Stochastic analysis of reactive processes in interacting particle systems

Most of the literature on deterministic and stochastic models of reacting mixtures focuses on point-like particles reacting in the absence of any interaction energy between them. However, many realizations in biological and soft-matter systems, naturally deviate from such an idealized picture by involving strongly interacting species. In such systems new collective phenomena can emerge as exemplified by the occurrence of chemically-driven phase separation. Therefore, we investigate the effects of particle interactions by means of a general formalism based on the chemical master equation. By using a local detailed balance condition, transition rates are generalized in order to account for interaction energies between the reacting species in a thermodynamically consistent way. As a first step, such interactions are assumed to be of mean-field type and spatial degrees of freedom are neglected. The formalism is then applied to the Schlögl model, a generic model for far-from-equilibrium bistability. Statistical averages, such as the mean and variance of the number of particles, can be analyzed both analytically and numerically through a singular perturbation analysis and the Gillespie's simulation algorithm, respectively. In particular, we address the effects of mean-field interactions on the resulting stochastic dynamics, both away from and in the non-equilibrium steady state.