How irreversible are steady-state trajectories of a trapped active particle?

TL;DR

This paper investigates whether the steady-state trajectories of trapped active particles exhibit time-reversal symmetry, finding that harmonic potentials preserve this symmetry while anharmonic ones generally break it.

Contribution

It reveals that steady-state trajectories of active particles in harmonic traps are time-reversal symmetric, contrasting with anharmonic traps where symmetry is typically broken.

Findings

Harmonic potential trajectories obey time-reversal symmetry.

Anharmonic potential trajectories generally break this symmetry.

The study uses active Ornstein-Uhlenbeck particles as a framework.

Abstract

The defining feature of active particles is that they constantly propel themselves by locally converting chemical energy into directed motion. This active self-propulsion prevents them from equilibrating with their thermal environment (e.g., an aqueous solution), thus keeping them permanently out of equilibrium. Nevertheless, the spatial dynamics of active particles might share certain equilibrium features, in particular in the steady state. We here focus on the time-reversal symmetry of individual spatial trajectories as a distinct equilibrium characteristic. We investigate to what extent the steady-state trajectories of a trapped active particle obey or break this time-reversal symmetry. Within the framework of active Ornstein-Uhlenbeck particles we find that the steady-state trajectories in a harmonic potential fulfill path-wise time-reversal symmetry exactly, while this symmetry is typically broken in anharmonic potentials.