Green–Kubo Memory and Irreversibility from Ordered Absorption

What dynamical information can be inferred when an experiment records only whether a system survives a controlled absorption protocol? Static state-dependent absorption is exactly blind to stationary time reversal, even when complete survival curves are known. We show that two ordered absorption pulses recover lagged covariances through an exact finite-amplitude identity. Swapping the pulses reveals time-antisymmetric correlations and provides a lower bound on Markov path irreversibility from two Bernoulli probabilities. Known profiles spanning a finite state space determine its transition matrix, whereas incomplete profiles can leave dynamical modes invisible. Finite-count confidence bounds and information-loss limits are derived, connecting zero-frequency Green–Kubo response to an explicitly time-resolved survival measurement protocol. This record contains the preprint, Supplemental Material, and the reproducibility package containing source code and numerical materials.