Microscopic field theory for active Brownian particles with translational and rotational inertia

While active matter physics has traditionally focused on particles with overdamped dynamics, recent years have seen an increase of experimental and theoretical work on active systems with inertia. This also leads to an increased need for theoretical models that describe inertial active dynamics. Here, we present a microscopic derivation for a general continuum model describing the nonequilibrium thermodynamics of inertial active matter that generalizes several previously existing works. It applies to particles with translational and rotational inertia and contains particle density, velocity, angular velocity, temperature, polarization, velocity polarization, and angular velocity polarization as dynamical variables. We moreover discuss to which extend commonly used approximations (factorization and local equilibrium) used in the derivation of hydrodynamic models are applicable to inertial active matter.