  We present a principled approach for estimating the matrix of microscopic
rates among states of a Markov process, given only its stationary state
population distribution and a single average global kinetic observable. We
adapt Maximum Caliber, a variational principle in which a path entropy is
maximized over the distribution of all the possible trajectories, subject to
basic kinetic constraints and some average dynamical observables. We show that
this approach leads, under appropriate conditions, to the continuous-time
master equation and a Smoluchowski-like equation that is valid for both
equilibrium and non-equilibrium stationary states. We illustrate the method by
computing the solvation dynamics of water molecules from molecular dynamics
trajectories.
