Direct simulation of rare events following Darwin

A situation often met in chemical reactions, protein folding and nucleation transitions is that the evolution breaks into fast local relaxations and rare activation processes. In the presence of such a separation of timescales, it is hopeless to try to characterize the rare transitions by a direct simulations of the microscopic dynamics, as the simulation time would be gigantic. To circumvent this difficulty, many tricks can be used to modify the microscopic dynamics and 'facilitate' the transition. Here I will follow a different approach: rather than evolving the system with its microscopic dynamics I will explain how one can directly simulate the probability current, which flows at long time between metastable states, thus yielding reaction paths and reaction rates.