Dynamical onset of quasiprobability negativity in quantum many-body systems

Time-dependent quasiprobability distributions provide a quasiprobabilistic description of sequential measurement statistics generated by quantum dynamics, and can reveal nonclassical features with no classical probabilistic counterpart. Yet the dynamical emergence of their negativity in many-body systems remains largely unexplored. We introduce the \emph{first-time negativity} (FTN) of the Margenau-Hill quasiprobability as a dynamical indicator of when local measurement sequences in an interacting quantum system begin to exhibit genuinely nonclassical behavior. Using the Ising chain, we show that FTN discriminates clearly between interaction-dominated and field-dominated regimes, is systematically reshaped by temperature, and responds sensitively to the breaking of integrability. For spatially separated measurements, FTN appears abruptly near the interaction-field crossover, while measurements at opposite boundaries exhibit a distinct weak-field branch whose onset time grows with chain length and is consistent with ballistic propagation across the system. We further compare the numerical onset of negativity with a recently proposed quantum speed limit (QSL) for quasiprobabilities, which provides a geometric benchmark for the observed dynamics. Our results identify FTN as a practical and experimentally accessible probe of the real-time onset of quasiprobability negativity and contextual sequential measurement statistics, directly suited to current platforms capable of sequential weak and strong measurements.