Switching rates of multi-step reactions

TL;DR

This paper analyzes the switching rates in complex multi-step reaction schemes using WKB approximation, providing detailed calculations of both exponential and pre-exponential factors, with illustrative examples.

Contribution

It introduces a method to evaluate switching rates in arbitrary multi-step reactions using WKB approximation, including both exponent and pre-exponential factors.

Findings

Derived explicit formulas for switching rates in multi-step reactions.

Validated the approach with multiple illustrative examples.

Provided insights into the dependence of rates on system parameters.

Abstract

We consider a switching rate of a meta-stable reaction scheme, which includes reactions with arbitrary steps, e.g. $kA\to(k+r)A$. Employing WKB approximation, controlled by a large system size, we evaluate both the exponent and the pre-exponential factor for the rate. The results are illustrated on a number of examples.