  The dominant reaction pathway (DRP) is a rigorous framework to
microscopically compute the most probable trajectories, in non-equilibrium
transitions. In the low-temperature regime, such dominant pathways encode the
information about the reaction mechanism and can be used to estimate
non-equilibrium averages of arbitrary observables. On the other hand, at
sufficiently high temperatures, the stochastic fluctuations around the dominant
paths become important and have to be taken into account. In this work, we
develop a technique to systematically include the effects of such stochastic
fluctuations, to order k_B T. This method is used to compute the probability
for a transition to take place through a specific reaction channel and to
evaluate the reaction rate.
