Statistical mechanics of active Ornstein-Uhlenbeck particles

We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest models, Gaussian white noise overdamped Brownian colloids is replaced by a colored noise. This suffice to grant system hallmark active matter, while still allowing for analytical progress. first detail perturbative derivation steady state AOUPs in small persistence time limit. show existence an effective equilibrium regime which detailed-balance obeyed with respect non-Boltzmann distribution corresponding fluctuation-dissipation theorem. then characterize departure from computing several relevant observables (entropy production, ratchet current). At collective level, we experience motility-induced phase separation both presence pairwise forces or due quorum-sensing interactions. The latter can be accounted considering steady-state spatially varying propulsion speed time. Finally, discuss how emerging characterized dynamics their modes, construct explicitly.