A simple model for cage breaking in active matter: three self-propelled disks in confinement

Cage breaking is the elementary rearrangement event in dense, slowly-relaxing particle systems, ranging from glasses to vibrated granular materials and biological collectives. We extend a recently-proposed minimal model of cage breaking – three distinguishable disks moving in circular confinement – to active matter by introducing disk self-propulsion. The model's simplicity allows us to extract a one-dimensional entropic landscape that characterizes rearrangements. Surprisingly, three different active matter models converge to the same landscape at high persistence, revealing that geometry, rather than microscopic propulsion details, controls these structural transitions. We further find an optimal persistence time for cage breaking that balances exploration and directional motion, connecting minimal geometric constraints to the enhanced dynamics observed in bulk active glasses.