Can one identify non-equilibrium in a three-state system by analyzing two-state trajectories?

TL;DR

This paper investigates whether non-equilibrium states in a three-state Markov system can be distinguished from equilibrium states using only two-state trajectory data, revealing a large non-equilibrium region beyond oscillatory relaxation criteria.

Contribution

It provides a comprehensive phase diagram showing conditions under which non-equilibrium states can be identified from two-state data, expanding previous criteria.

Findings

Large non-equilibrium region identified

Two-state data can indicate non-equilibrium beyond oscillatory criteria

Method applicable to stationary three-state Markov systems

Abstract

For a three-state Markov system in a stationary state, we discuss whether, on the basis of data obtained from effective two-state (or on-off) trajectories, it is possible to discriminate between an equilibrium state and a non-equilibrium steady state. By calculating the full phase diagram we identify a large region where such data will be consistent only with non-equilibrium conditions. This regime is considerably larger than the region with oscillatory relaxation, which has previously been identified as a sufficient criterion for non-equilibrium.