Mobility, response and transport in non-equilibrium coarse-grained models

TL;DR

This paper compares two non-Markovian coarse-grained models derived from a non-equilibrium microscopic system, revealing their differing behaviors and implications for work extraction and modeling of non-equilibrium dynamics.

Contribution

It introduces and compares two different coarse-grained models for non-equilibrium systems, highlighting their distinct properties and suitability for work extraction.

Findings

Analytic model has a well-defined friction kernel and allows work extraction.

Projection model behaves as an effective equilibrium model, unsuitable for work extraction.

Study applies models to time-delay feedback control and active Ornstein-Uhlenbeck processes.

Abstract

We investigate two different types of non-Markovian coarse-grained models extracted from a linear, non-equilibrium microscopic system, featuring a tagged particle coupled to underdamped oscillators. The first model is obtained by analytically ``integrating out'' the oscillators and the second is derived using projection operator techniques. We observe that these two models behave very differently when the tagged particle is exposed to external harmonic potentials or pulling forces. Most importantly, we find that the analytic model has a well defined friction kernel and can be used to extract work, consistent with the microscopic system, while the projection model corresponds to an effective equilibrium model, which cannot be used to extract work. We apply the analysis to two popular non-equilibrium systems, time-delay feedback control and the active Ornstein-Uhlenbeck process. Finally, we highlight that our study could have important consequences for dynamic coarse-graining of non-equilibrium systems going far beyond the linear systems investigated in this manuscript.