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

Abstract

Finite-time quantum thermal machines require diagnostics beyond average work and efficiency, because microscopic engines operate in regimes where fluctuations, incomplete thermalization, and coherence are equally important. Here we develop a measurement-backaction-free (coherence-preserving) fluctuation diagnostic for an engineered qubit Otto engine coupled to an actively maintained population-inverted hot channel. The engine is analyzed using a dynamic Bayesian network (DBN) reconstruction of the unmeasured coherent cycle, yielding work, heat, power, and normalized efficiency-proxy fluctuations without imposing the projective dephasing inherent in two-point energy measurements. The inverted channel is treated as an active reduced-model resource; accordingly, all reported power and efficiency enhancements represent gross working-medium advantages, not net device efficiencies. In the full-thermalization limit, population inversion enhances extracted work and output power while opening a stability sector with markedly reduced relative power fluctuations. When finite-duration isochores are implemented, this gross enhancement reorganizes into a structured operating landscape with distinct high-power, high-efficiency, and low-relative-noise sectors, whose boundaries are governed by the competing timescales of nonadiabatic driving and thermalization rates. A direct comparison reveals that DBN and conventional two-point measurement predictions diverge precisely in coherence-rich regimes, identifying where a backaction-free reconstruction is essential. A coherence-sensitive analysis further shows that the positive-temperature reference operates optimally in an almost decohered region, whereas the inverted high-efficiency branch remains aligned with the dominant post-hot-bath coherence ridge. These results provide a reduced-model benchmarking framework for engineered qubit thermal machines.

The paper asks how population inversion, incomplete thermalization, and coherence affect the output and fluctuations of a finite-time qubit Otto engine. It models noncommuting hot and cold Hamiltonians, driven unitary strokes, and Lindblad isochores with an actively maintained inverted hot-channel stationary state. A dynamic Bayesian network (DBN) reconstructs positive energy-history probabilities from corner-state eigenprojectors, preserving unmeasured-cycle mean energetics rather than imposing energy-measurement dephasing. Numerical stationary-cycle scans identify distinct output–noise sectors. In the ideal-reset benchmark, the inverted performance optimum gives roughly $2.3$ times the work and power of the best positive-temperature point, with gross efficiency $0.979$ versus $0.493$. A separate inverted stability point has comparable power and relative power fluctuation $\phi_P=\sigma(P)/|\langle P\rangle|=0.338$, versus $1.38$ for the positive-temperature optimum. With finite isochores, maximum power is approximately seven times the inverted reset benchmark; the maximum-efficiency point reaches $0.980$ but has $\phi_P=14.3$. The inverted high-efficiency sector aligns with residual post-hot-stroke coherence. An average-level DBN–TPM comparison finds discrepancies in short-time coherent regimes and convergence at long driving times. These are gross working-medium results: inversion-maintenance costs, implementation-specific reservoir physics, and tomography errors are excluded. The Markovian approximation may fail at short contacts. The efficiency-fluctuation variable is normalized work, $-W/\langle Q_h\rangle$, not trajectory efficiency; its relative noise equals $\phi_P$. DBN is an ensemble reconstruction, not a backaction-free single-shot measurement, and no distribution-level DBN–TPM comparison is provided.