Statistical mechanics of transport processes in active fluids

Active matter systems provide an opportunity to revisit the notions of statistical mechanics and condensed matter physics from a fresh nonequilibrium perspective. The concept of pressure has recently received particular emphasis. In order to explain the anomalous mechanical and transport characteristics in these systems, the balance equations of mass, momentum, and energy, and the associated microscopic expressions for the stress tensor and body forces need to be derived. We utilize the Irving-Kirkwood procedure to derive the balance laws governing the macroscopic behavior of rotating active dumbbells starting from their microscopic dynamics. In deriving the balance of linear momentum, we find that the symmetry of the stress tensor is broken due to the presence of non-zero active torques on individual particles. The broken symmetry of the stress tensor induces internal spin in the fluid. In deriving the form for the balance of total angular momentum, we find microscopic expressions for the couple stress tensor that drives the spin field. We also show how the expressions for the stress tensor and body forces change in the case of purely convective dumbbells with no internal torques and comment on the implications for understanding pressure in convective and rotary active systems.