  We consider particle-based stochastic reaction-drift-diffusion models where
particles move via diffusion and drift induced by one- and two-body potential
interactions. The dynamics of the particles are formulated as measure-valued
stochastic processes (MVSPs), which describe the evolution of the singular,
stochastic concentration fields of each chemical species. The mean field large
population limit of such models is derived and proven, giving coarse-grained
deterministic partial integro-differential equations (PIDEs) for the limiting
deterministic concentration fields' dynamics. We generalize previous studies on
the mean field limit of models involving only diffusive motion, with care to
formulating the MVSP representation to ensure detailed balance of reversible
reactions in the presence of potentials. Our work illustrates the more general
set of PIDEs that arise in the mean field limit, demonstrating that the
limiting macroscopic reactive interaction terms for reversible reactions obtain
additional nonlinear concentration-dependent coefficients compared to the
purely diffusive case. Numerical studies are presented which illustrate that
two-body repulsive potential interactions can have a significant impact on the
reaction dynamics, and also demonstrate the empirical numerical convergence of
solutions to the PBSRDD model to the derived mean field PIDEs as the population
size increases.
