Fluctuation theorems for thermally isolated driven quantum systems: nonadiabaticity, excess work and strong inequalities

What the math gives to ML

The paper provides a nonadiabatic fluctuation-theorem framework in which irreversibility of a finite-time driven process is quantified by a relative entropy between the actual final state and an adiabatically evolved reference state. Its transferable asset is an excess-work identity: finite-rate driving generates a nonnegative dissipative cost whose mean is proportional to this relative entropy, together with exponential fluctuation relations that give tail-sensitive inequalities. A neural-network analogue is to treat stochastic training as a driven nonequilibrium process and use an ensemble-estimated nonadiabaticity signal to adapt the learning rate before training enters an irreversible, unstable regime.