Nonequilibrium History-Dependent Latency and Precision Clock Tests Hysteresis, Relaxation, Irreversible-Update Signatures, and Differential Clock Bounds in a Finite-Capacity Physical Theory

We develop the nonequilibrium laboratory branch of the finite-capacity latency–erasure program by introducing a history-dependent latency sector whose dynamics depend not only on instantaneous load but also on prior irreversible update activity. The central proposal is that local proper-time flow may carry a hysteretic correction whenever a physical system has undergone recent nonequilibrium overwrite, dissipation, or state-reconfiguration events. This correction is modeled by a relaxation equation for a history-latency field , driven by an effective irreversible update rate . The total latency is then written as the sum of an instantaneous load component and a history-dependent component, leading to a modified clock-rate law . In the weak-latency regime, the theory predicts that systems brought to the same final macroscopic state through different preparation histories may retain different transient clock-rate corrections. We derive the general solution of the relaxation equation, construct step-response and pulse-response branches, quantify hysteresis loops under cyclic driving, formulate a differential precision-clock test strategy, and derive exclusion logic in the plane. Concrete pulse-vs-quasi-static laboratory protocols are proposed, the relevant observable is identified as a transient differential fractional clock-rate shift after controlled nonequilibrium preparation, and a first-pass order-of-magnitude admissibility framework is introduced. The result is the first nonequilibrium laboratory phenomenology of the finite-capacity program and the third major testable branch after weak-field gravity and moderated cosmology.