  Transition pathways of stochastic dynamical systems are typically
approximated by instantons. Here we show, using a dynamical system containing
two competing pathways, that at low-to-intermediate temperatures, instantons
can fail to capture the most likely transition pathways. We construct an
approximation which includes fluctuations around the instanton and, by
comparing with the results of an accurate and efficient path-space Monte Carlo
sampling method, find this approximation to hold for a wide range of
temperatures. Our work delimits the applicability of large deviation theory and
provides methods to probe these limits numerically.
