Large deviations of reaction fluxes

TL;DR

This paper establishes a large deviation principle for reaction fluxes in a particle system with reactions, providing insights into the probabilities of rare reaction events under general conditions including mass-action kinetics.

Contribution

It introduces a dynamic large deviation principle for reaction fluxes, extending the understanding of rare events in interacting particle systems with reactions.

Findings

Proves a large deviation principle for reaction fluxes.

Derives large deviations for empirical concentration.

Applicable under general assumptions including mass-action kinetics.

Abstract

We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction fluxes under general assumptions that include mass-action kinetics. This result immediately implies the dynamic large deviations for the empirical concentration.