  The time evolution of many physical, chemical, and biological systems can be
modelled by stochastic transitions between the minima of the potential energy
surface describing the system of interest. We show that in cases where there
are two (or more) possible pathways that the system can take, the time
available for the transition to occur is crucially important. The well-known
results of reaction rate theory for determining the rates of the transitions
apply in the long-time limit. However, at short times, the system can instead
choose to pass over higher energy barriers with much higher probability, as
long as the distance to travel in phase space is shorter. We construct two
simple models to illustrate this general phenomenon. We also present an
extension of the gMAM algorithm of Vanden-Eijnden and Heymann [J. Chem. Phys.
{\bf 128}, 061103 (2008)] to determine the most likely path at both short and
long times.
