Non-perturbatively generated effective potentials play an extremely useful, often critical, role in string and inflationary model building. These potentials are typically computed by Euclidean methods (i.e. instantons) which assume the system is in equilibrium. For systems out of equilibrium---for instance, an inflaton rolling down its potential---we expect there are corrections to the semi-classical evolution due to transient phenomena. How do we determine these corrections, and when do they become large? I will introduce a picture of non-perturbative effects that does not rely on the Euclidean path integral and answer these questions for a wide class of toy quantum mechanical models.