Stochastic models of the interconversion of three or more chemical species

Abstract

The phenomenological rate equations for reactions in which three or more chemical species are simultaneously interconverting are derived from a microscopic stochastic model. Particular attention is focused on the establishment of long chemical relaxation times, and on an important orthogonality property which guarantees that the principle of detailed balancing is obeyed. By developing a quantum mechanical analog, the mathematical origins of both of the above properties are related to a resonance phenomenon associated with three or more wells separated by high energy barriers. The quantum analog is itself equivalent to a stochastic master equation, the rate constants of which are analytically determined. These are shown to contain the expected Arrhenius factors and to obey the principle of the independent coexistence of reactions. © 1974, American Institute of Physics. All rights reserved.