A note on thermal activation

Thermal activation is mediated by field configurations that correspond to saddle points of the energy functional. The rate of probability flow along the unstable functional directions, i.e. the activation rate, is usually obtained from the imaginary part of a suitable analytic continuation of the equilibrium free energy. In this note we provide a real-time, non-equilibrium interpretation of this imaginary part which is analogous to the real-time interpretation of the imaginary part of the one-loop effective potential in theories with symmetry breaking. We argue that in situations in which the system is strongly out of equilibrium the rate will be time dependent, and illustrate this with an example.