Mpemba effect in a chemomechanical model of the Kinesin molecular motor

What the math gives to ML

The paper identifies a concrete anomalous-relaxation mechanism: a preparation that is farther from steady state can relax faster when its projection onto the slowest relaxation mode is smaller, even if its initial free-energy distance is larger. In the six-state kinesin network this effect survives nonequilibrium driving and is visible not only in the full probability distribution but also in the motor velocity, providing an observable signature. The transferable neural-network construction is to decompose parameter or activation errors into slow and fast Hessian or Jacobian modes, and deliberately compare or design initial states with different slow-mode overlap. This predicts a measurable crossover in recovery curves rather than merely a benchmark improvement.