Non-reciprocity · active matter simulation

What does breaking Newton's third law — non-reciprocal forces, where i chases j while j flees i — do to an emergent world?

▶ Run the simulationSee the measured result

Units: per-sim-step (dt = 1/45 s) COM velocity decay factor at α = 0 — Newton's third law makes the interaction term contribute exactly zero, so the N-body COM inherits the bare single-particle friction factor

How the lab tests it

Split the seed's interaction matrix into its reciprocal part S=(A+Aᵀ)/2 and non-reciprocal part Q=(A−Aᵀ)/2, then sweep a knob α from 0 (forces made fully reciprocal) to 1 (the genome's own asymmetry), measuring the activity ⟨|v|⟩ (mean particle speed once settled) and the net drift |v_cm| (centre-of-mass speed) at each α.

What it looks for

a transition from STATIC to ACTIVE: at α=0 the reciprocal forces relax to a still equilibrium (⟨|v|⟩→0) with net drift EXACTLY zero (internal forces cancel ⇒ momentum conserved); turning on non-reciprocity dissolves the equilibrium into perpetual chasing/fleeing motion (⟨|v|⟩ climbs ~30–250× depending on seed, ≈33× at the default) and the centre of mass starts to drift (momentum no longer conserved) — 'active matter' from a broken symmetry. An OPEN question on the substrate, the asymmetry axis of its phase diagram