  Interacting-Particle Reaction Dynamics (iPRD) simulates the spatiotemporal
evolution of particles that experience interaction forces and can react with
one another. The combination of interaction forces and reactions enable a wide
range of complex reactive systems in biology and chemistry, but give rise to
new questions such as how to evolve the dynamical equations in a
computationally efficient and statistically correct manner. Here we consider
reversible reactions such as A + B <--> C with interacting particles and derive
expressions for the microscopic iPRD simulation parameters such that desired
values for the equilibrium constant and the dissociation rate are obtained in
the dilute limit. We then introduce a Monte-Carlo algorithm that ensures
detailed balance in the iPRD time-evolution (iPRD-DB). iPRD-DB guarantees the
correct thermodynamics at all concentrations and maintains the desired kinetics
in the dilute limit, where chemical rates are well-defined and kinetic
measurement experiments usually operate. We show that in dense particle
systems, the incorporation of detailed balance is essential to obtain
physically realistic solutions. iPRD-DB is implemented in ReaDDy 2
(https://readdy.github.io).
