Magnus expansions and pseudospectra of Master Equations
It provides new analytical tools for researchers studying master equations in chemical kinetics and stochastic processes, but the results are illustrative rather than broadly impactful.
This paper demonstrates new approaches for analyzing master equations using Magnus expansions and pseudospectra, revealing large errors in standard numerical methods for eigenvalue computation, with applications to isomerization and the totally asymmetric exclusion process.
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.