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

The chemical fluctuations in a disordered system are described in terms of a random point process of the Ramakhrisnan type. A direct path summation technique is used for computing the grand canonical Janossy densities, the product densities as well as the multiple correlation functions of the process. In the limit of large systems the probability of fluctuations is described by a stochastic potential Φ with a structure similar to that of the Gibbs free energy in equilibrium thermodynamics. The potential Φ has a minimum value for the most probable value of the survival function of the reacting particles, which is the same as the nonequilibrium average of the survival function. A method for evaluating the stochastic properties of the reaction volume is suggested by comparing the most probable theoretical survival function with the observed survival functions reported in the literature. General scaling relations are derived between the cumulants of the reaction volume and the experimental values of the time-dependent effective rate coefficients. The theory is applied to the case of stretched exponential kinetics. The fluctuations of the reaction volume are investigated in the limits of small and large times: in both limits the fluctuations of the reaction volume are intermittent and display statistical fractal features