"The Identical Strangers"
# The Identical Strangers
Non-reciprocal interactions — where A attracts B but B repels A — require a broken symmetry. In mixtures of different species, the asymmetry is built in: the species have different properties, so they respond differently to each other's signals. In single-species systems, all particles are identical. They should interact reciprocally. Newton's third law, applied to effective interactions mediated by chemical gradients, predicts symmetric forces between identical objects.
The authors of arXiv:2603.21863 (March 2026) show that identical colloidal particles can interact non-reciprocally. The mechanism: bistable internal chemistry.
Each colloid is a semi-permeable vesicle containing enzymes that catalyze a non-linear chemical reaction. The reaction has two stable steady states — one where the vesicle is a net producer of a chemical, another where it is a net consumer. Which state a given colloid occupies depends on the local chemical concentrations, which depend on the states of nearby colloids. The particles are materially identical — same enzymes, same membrane, same size — but their dynamic chemical states can differ.
A producer emits chemicals. A consumer absorbs them. A consumer moves toward a producer (attracted by the gradient). The producer moves away from the consumer (repelled by the depletion). The same pair of particles, built from the same materials, exerts asymmetric forces on each other because they occupy different internal states. Switch the states and the forces reverse.
The non-reciprocity is not structural — it is dynamic. It emerges from the bistability of the internal chemistry and the self-consistent coupling between internal state and external gradient. Tuning the chemical parameters can induce bifurcations that switch the system between chasing, fleeing, attracting, and ignoring. Collective behaviors follow: polar swarming, for instance, emerges from the same mechanism scaled to many particles.
The structural insight: identity of components does not guarantee reciprocity of interactions. When internal dynamics have multiple stable states, identical particles can occupy different states and thereby break the symmetry that reciprocity requires. The asymmetry is not in what they are — it is in what they are doing.
