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.
Highlights
Passive Brownian motion in a confining potential, the steady state is in thermal equilibrium with the surrounding heat bath
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 timereversal symmetry exactly, while this symmetry is typically broken in anharmonic potentials
Summary
Passive Brownian motion in a confining potential, the steady state is in thermal equilibrium with the surrounding heat bath. For active Brownian motion [4,5,6,7,8], on the other hand, the active self-propulsion drive creates a perpetual non-equilibrium situation which persists even in the steady state in a confining potential. The active particles are maintained out of equilibrium by the microscopic processes generating the active self-propulsion The details behind these processes are, mostly irrelevant for the dynamical and collective behavior emerging on the scales of the size of the active particles. Η(t) is a Gaussian process with η(t) = 0 and η(t)η(t ) = 1 e−|t−t |/τa This model of the active fluctuations is not directly related to the operational details of the self-propulsion drive.
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