A universal scaling law for active diffusion in complex media

Using granular experiments and computer simulations, we investigate the long-time diffusion of active tracers in a broad class of complex media composed of frozen obstacles of diverse structures. By introducing a dimensionless persistence length $Q=v_d{\tau }_r\mathrm{/}{d}_t$, we propose a modified scaling relation that independently collapses experimental and simulation results across active and passive particles, diverse media, and distinct propulsion mechanisms. Our results reveal a universal active diffusion-structure relation that holds across both equilibrium and nonequilibrium regimes, providing a simple predictive framework for active diffusion in complex environments.