Magnus expansions and pseudospectra of Master Equations

TL;DR

This paper explores advanced mathematical techniques like Magnus expansions and pseudospectra to analyze master equations, highlighting their advantages over standard numerical methods through examples in chemical kinetics and exclusion processes.

Contribution

It introduces the application of Magnus expansions and pseudospectra to master equations, demonstrating improved eigenvalue computation accuracy.

Findings

Exact eigenvalues are obtained for specific master equations.

Standard numerical methods can produce large errors.

Applications include chemical kinetics and exclusion processes.

Abstract

New directions in research on master equations are showcased by example. Magnus expansions, time-varying rates, and pseudospectra are highlighted. Exact eigenvalues are found and contrasted with the large errors produced by standard numerical methods in some cases. Isomerisation provides a running example and an illustrative application to chemical kinetics. We also give a brief example of the totally asymmetric exclusion process.