First Empirical Survival Curve of the Margenau–Hill Coherent Thermodynamic Witness in Commercial NISQ Hardware

We demonstrate empirically the construction-level blindness of the standard Two-Point Measurement (TPM) protocol to coherence in quantum thermodynamic entropy production: TPM applied to coherent and population-matched diagonal states yields total variation TVₘax = 0. 006 across 16, 384 shots, statistically indistinguishable. We establish the Margenau–Hill quasiprobability (MHQ) as the operational witness of coherent thermodynamic signature where TPM fails by construction. The MHQ protocol is implemented via Hadamard-test interferometry with controlled energy phases (CRZ) and amplitude-damping channel dilation (CRY+CX), and validated against four mandatory Kraus consistency tests at machine precision (~10^-16). We present the first complete empirical survival curve of a coherent thermodynamic witness in commercial NISQ quantum hardware. Eleven independent jobs executed on IBM ibmfez (Heron r2 architecture, 156 qubits) across six dissipation values gamma in 0. 05, 0. 10, 0. 15, 0. 20, 0. 25, 0. 30 reveal three structured regions: sustained ignition (gamma ≤ 0. 20, SNRdiff = 3. 5–5. 6 with replication), edge transition (gamma = 0. 25, SNRdiff = 3. 2), and practical extinction (gamma = 0. 30, SNRdiff = 1. 46). The survival frontier is empirically localized at gammacrit in (0. 25, 0. 30). Diagonal control yields exactly zero negativity in all eleven hardware runs — including the practical-extinction regime — establishing the witness signal as coherence-specific rather than channel-induced or systematic-error artifact. Topological robustness is confirmed across three distinct qubit layouts. Cross-platform replication on IonQ, Rigetti, and IQM remains pending administrative resolution of AWS Braket access. A direct quantitative mapping to the Francica–Goold–Plastina Xi remains an open theoretical question. This is the preprint version of the manuscript submitted to Physical Review X Quantum (April 2026). Raw experimental data and source code are publicly available on Zenodo at DOI: 10. 5281/zenodo. 19801980 under the Creative Commons Attribution 4. 0 International license. Released under CC-BY 4. 0.