A universal scaling law for active diffusion in complex media

Understanding how active particles transport in structurally heterogeneous environments is a fundamental and challenging problem, with relevance to biological and synthetic microswimmers in tissues and porous media. Here, using granular experiments and computer simulations, we investigate the long-time diffusion of active tracers in quasi-two-dimensional heterogeneous media. We show that diffusion-structure relations established for passive systems fail to describe active transport across different activity levels. To resolve this, we formulate a modified diffusion-structure relation by incorporating the dimensionless persistence length Q = v_dτ_r/d_t, which captures the activity-induced extension of the effective interaction range. The proposed relation yields a consistent collapse within both experimental and simulation datasets across active and passive tracers, diverse environmental structures, and propulsion mechanisms. Our results thus provide a universal predictive framework for transport in non-equilibrium heterogeneous systems.