Irreversibility in active matter: General framework for active Ornstein-Uhlenbeck particles

TL;DR

This paper develops a general framework to quantify irreversibility in active matter systems modeled by active Ornstein-Uhlenbeck particles, linking trajectory irreversibility to measurable quantities and extending previous results.

Contribution

It provides a new, explicit expression for the irreversibility of AOUP trajectories, accommodating arbitrary initial conditions and active driving states.

Findings

Derived a general formula for trajectory irreversibility in AOUPs.

Extended previous results to include arbitrary initial distributions.

Linked irreversibility measures to observable particle trajectories.

Abstract

Active matter systems are driven out of equilibrium by conversion of energy into directed motion locally on the level of the individual constituents. In the spirit of a minimal description, active matter is often modeled by so-called active Ornstein-Uhlenbeck particles (AOUPs), an extension of passive Brownian motion where activity is represented by an additional fluctuating non-equilibrium "force" with simple statistical properties (Ornstein-Uhlenbeck process). While in passive Brownian motion, entropy production along trajectories is well-known to relate to irreversibility in terms of the log-ratio of probabilities to observe a certain particle trajectory forward in time in comparison to observing its time-reversed twin trajectory, the connection between these concepts for active matter is less clear. It is therefore of central importance to provide explicit expressions for the irreversibility of active particle trajectories based on measurable quantities alone, such as the particle positions. In this technical note, we derive a general expression for the irreversibility of AOUPs in terms of path probability ratios (forward versus backward path), extending recent results from [PRX 9, 021009 (2019)] by allowing for arbitrary initial particle distributions and states of the active driving.