  In this paper, we generalize the results of Evans and Tabrizian, by deriving
asymptotics for the time-rescaled Kramers-Smoluchowski equations, in the case
of a general non-symmetric potential function with multiple wells. The
asymptotic limit is described by a system of reaction-diffusion equations whose
coefficients are determined by the Kramers constants at the saddle points of
the potential function and the Hessians of the potential function at global
minima.
