Finite-size reliability of homothetic quantum Otto engines

• URL: http://arxiv.org/abs/2607.29050v1
• Date: Fri, 31 Jul 2026 06:09:15 GMT
• Title: Finite-size reliability of homothetic quantum Otto engines
• Abstract summary: Homothetic quantum Otto engines provide a reference model in which the quasistatic efficiency is trajectory-independent while work remains fluctuating.<n>Specializing to a uniformly spaced ladder gives closed finite-$N$ expressions for the full work distribution, mean work, variance, and signal-to-width reliability.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Homothetic quantum Otto engines---where all populated energy gaps are rescaled by a common factor---provide a reference model in which the quasistatic stochastic efficiency is trajectory-independent while work remains fluctuating. For arbitrary finite homothetic spectra we derive the two-point-measurement work distribution and reduce the first two work moments to endpoint energy moments. Specializing to a uniformly spaced ladder gives closed finite-$N$ expressions for the full work distribution, mean work, variance, and signal-to-width reliability. This ladder connects the qubit and oscillator limits, reveals a finite-$N$ reliability crossover, and demonstrates that the high-temperature and infinite-dimensional limits do not commute. The noncommutation reflects a bounded-versus-unbounded spectral distinction: at fixed finite $N$ the Gibbs state has a normalizable infinite-temperature limit, whereas the oscillator retains an ever-expanding thermal tail. The exact formulas are used to compare standard mean-output prescriptions with work reliability, showing that maximum mean output and maximum dimensionless reliability select different operating points. The benchmark is extended to incomplete diagonal reset and to finite-time unitary strokes described by transition matrices, with a finite-ladder protocol and a harmonic sudden-switch oscillator benchmark as controlled examples. Weak deviations from exact homothety are treated perturbatively, showing how level-dependent gap distortions reintroduce quasistatic efficiency fluctuations and modify work reliability. Together, these results separate finite-size, incomplete thermalization, finite-time, and weak spectral-distortion contributions to work unreliability in quantum Otto engines.

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