Stochastic properties of systems controlled by autocatalytic reactions I

TL;DR

This paper investigates the stochastic dynamics of autocatalytic reaction systems, introduces a point model for reaction kinetics, and reveals that classical mass action laws do not align with the stochastic behavior.

Contribution

It presents a novel stochastic model for autocatalytic reactions and demonstrates the inconsistency of traditional mass action kinetics with stochastic dynamics.

Findings

Derived differential equations for particle number probabilities

Found mass action law incompatible with stochastic model

Introduced the point model of reaction kinetics

Abstract

We analyzed the stochastic behavior of systems controlled by autocatalytic reaction A+X -> X+X. Assuming the distribution of reacting particles in the system volume to be uniform, we introduced the notion of the point model of reaction kinetics, and derived a system of differential equations for probabilities of finding n=0,1,... autocatalytic particles at a given time moment. It has been found that the kinetic law of the mass action cannot be supported by stochastic model.