Stochastic thermodynamics of the transition path ensemble

The reaction coordinate is a fundamental concept in the theory of chemical reactions, yet a precise definition and methodology for finding the reaction coordinate is an unsolved problem of theoretical and computational interest. In many applications from biology to materials design, a reaction may be studied in simulation by monitoring or controlling a few physical coordinates of the system (ie. dihedral angles, bond lengths, etc.). Currently, this choice of coordinates relies on human intuition about the reaction mechanism and may miss unintuitive but important details. It is thus desirable to develop procedures for determining which physical coordinates contribute to the overall reaction and which coordinates are unimportant. We investigate the committor as a definition of the reaction coordinate, the probability that a trajectory initiated from a given system state will next reach the products before the reactants, and find that the committor is the only 1D coordinate of the system that contains all information about the reaction dynamics. We discuss how work transfer from one coordinate to the rest of the system during a reaction indicates how that coordinate contributes to the reaction mechanism. We use these ideas to study the spin-inversion mechanism for a 2D Ising model.