Delta-Function Kicks are Optimal for Rapidly Driven Inertial Stochastic Systems

What the math gives to ML

The paper identifies a nonstandard optimal-control mechanism for rapidly driven inertial stochastic systems: impulsive, delta-function control kicks reduce short-duration work from quadratic scaling to linear scaling in protocol duration. The transferable asset is not the specific thermodynamic plant, but the recognition that a second-order system should use concentrated momentum injection at protocol boundaries rather than distribute the same control smoothly over time. A neural analogue is an impulsive momentum optimizer that reserves part of each short training window for analytically chosen parameter-velocity kicks, with the prediction that the cumulative optimization-control cost scales linearly rather than quadratically with the window duration.