Exact Fluctuation-Response Relations for Underdamped Langevin Dynamics

Key points

It derived exact finite-time fluctuation-response identities for underdamped Langevin dynamics that hold under arbitrary time-dependent driving and for general accumulated observables.
Using a Doob martingale, it exactly decomposed observable variance into a component attributable to the initial state and a component dynamically generated by subsequent noise.
Choosing a friction perturbation in the direction of the irreversible probability current yields an uncertainty relation saturable even at finite times and a variational principle for total entropy production.
In driven free diffusion, the friction-response-based factor maintained a universal lower bound even when the existing mean-current-based factor collapsed exponentially with dissipation.
The results are a theoretical analysis of underdamped Langevin processes and accumulated observables, so applicability to other noise structures, nonadditive observables, and actual experimental data requires separate validation.

External research summaries. These are not HDATF publications or measured product results.