Absolute transition rates for rare events from dynamical decoupling of reaction variables

We introduce a new approach to evaluate transition rates for rare events in complex many-particle systems. Building on a path-integral representation of transition probabilities for Markov processes, the rate is first expressed in terms of a free energy in the transition-path ensemble. We then define an auxiliary process where a suitably defined reaction variable is dynamically decoupled from all the others, whose dynamics is left unchanged. For this system the transition rates coincide with those of a unidimensional process whose only coordinate is the reaction variable. The free-energy difference between the auxiliary and the physical transition-path ensembles is finally evaluated using standard techniques. The efficiency of this method is deemed to be optimal because the physical and auxiliary dynamics differ by one degree of freedom only at any system size. Our method is demonstrated numerically on a simple model of Lennard-Jones particles ruled by the overdamped Langevin equation.