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Studies in active matter systems and in the collective motility of organismsutilize a range of analytical approaches to formulate continuous kinetic modelsof collective dynamics from the rules or equations describing agentinteractions. However, the derivation of these models often relies onBoltzmann's hypothesis of "molecular chaos", often simply called statisticalindependence. While it is often the simplest way to derive tractable models itis not clear whether the statistical independence assumption is valid inpractice. In this work, we develop a Boltzmann-type kinetic model for thenematic alignment of self-propelled rods where rod reorientation occurs uponbinary collisions. We identify relevant parameters and derive kinetic equationsfor the corresponding asymptotic regime. By comparing numerical solutions ofthe kinetic equations to an agent-based model that implements our microscopicalignment rules, we examine the accuracy of the continuous model. The resultsindicate that our kinetic model fails to replicate the underlying dynamics dueto the formation of clusters that violate statistical independence.Additionally, we show that a mechanism limiting cluster formation helps toimprove the agreement between the analytical model and agent simulations. Theseresults highlight the need to improve modeling approaches for active mattersystems.

Breakdown of Boltzmann-type Models for Nematic Alignment of Self-propelled Rods