Entropy production and coarse-graining in Markov processes

TL;DR

This paper investigates how coarse-graining in Markov processes affects entropy production, showing it remains largely unchanged unless key probability current loops are removed, with applications to biomolecular motors.

Contribution

It provides evidence that entropy production is robust under coarse-graining unless essential loops are eliminated, and proposes a general theory based on network analysis.

Findings

Entropy production is unaffected by decimating fast states unless loops with net current are removed.

Application to kinesin motor network demonstrates practical relevance.

Proposes a theoretical framework based on Schnakenberg's network theory.

Abstract

We study the large time fluctuations of entropy production in Markov processes. In particular, we consider the effect of a coarse-graining procedure which decimates {\em fast states} with respect to a given time threshold. Our results provide strong evidence that entropy production is not directly affected by this decimation, provided that it does not entirely remove loops carrying a net probability current. After the study of some examples of random walks on simple graphs, we apply our analysis to a network model for the kinesin cycle, which is an important biomolecular motor. A tentative general theory of these facts, based on Schnakenberg's network theory, is proposed.