Studies in fluctuation analysis: I. On relations between rate constants and relaxation times in chemical systems and the multivariate power spectrum of noise and fluctuations

Abstract

An investigation of the stochastic fluctuations that occur in chemically reactive solutions is presented in terms of irreversible chemical thermodynamics. The approach considers in some detail the properties of the fluctuations in the frequency domain (e.g., the power spectrum) and it is found that (1) the kinetic rate constants of the reaction process can be obtained directly from the inverse of the normalized power spectrum extrapolated to the zero frequency point, (2) the Onsager flow coefficients are derived from the second moments and the inverse of the power spectrum at the zero frequency extrapolation, and (3) the eigenvalues of the normalized spectrum are the chemical relaxation times. It is suggested that the approach outlined in this article may prove useful in studies of chemical kinetics without the necessity of resorting to macroscopic relaxation methods.