Reaction volume statistics for rate processes in disordered systems. Thermodynamic analogies and extracting information from experimental data

The chemical fluctuations in a disordered system are described in terms of a random point process of the Ramakhrisnan type. A direct path summation te chnique is used for computing the grand canonical Janossy densities, the pr oduct densities as well as the multiple correlation functions of the proces s. In the limit of large systems the probability of fluctuations is describ ed by a stochastic potential Phi with a structure similar to that of the Gi bbs free energy in equilibrium thermodynamics. The potential Phi has a mini mum value for the most probable value of the survival function of the react ing particles, which is the same as the nonequilibrium average of the survi val function. A method for evaluating the stochastic properties of the reac tion volume is suggested by comparing the most probable theoretical surviva l function with the observed survival functions reported in the literature. General scaling relations are derived between the cumulants of the reactio n volume and the experimental values of the time-dependent effective rate c oefficients. The theory is applied to the case of stretched exponential kin etics. The fluctuations of the reaction volume are investigated in the limi ts of small and large times: in both limits the fluctuations of the reactio n volume are intermittent and display statistical fractal features (C) 1999 Published by Elsevier Science B.V. All rights reserved.