Anticipatory Active Matter Framework Maps Pedestrian Paths to Transverse-Fluctuating Polymer Chains

The framework replaces purely reactive interactions with explicit anticipation horizons, allowing agents to select trajectories that minimize expected costs constructed from observations. By embedding the dynamics in an extra dimension, transverse noise encodes uncertainty beyond the horizon, recovering mean-field behavior at long range. This directly reproduces experimental crossing flows and train-alighting data where standard social-force or velocity-obstacle models produce persistent jams.

The polymer-physics analogy supplies analytic tools for chain statistics that predict the onset of collective lane formation and bottleneck resolution without ad-hoc rules. Minimal cost expressions already outperform state-of-the-art agent-based simulators on cluttered environments, revealing that operational and tactical decisions emerge from the same anticipation kernel.

The approach highlights a missing ingredient in current collective-motion theories: agents do not merely react to instantaneous positions but pre-empt future configurations. Extending the model to heterogeneous anticipation horizons or coupling it with real-time tracking data would test whether the transverse-fluctuation statistics remain robust under empirical noise levels.

Validation against larger-scale datasets and incorporation of visual occlusion effects constitute the immediate next steps required to move from proof-of-concept to deployable crowd-management tools.