Information Thermodynamics of the Transition-Path Ensemble

The reaction coordinate describing a transition between reactant and product is a fundamental concept in the theory of chemical reactions. Within transition-path theory, a quantitative definition of the reaction coordinate is found in the committor, which is the probability that a trajectory initiated from a given microstate first reaches the product before the reactant. Here we demonstrate an information-theoretic origin for the committor, show how it naturally arises from selecting out the transition-path ensemble from the equilibrium ensemble, and prove that the resulting entropy production is fully determined by committor dynamics. Our results provide parallel stochastic-thermodynamic and information-theoretic measures of the relevance of any system coordinate to the reaction, each of which are maximized by the committor, providing further support for its status as the ‘true’ reaction coordinate.