Response theory for random channel kinetics in complex systems. Application to lifetime distributions of active intermediates

We present a response theory for random channel kinetics, based on the method of characteristic functionals. We assume that the fluctuations of the rate coefficients are generated by the contributions of a large number of reaction channels, and can be described in terms of a set of grand canonical probability density functionals. We consider linear as well as nonlinear responses for systems with static or dynamic disorder. For all cases considered we derive analytical expressions for the ensemble average of the response of the system to an external perturbation. The theory is applied for developing a new approach to the analysis of the kinetics in complex chemical systems, based on a random channel approach. We assume that the total transition rate from one state of the system to another is made up of the contributions of a large number of random reaction pathways, which can be described in terms of a stochastic point process. We study the response of such a system to an external perturbation and show that it can be expressed in terms of a set of lifetime distributions of reaction intermediates. We examine the possibilities of applying the technique to the study of large chemical systems by means of tracer experiments and suggest methods for computing rate distributions from measured lifetime distributions. We generalize the method of spectral kinetic analysis for the interpretation of measured lifetime distributions. We investigate the relationships between spectral kinetics analysis and random channel statistics.