  A central concern across the natural sciences is a quantitative understanding
of the mechanism governing rare transitions between two metastable states.
Recent research has uncovered a fundamental equality between the time-reversal
asymmetry of the ensemble of such transition paths and the informativeness of
system dynamics about the reactivity of a given trajectory, immediately leading
to quantitative criteria for judging the importance of distinct system
coordinates for the transition. Here we generalize this framework to multiple
mesostates. We find that the main system-wide and coordinate-specific results
generalize intuitively, while the combinatorial diversity of pairwise
transitions raises new questions and points to new concepts. This work
increases the previous framework's generality and applicability and forges
connections to enhanced-sampling and coarse-grained dynamical approaches such
as milestoning and Markov-state models.
