On the macroscopic equivalence of descriptions of fluctuations for chemical reactions

Abstract

Three descriptions of spontaneous fluctuations in macroscopic systems have been proposed: One uses generalized Fokker–Planck equations and treats fluctuations as a stochastic diffusion process; another uses a connection between fluctuations and dissipation and generalizes the Langevin method; the third is the master equation theory which treats fluctuations as arising from a birth and death process. For a variety of systems it is known that the master equation theory is identical to the fluctuation–dissipation theory in the macroscopic limit. For chemical reactions it is shown here that the appropriate diffusion process also becomes identical with the fluctuation–dissipation theory in the macroscopic limit.