Direct generation of loop-erased transition paths in non-equilibrium reactions

A computational procedure is proposed to generate directly loop-erased transition paths in the context of non-equilibrium reactions, i.e. reactions that occur in systems whose dynamics is not in detailed balance. The procedure builds on results from Transition Path Theory (TPT), and it avoids altogether the need to generate reactive trajectories, either by brute-force calculations or using importance sampling schemes such as Transition Path Sampling (TPS). This is computationally advantageous since these reactive trajectories can themselves be very long and intricate in complex reactions. The loop-erased transition paths, on the other hand, are shorter and simpler because, by construction, they are pruned of all the detours typical reactive trajectories make and contain only their productive pieces that carry the effective current of the reaction. As a result they give direct access to the reaction rate and mechanism.