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We present a method that captures the fluctuations beyond mean field inchemical reactions in the regime of small copy numbers and hence largefluctuations, using self-consistently determined memory: by integratinginformation from the past we can systematically improve our approximation forthe dynamics of chemical reactions. This memory emerges from a perturbativetreatment of the effective action of the Doi-Peliti field theory for chemicalreactions. By dressing only the response functions and by the self-consistentreplacement of bare responses by the dressed ones, we show how a very smallclass of diagrams contributes to this expansion, with clear physicalinterpretations. From these diagrams, a large sub-class can be further resummedto infinite order, resulting in a method that is stable even for large valuesof the expansion parameter or equivalently large reaction rates. We demonstratethis method and its accuracy on single and multi-species binary reactionsacross a range of reaction constant values.

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