Master equation for site distributions describing barrier crossing in the presence of anisotropic diffusion

When the barrier crossing is coupled to a nonreactive coordinate which equilibrates very slowly, it may not be possible to describe the long-time behaviour of a system only in terms of the interconversion rates. The usual kinetic equations, i.e. the master equation for site populations, must be generalized to account for the time evolution of the nonreactive variable. A suitable formalism is represented by the master equation for site distributions (MESD). Starting from the two-dimensional diffusion equation with anisotropic diffusion matrix, the MESD is derived by means of a projection procedure which generates site distributions in the nonreactive coordinate. The numerical solution of the MESD for a bistable symmetric potential shows that different motional regimes are recovered by varying the geometry of the diffusion matrix and the magnitude of its anisotropy.