General Reaction-Diffusion Processes With Separable Equations for Correlation Functions

TL;DR

This paper derives conditions under which multi-species reaction-diffusion models have closed-form equations for correlation functions, applicable in any dimension and lattice type, with examples relevant to social and epidemiological processes.

Contribution

It establishes a set of rate constraints ensuring closed equations for correlation functions in general reaction-diffusion models, including time-dependent two-point functions.

Findings

Derived rate constraints for closed correlation equations

Applicable to any dimension and lattice type

Introduced models relevant to voting and epidemic spreading

Abstract

We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on any type of lattice. We also show that under these conditions the evolution equations for two point functions at different times are also closed. As an example we introduce a class of two species models which may be useful for the description of voting processes or the spreading of epidemics.