Structure and memory control self-diffusion in active matter.

Despite extensive progress in characterizing the emergent behavior of active matter, the microscopic origins of self-diffusion in interacting active systems remain poorly understood. Here, we develop a framework that quantitatively links self-diffusion to collisional forces and their temporal correlations in active fluids. We show that transport is governed by two contributions: an equal-time suppression of motion arising from anisotropic collisional forces, and a memory correction associated with the temporal persistence of these forces. Together, these effects yield an exact expression for the self-diffusivity in terms of measurable force statistics and correlation times. We apply this framework to purely repulsive active Brownian particles and find that self-diffusion is always reduced as a function of packing fraction and activity. We identify the regimes in which equal-time force fluctuations and collisional memory dominate and how their relative contributions vary with activity and packing fraction. Our results establish a direct connection between microscopic force correlations and macroscopic transport, providing a general mechanical perspective for interpreting self-diffusion in active matter.