Chemical kinetics and stochastic differential equations

TL;DR

This paper introduces a stochastic formalism for chemical kinetics that aligns with the Chemical Master Equation and Gillespie algorithm, offering practical benefits and connecting to quantum transitions.

Contribution

It presents a new stochastic framework for chemical reactions involving finite molecules, bridging classical and quantum descriptions.

Findings

Formalism consistent with Chemical Master Equation

Addresses practical advantages of stochastic modeling

Connects chemical kinetics with quantum transitions

Abstract

We propose a general stochastic formalism for describing the evolution of chemical reactions involving a finite number of molecules. This approach is consistent with the statistical analysis based on the Chemical Master Equation, and provides the formal setting for the existing algorithmic approaches (Gillespie algorithm). Some practical advantages of this formulation are addressed, and several examples are discussed pointing out the connection with quantum transitions (radiative interactions).