Maxwell-Boltzmann velocity distribution for noninteracting active matter.

Abstract

We theoretically and computationally find a Maxwell-Boltzmann-like velocity distribution for noninteracting active matter (NAM). To achieve this, mass and moment of inertia are incorporated into the corresponding noninteracting active Fokker-Planck equation (NAFP), thus solving for the first time, the underdamped scenario of NAM following a Fokker-Planck formalism. This time, the distribution results in a bimodal symmetric expression that contains the effect of inertia on transport properties of NAM. The analytical distribution is further compared to experiments dealing with vibrobots. A generalization of the Brinkman hierarchy for NAFP is also provided and used for systematically solving the NAFP in position space. This work is an important step toward characterizing active matter using an equivalent nonequilibrium statistical mechanics.