Optimal Finite-Time Control of Nonreciprocal Brownian Dimers: Thermodynamic Anomaly and Multiple Transitions

What the math gives to ML

The paper provides a constructive mechanism for exploiting and controlling nonreciprocal coupling between center and separation modes in a driven stochastic system. In center/separation coordinates, the interaction asymmetry produces an active force proportional to \(\alpha=(a-b)/2\), while the separation mode relaxes at rate \(\rho=1+a+b\); optimal finite-time protocols therefore use auxiliary excursions rather than monotone motion. A transferable neural-network construction is a two-state optimizer with a trainable parameter center and an auxiliary separation state, together with bounded control. The key falsifiable prediction is that removing control bounds permits growing auxiliary excursions, whereas hard saturation produces abrupt transitions and smooth saturation produces continuous onset.