Rare transitions in stochastic processes can often be rigorously described
via an underlying large deviation principle. Recent breakthroughs in the
classification of reversible stochastic processes as gradient flows have led to
a connection of large deviation principles to a generalized gradient structure.
Here, we show that, as a consequence, metastable transitions in these
reversible processes can be interpreted as heteroclinic orbits of the
generalized gradient flow. This in turn suggests a numerical algorithm to
compute the transition trajectories in configuration space efficiently, based
on the string method traditionally restricted only to gradient diffusions
