In equilibrium matter, Newton's third law guarantees reciprocity: if particle A pushes particle B rightward, B pushes A leftward with equal force. Fan Bo and colleagues built a robotic swarm called MASBot -- spinning magnetic robots whose interactions explicitly violate this symmetry. By tuning the balance between repulsive, attractive, and transverse forces, they observed three distinct phases: an odd elastic crystal, an odd viscous liquid, and a chiral active gas. The gas phase behaves like a system of self-gravitating point vortices. Symmetry breaking at the particle level produces emergent macroscopic states including phase separation and collective translation.
The structural insight is that nonreciprocity acts as a phase parameter. In equilibrium thermodynamics, phases are determined by temperature, pressure, and composition. In this active system, the degree of force asymmetry between particles serves an analogous role -- continuously tuning it drives transitions between qualitatively different collective states. The odd elastic crystal has rigidity but not the kind found in equilibrium crystals; its elastic moduli include antisymmetric components that store energy in rotational modes. The odd viscous liquid flows but with a transverse stress response absent in normal fluids. These are not distortions of familiar phases -- they are genuinely new states of matter that exist only because reciprocity is broken. The robot platform makes this tangible: by programming individual spinning frequencies and interaction anisotropies, the experimenters dial through a phase diagram that has no equilibrium analog. Nonreciprocity is not noise, not a perturbation, not a defect to be corrected. It is a thermodynamic-like variable that opens regions of state space that reciprocal systems cannot access.
(arXiv:2603.09897)