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Averaged Trajectory of Random Walk Fluctuations Having a Fixed Lifetime and its Application in Characterization of Simplest Chemical Equilibrium

Abstract Recently, we found that for a simple first-order reaction having equilibrium constant equal to 1, the amplitudes of equilibrium fluctuations can be, on the discrete time scale (scale of reaction events), satisfactorily described using the random walk approximation for the distribution and mean amplitude of fluctuation having the fixed lifetime 2r reaction events. Below, we propose another characterization of fluctuations in the random walk introducing an averaged trajectory of fluctuations and suggest another formula for the mean amplitude of fluctuations having a fixed length. The results are used in characterization of equilibrium fluctuations of first order reversible chemical reaction having the equilibrium constant equal to 1.