Differently from passive Brownian particles, active particles, also known as self-propelled
Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy …

Active matter encompasses systems whose individual constituents dissipate energy to exert
propelling forces on their environment. These systems exhibit dynamical phenomena with …

We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this
simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced …

Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-
Einstein relation between injection and dissipation of energy at the microscopic scale. We …

Active colloids are microscopic particles, which self-propel through viscous fluids by
converting energy extracted from their environment into directed motion. We first explain …

We consider a Brownian particle which, in addition to being in contact with a thermal bath, is
driven by fluctuating forces which stem from active processes in the system, such as self …

For a large class of nonequilibrium systems, thermodynamic notions like work, heat, and, in
particular, entropy production can be identified on the level of fluctuating dynamical …

Active-matter systems operate far from equilibrium because of the continuous energy
injection at the scale of constituent particles. At larger scales, described by coarse-grained …

Motility-induced phase separation leads to cohesive active matter in the absence of
cohesive forces. We present, extend and illustrate a recent generalized thermodynamic …

We review the general aspects of the concept of temperature in equilibrium and non-
equilibrium statistical mechanics. Although temperature is an old and well-established …