starts by choosing a set of points, called milestones, and initiating short trajectories from each milestone, which are terminated when they reach an adjacent milestone for the first time. From the average duration of these trajectories and the probabilities of where they terminate, a rate matrix can be constructed and then used to calculate the mean first-passage time (MFPT) between any two milestones. All these MFPT's turn out to be exact. Here we adopt a point of view from which this remarkable result is not unexpected. In addition, we clarify the nature of the states whose interconversion is described by the rate matrix constructed using information obtained from short trajectories and provide a microscopic expression for the equilibrium population of these states in terms of equilibrium averages of the committors.