Cycle representatives for the coarse-graining of systems driven into a non-equilibrium steady state

TL;DR

This paper introduces a novel method for coarse-graining non-equilibrium systems by extending Markov state models to include cycle representatives, preserving entropy production in simplified models.

Contribution

It presents a new cycle-based coarse-graining approach for driven systems that maintains key thermodynamic properties, extending existing Markov modeling techniques.

Findings

Successfully applied to a driven particle system

Preserves entropy production in coarse-grained models

Reduces complexity while maintaining key dynamics

Abstract

A major current challenge poses the systematic construction of coarse-grained models that are dynamically consistent, and, moreover, might be used for systems driven out of thermal equilibrium. Here we present a novel prescription that extends the Markov state modelling approach to driven systems. The first step is to construct a complex network of microstates from detailed atomistic simulations with transition rates that break detailed balance. The coarse-graining is then carried out in the cycle space of this network. To this end we introduce the concept of representatives, which stand for many cycles with similar properties. We show how to find these cycle communities using well-developed standard algorithms. Removing all cycles except for the representatives defines the coarse-grained model, which is mapped back onto a network with far fewer states and renormalized transition rates that, however, preserve the entropy production of the original network. Our approach is illustrated and validated for a single driven particle.