Coarse graining of master equations with fast and slow states

TL;DR

This paper introduces a general method for simplifying master equations by removing fast-evolving states, involving rate renormalization, with applications demonstrated in diffusion and enzymatic reaction models.

Contribution

The paper presents a novel coarse-graining technique for master equations that systematically eliminates rapid states and renormalizes remaining rates, applicable to complex systems.

Findings

Method effectively simplifies master equations with fast states

Analytical decimation aligns with existing approaches in specific cases

Applicable to diffusion with defects and enzymatic reactions

Abstract

We propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the surviving states. In some cases, this decimation procedure can be analytically carried out and is consistent with other analytical approaches, like in the problem of the random walk in a double-well potential. We discuss the application of our method to nontrivial examples: diffusion in a lattice with defects and a model of an enzymatic reaction outside the steady state regime.