(168e) Identifying the Reaction Coordinate without Transition Paths: Dynamically Self-Consistent Projections

Several methods can now identify reaction coordinates from transition paths.  We show how much shorter trajectories can also reveal physically meaningful and accurate reaction coordinates.  The new method effectively tests whether trial coordinates are sufficient to predict their own short time dynamical evolution, or whether other coordinates are needed.  For each trial coordinate projections of individual swarms are compared to the projected ensemble of swarms from different locations. This comparison, quantified by the Kullback Leibler divergence, is performed for each isosurface of the trial coordinate.  Importantly, the short dynamical trajectories are generated only once by sampling along an initial coordinate.  The initial data can then be used to screen any number of alternative trial reaction coordinates.  The results are consistent with the reaction coordinates identified by Kramers-Langer-Berezhkovskii-Szabo (KLBS) theory.  Additionally, the results are not sensitive to the choice of the initial coordinate.  The new test with short trajectory data is related (through the Chapman-Kolmogorov equation) to the earlier committor analysis procedures which use longer transition paths.  Other methods that already use short trajectory swarms can now use this method to obtain an accurate reaction coordinate for later analyses.  The new method also provides insight on the relationship between reaction coordinates and dynamical coarse graining from complex systems to one-dimensional Smoluchowski equations.