Two-dimensional noninteractive active Fokker-Planck equation*

We solve the noninteractive active Fokker-Planck equation (NAFP) in two dimensions by introducing a perturbation parameter containing the inertia of the system. From this NAFP and in velocity space, we obtain a 'Maxwell-Boltzmann' velocity distribution in the stationary state. The shape of this velocity distribution is the result of a bimodal distribution rotated about its symmetry axis. This distribution is used to calculate the system's mean-square speed and the results are validated by means of Langevin dynamics simulations.