Product molecule numbers and reaction rate fluctuations in elementary reactions

In many chemical reactions, reaction rate fluctuations are inevitable. Whenever chemical reactions occur, reaction rates vary due to their dependence on the number of reaction events or products. Accordingly, understanding the impact of rate fluctuations on the product number counting statistics is of the utmost importance when developing a quantitative explanation of chemical reactions. In this work, we examine the relationship between the reaction rate and product number fluctuations. Product number counting statistics uncover stochastic properties of the product number; the latter directly manipulates the reaction rate. Specifically, we find that the product number displays super-Poisson characteristics as the reaction rate increases with the product number. On the other hand, when the product number shows sub-Poisson behavior, a decrease in the reaction rate follows. Furthermore, our analysis, dealing with reaction rate fluctuations, allows for quantifying the deviations of an elementary reaction process from a renewal process.