From Meso- to Microscopic Stochastic Modeling in Physico-Chemical Processes – the Paradigm of Chemical Reacting Systems

The stochastic modelling of chemical physical processes is essentially based on a coarse-grained formulation of fluctuations, usually described by means of Wiener processes. By taking the paradigmatic example of chemical reaction kinetics, we propose a simple representation of microscopic stochastic dynamics grounded on the use of distributional derivatives of counting processes that account for elementary reactive events. This approach is consistent with the statistical analysis based on the Chemical Master Equation, and provides the formal setting for the existing algorithmic approaches (Gillespie algorithm). Some practical advantages of this formulation are addressed, and several other examples are discussed in connection with cluster formation, velocity fluctuations in liquid systems, and quantum transitions (radiative interactions) at the molecular level.