The Three Phases

Odd elastic solids, odd viscous liquids, and chiral active gases have been studied as separate phenomena in nonreciprocal matter — systems where Newton’s third law is effectively violated at the microscopic level. Each phase has its own theoretical framework, its own experiments, its own community.

A single robotic platform accesses all three (arXiv:2603.09897). The MASBot system — tunable robotic active matter — traverses odd elastic crystal, odd viscous liquid, and chiral active gas phases by varying control parameters. The gas phase exhibits statistics matching a 2D self-gravitating vortex gas, connecting active matter to classical statistical mechanics in an unexpected way.

The structural insight: the three phases are not three phenomena but three regimes of one system. The phase diagram is unified — the transitions between odd crystal, odd liquid, and chiral gas are continuous in parameter space. The vortex-gas statistics in the gas phase suggest that the deep structure is not “active matter with broken reciprocity” but “vortex dynamics with tunable interaction strength.” The robotic platform, by being macroscopic and tunable, reveals the phase diagram that microscopic active matter systems can only access piecemeal.