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.

活性粒子的定义特征是它们通过局部将化学能转化为定向运动来不断推进自己。这种主动的自推进会阻止它们与它们的热环境（例如水溶液）平衡，从而使它们永久失去平衡。然而，活性粒子的空间动力学可能具有某些平衡特征，特别是在稳态下。我们在这里重点关注个体空间轨迹的时间反转对称性，作为一种独特的平衡特征。我们研究了被捕获的活性粒子的稳态轨迹在多大程度上遵守或打破了这种时间反转对称性。