Non-reciprocity drives a Brownian dimer out of equilibrium

What the math gives to ML

The paper provides a constructive nonequilibrium mechanism: a pair of overdamped degrees of freedom coupled by unequal action-reaction coefficients reaches a stationary state with a nonzero probability current, even under one thermal bath and static harmonic confinement. In the zero-rest-length limit the dynamics is an exactly solvable Ornstein-Uhlenbeck process, so its stability boundary, stationary covariance, current, and entropy-production rate are computable. A transferable neural-network construction is a two-replica or auxiliary-state optimizer with deliberately non-symmetric cross-coupling, allowing controlled rotational probability currents rather than purely gradient descent. The key falsifiable prediction is that the current and nonequilibrium entropy production vanish at reciprocity and grow quadratically with coupling asymmetry, while training remains bounded only inside the derived Hurwitz-stability region.