Ordered motion of active colloids and effective temperature

Abstract

Using recent developments of non-equilibrium thermodynamics, we introduce an effective temperature for active colloidal systems, which is a product of two factors. The first one arises due to the motor activity and describes the randomized motion of the active particles, whereas the second one is a consequence of the ordered (collective) motion due to the alignment effects or initially ordered configuration. These factors depend on the corresponding characteristic velocities: the first one is expressed in terms of the propelled (swimming) velocity of an individual active particle, while the second one — in terms of the local drift velocity, which characterizes the collective motion of the active particles and plays a role analogous to that of an order parameter. The behavior of the active systems is governed by the interplay between these two factors, which leads to a hierarchy of anomalous diffusion regimes with different characteristic time scales and corresponding effective diffusion coefficients.