Polar active liquids: a universal classification rooted in   nonconservation of momentum
  We study the spatially homogeneous phases of polar active particles in the low density limit, and specifically the transition from the isotropic phase to collective polar motion. We show that the fundamental quantity of interest for the stability of the isotropic phase is the forward component of the momentum change induced by binary scattering events. Building on the Boltzmann formalism, we introduce an ansatz for the one-particle distribution and derive a closed-form evolution equation for the order parameter. This approach yields a very intuitive and physically meaningful criterion for the destabilization of the isotropic phase, where the ansatz is exact. The criterion also predicts whether the transition is continuous or discontinuous, as illustrated in three different classes of models. The theoretical predictions are in excellent agreement with numerical results. 
Khanh-Dang Nguyen Thu Lam, Michael Schindler and Olivier Dauchot
cond-mat.soft