'Steady/equilibrium approximation' in relaxation and fluctuation. I. Procedure to simplify first-order reaction

A general procedure to simplify a complex first-order reaction by two approximations, the principle of fast equilibration and the steady-state approximation, is presented. Rate constants are classified into two groups: those of the order of unity and those of the order of epsilon (much less than 1) or less, and are represented in the schemes by thick and thin arrows, respectively. The fast and the slow components are defined: from the fast component at least one thick arrow originates and from the slow component no thick arrow originates. Fast components are divided into several groups. In a group, the fast components are connected by thick arrows in both directions in each reaction step. When at least one thick arrow originates from the components in a group G and terminates on a component not belonging to group G (group G is open), then the steady-state approximation or principle of fast equilibration holds on each component in group G after an induction period To. When no thick arrow originating from group G is directed to components not belonging to group G (group G is closed), the principle of fast equilibration holds on the fast components in group G after To. The induction period To is less than the order of 1/epsilon.