Diffusion sensitivities of Langevin Dynamics

Analyzing the response properties of systems subject to perturbations provides useful insights on the structural properties of the system, and is of paramount importance in identifying phase transitions. For equilibrium Langevin systems, the fluctuation-dissipation theorem (FDT) relates response to spontaneous fluctuations, such that sensitivity analysis can be carried out without actually perturbing the system. Out of equilibrium, the FDT does not hold; however we construct general non-equilibrium response estimators that allow sensitivity analysis for both stationnary (NESS) and non stationnary systems. This estimator is based on the instantaneous score $\nabla \log \rho_t$ of the system, a by-now classical object in machine learning, that can be estimated from system snapshots.