Studies in fluctuation analysis. II. Injected white noise as a solution to the phase problem of relaxation spectrometry

摘要

As a continuation of the first paper in this series, we extend the analysis of the theory for obtaining kinetic rate constants, relaxation times, and Onsager flow coefficients to a macroscopic rsquo;rsquo;fluctuationrsquo;rsquo; level. The concept is based on the injection of a stochastic Markoffian (Gaussian) white noise as a thermodynamic perturbation in lieu of the classical relaxation approaches involving deterministic signals. As found with the case of microscopic statistics studied in the previous paper, we find that certain relations hold between the rate coefficients and the power spectral matrix, these being as follows: (1) the matrix of rate coefficients is four times the inverse of the rsquo;rsquo;normalizedrsquo;rsquo; power spectrum of the measured reactant fluctuations in reduced (exactly determined) form at the zero frequency extrapolation; (2) the eigenvalues of the normalized spectral matrix at the zero frequency point are the relaxation times; (3) the coefficients of the Onsager rsquo;rsquo;flowrsquo;rsquo; or rsquo;rsquo;conductancersquo;rsquo; matrixLare readily obtained from the spectral matrix inverse, the externally induced second moments, and the calculated intrinsic statistical mechanical second moments. The implications at the experimental level, notably with regard to this approach being a suitable solution to the rsquo;rsquo;phase problemrsquo;rsquo; of relaxation spectrometry, are discussed.