Transition-rate theory for nongradient drift fields

Classical transition-rate theory provides analytic techniques for computing the asymptotics of a weakly perturbed particle's mean residence time in the basin of attraction of a metastable state. If the dynamics of the particle are derivable from a potential, it typically escapes over a saddle point. In the nonpotential case exit may take place over an unstable point instead, leading to unexpected phenomena. These may include an anomalous pre-exponential factor, with a continuously varying exponent, in the residence time asymptotics. Moreover, the most probable escape trajectories may eventually deviate from the least-action escape path.