Dynamics of the Fokker-Planck equation

In this note we should like to explain why the Fokker-Planck equation is a gradient flow for the system energy by exhibiting an appropriate discrete scheme. We shall then explain, from the standpoint of students of transforming materials, why it might be of interest. This is because we are able to offer an interpretation of metastable behavior in terms of competition between energy and system states at successive times. An example will be an application to the kinetics of microstructural evolution under mechanical loading in a shape memory alloy that is based on the work of Abeyaratne, Chu and James (Phil. Mag. A, 73(2), 457-497). This system, it will be seen, nearly but not guile in equilibrium during the loading process, is metastable.