Generalized Diffusion Theory of Nonequilibrium Reaction Rates

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Abstract
A simple expansion procedure is used in conjunction with the detailed balancing condition to show that the linear master equation describing the relaxation of an atomic system in a background of inert atoms can be approximated by an equivalent diffusion equation with appropriate boundary conditions. This equation has the form of the ordinary heat‐conduction equation for a medium of variable heat capacity and thermal conductivity and is simplier than the commonly used Fokker—Planck equation. It is expected to be a reasonable approximation under conditions where the changes in the constants of the motion are small in a single collision. A similar equation has been derived by Van Kampen who showed that it implies the phenomenological equations of nonequilibrium thermodynamics. However, he did not consider the boundary condiditions necessary to deal with chemical reactions or phase changes.