Active Boltzmann equation for self-propelled particles with non-reciprocal interactions

We study models of self-propelled particles with alignment interactions by means of an active Boltzmann equation. To this end, we evaluate the collision integral directly based on the microscopic equations of motion. This kinetic theory is founded on the assumption of one-sided molecular chaos, a refinement to the molecular chaos assumption underlying commonly employed mean-field approaches. We have introduced the methods for Vicsek-type active particles with anti-alignment that allows for an asymptotically exact analytical solution. One direct application is the extraction of the self-diffusion coefficient which cannot be done to mean-field order. This exact solution has then been used to study the behaviour of binary mixtures with non-reciprocal and chiral interactions. In addition to analytical approaches, the methodology allows for numerical calculation of the collision integral in systems that cannot be treated analytically which we use to evaluate the beyond mean-field corrections to the flocking transition under noise.