Coherence‐Preserving Fluctuation Diagnostics for an Engineered Population‐Inverted Qubit Otto Engine

Finite‐time quantum thermal machines require diagnostics beyond average work and efficiency because microscopic engines operate where fluctuations, incomplete thermalization, and coherence strongly affect performance. A coherence‐preserving fluctuation diagnostic is developed for an engineered qubit Otto engine coupled to an actively maintained population‐inverted hot channel. The cycle is analyzed through a Dynamic Bayesian Network (DBN) reconstruction of the unmeasured coherent dynamics, yielding work, heat, power, and regularized efficiency fluctuations without the projective dephasing imposed by two‐point measurement (TPM) schemes. Because the inverted channel is treated as an active reduced‐model resource, the reported enhancements represent gross working‐medium advantages rather than net device efficiencies. In the full‐thermalization limit, population inversion increases extracted work and output power and opens a stability sector with substantially reduced relative power fluctuations. For finite hot and cold isochores, this enhancement reorganizes into distinct high‐power, high‐efficiency, and low‐noise operating sectors governed by the competition between nonadiabatic driving and thermalization timescales. Comparison with TPM shows that the two reconstructions diverge in coherence‐rich regimes, while coherence analysis indicates that the inverted high‐efficiency branch remains aligned with the dominant post‐hot‐bath coherence ridge.