Finite relaxation protocols with minimal dissipation

What the math gives to ML

The paper provides a constructive finite-protocol mechanism: when a system can only perform a finite number of quench-relax steps, intermediary distributions should be chosen to minimize total dissipated work rather than spaced uniformly in the control parameter. In the large-step limit, the optimal protocol approaches a Fisher-Rao geodesic, while finite-step corrections are characterized by a Lambert-function recurrence. A transferable neural-network version is an adaptive annealing or diffusion-sampling schedule that places intermediary distributions at approximately equal Fisher-Rao distance and allocates more relaxation computation where the distribution changes rapidly, predicting inverse-square local discretization error and approximately inverse-linear cumulative dissipation.