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We study a stochastic system of $N$ interacting particles which modelsbimolecular chemical reaction-diffusion. In this model, each particle $i$carries two attributes: the spatial location $X_t^i\in \mathbb{T}^d$, and thetype $\Xi_t^i\in \{1,\cdots,n\}$. While $X_t^i$ is a standard (independent)diffusion process, the evolution of the type $\Xi_t^i$ is described by pairwiseinteractions between different particles under a series of chemical reactionsdescribed by a chemical reaction network. We prove that in the large particlelimit the stochastic dynamics converges to a mean field limit which isdescribed by a nonlocal reaction-diffusion partial differential equation. Inparticular, we obtain a quantitative propagation of chaos result for theinteracting particle system. Our proof is based on the relative entropy methodused recently by Jabin and Wang \cite{JW18}. The key ingredient of the relativeentropy method is a large deviation estimate for a special partition function,which was proved previously by technical combinatorial estimates. We give asimple probabilistic proof based on a novel martingale argument.

Quantitative Propagation of Chaos in the bimolecular chemical reaction-diffusion model