Quantum Techniques for Studying Equilibrium in Reaction Networks

TL;DR

This paper presents a quantum-inspired proof of a theorem linking equilibrium states in stochastic and deterministic chemical reaction networks, using second quantization tools from quantum mechanics.

Contribution

It introduces a novel proof of the complex balance theorem in reaction networks utilizing quantum mechanics techniques like Fock space and coherent states.

Findings

Proof of the complex balance theorem using quantum mechanics tools

Establishment of a connection between stochastic and deterministic models

Application of stochastic mechanics to reaction network analysis

Abstract

Anderson, Craciun, and Kurtz have proved that a stochastically modelled chemical reaction system with mass-action kinetics admits a stationary distribution when the deterministic model of the same system with mass-action kinetics admits an equilibrium solution obeying a certain "complex balance" condition. Here we present a proof of their theorem using tools from the theory of second quantization: Fock space, annihilation and creation operators, and coherent states. This is an example of "stochastic mechanics", where we take techniques from quantum mechanics and replace amplitudes by probabilities.