Statistical Mechanics of Active Ornstein Uhlenbeck Particles

TL;DR

This paper reviews and extends the statistical understanding of Active Ornstein Uhlenbeck particles, highlighting their equilibrium-like regimes, collective behaviors like phase separation, and the dynamics of their collective modes.

Contribution

It provides a comprehensive analysis of AOUPs, including steady-state derivations, effective equilibrium regimes, and collective phenomena, with new insights into their fluctuation-dissipation relations and phase behavior.

Findings

Existence of an effective equilibrium regime obeying detailed balance.

AOUPs exhibit motility-induced phase separation.

Characterization of collective modes and their dynamics.

Abstract

We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffice to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We first detail the perturbative derivation of the steady state of AOUPs in the small persistence time limit. We show the existence of an effective equilibrium regime in which detailed-balance is obeyed with respect to a non-Boltzmann distribution and detail the corresponding fluctuation-dissipation theorem. We then characterize the departure from equilibrium by computing several relevant observables (entropy production, ratchet current). At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. The latter can be accounted for by considering the steady-state of AOUPs with spatially varying propulsion speed or persistence time. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes, which we construct explicitly.