Microscopic derivation of the hydrodynamics of active-Brownian-particle   suspensions
  We derive the hydrodynamic equations of motion for a fluid of active particles described by under- damped Langevin equations that reduce to the Active-Brownian-Particle model, in the overdamped limit. The contraction into the hydrodynamic description is performed by locally averaging the par- ticle dynamics with the non-equilibrium many-particle probability density, whose formal expression is found in the physically relevant limit of high-friction through a multiple-time-scale analysis. This approach permits to identify the conditions under which self-propulsion can be subsumed into the fluid stress tensor and thus to define systematically and unambiguously the local pressure of the active fluid. 
Stefano Steffenoni and Gianmaria Falasco and Klaus Kroy
cond-mat.stat-mech cond-mat.soft