Accurate dynamics from self-consistent memory in stochastic chemical reactions with small copy numbers

We present a method that captures the fluctuations beyond mean field in chemical reactions in the regime of small copy numbers and hence large fluctuations, using self-consistently determined memory: by integrating information from the past we can systematically improve our approximation for the dynamics of chemical reactions. This memory emerges from a perturbative treatment of the effective action of the Doi-Peliti field theory for chemical reactions. By dressing only the response functions and by the self-consistent replacement of bare responses by the dressed ones, we show how a very small class of diagrams contributes to this expansion, with clear physical interpretations. From these diagrams, a large sub-class can be further resummed to infinite order, resulting in a method that is stable even for large values of the expansion parameter or equivalently large reaction rates. We demonstrate this method and its accuracy on single and multi-species binary reactions across a range of reaction constant values.