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arXiv:2609.06695

Thermodynamic Performance of a Measurement-Driven Quantum Engine with a Two-Parameter $(p,q)$-Deformed Harmonic Oscillator

Tunde Joseph Osunmusanmi, Berihu Teklu

quant-phSubmitted Sep 6, 2026• Announced Sep 8, 2026• 0 citations
arXivHTMLPDF

Abstract

We address a measurement-driven, single-bath quantum engine that generates usable work using quantum measurement backaction. The working medium is a two-parameter $(p,q)$-deformed harmonic oscillator, whose nonlinear spectrum modifies the energy gaps sampled by a nonselective Gaussian measurement and the work exchanged during quasistatic adiabatic strokes. The cycle starts from a Gibbs state and consists of an adiabatic change of $(ω,p,q)$, measurement of the final effective position quadrature, a reverse adiabatic stroke, and thermalization with the original bath. Using a consistent first-law convention, we derive the measurement heat, adiabatic work contributions, thermalization heat, and reduced working-medium efficiency. We also express the measurement stroke via a transition matrix and identify passivity/unitality conditions that ensure nonnegative measurement heat. Numerical scans show that, within the finite-basis, spectral-ordering, and engine-operation checks used in this work, deformation can enhance measurement-induced energy input and extracted work relative to the undeformed oscillator. The physical engine regime is selected by $\QM>0$, $\Wcyc<0$, $\QT<0$, and $0<η<1$. The reported efficiency is reduced and excludes measurement-apparatus costs.

Comments
17 pages, 18 figures

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Thermodynamic Performance of a Measurement-Driven Quantum Engine with a Two-Parameter (p,q)(p,q)(p,q)-Deformed Harmonic Oscillator
We address a measurement-driven, single-bath quantum engine that generates usable work using quantum measurement backaction. The working medium is a two-parameter (p,q)(p,q)(p,q)-deformed harmonic oscillator, whose nonlinear spectrum modifies the energy gaps sampled by a nonselective Gaussian measurement and the work exchanged during quasistatic adiabatic strokes. The cycle starts from a Gibbs state and consists of an adiabatic change of (ω,p,q)(ω,p,q)(ω,p,q), measurement of the final effective position quadrature, a reverse adiabatic stroke, and thermalization with the original bath. Using a consistent first-law convention, we derive the measurement heat, adiabatic work contributions, thermalization heat, and reduced working-medium efficiency. We also express the measurement stroke via a transition matrix and identify passivity/unitality conditions that ensure nonnegative measurement heat. Numerical scans show that, within the finite-basis, spectral-ordering, and engine-operation checks used in this work, deformation can enhance measurement-induced energy input and extracted work relative to the undeformed oscillator. The physical engine regime is selected by \QM>0\QM>0\QM>0, \Wcyc<0\Wcyc<0\Wcyc<0, \QT<0\QT<0\QT<0, and 0<η<10<η<10<η<1. The reported efficiency is reduced and excludes measurement-apparatus costs.
A four-stroke quantum engine which alternately interacts with a measurement apparatus and a single heat bath is discussed in detail with respect to the average work and heat as well as to the fluctuations of work and heat. The efficiency and the reliability of such an engine with a harmonic oscillator as working substance are analyzed under different conditions, such as different speeds of the work strokes, different temperatures of the heat bath, and various strengths of the energy supplying measurement. For imperfect thermalization strokes of finite duration also the power of the engine is analyzed. A comparison with a two-temperature Otto engine is provided in the particular case of adiabatic work and ideal thermalization strokes.
Measurement-based quantum heat engines have attracted significant interest as alternatives to conventional thermal engines, as they replace the hot thermal reservoir with quantum measurements, thereby offering greater controllability and simpler implementation. Motivated by these advantages, we investigate a measurement-driven quantum Otto engine with a qubit working substance and study the optimal work extractable from such engines, including whether their performance can surpass that of conventional quantum Otto cycles. We analyze the engine in both the infinite-time (adiabatic) and finite-time (non-adiabatic) regimes, considering two distinct implementations obtained through optimization over all projection-valued measurements (PVMs) and over all two-outcome positive operator-valued measurements (POVMs). We show that measurement-based engines can outperform conventional quantum Otto engines within specific parameter regimes and that POVM-based engines can yield higher optimal work extraction than PVM-based ones. Furthermore, by incorporating the thermodynamic cost associated with resetting the auxiliary system required for POVM implementation, we demonstrate that the resulting net work output can still exceed that of PVM-based engines under suitable conditions on the spectral gaps and cold bath temperature. We also identify regimes in which non-adiabatic implementations can yield higher work output and efficiency than their adiabatic counterparts. Our study provides operational guidelines for designing improved measurement-driven quantum Otto engines.
This paper investigates a coupled two-qubits heat engine fueled by generalized measurements of the spin components and using a single heat reservoir as sink. Our model extends the proposal of Yi, Talkner, and Kim [Phys. Rev. E 96, 022108 (2017)2470-004510.1103/PhysRevE.96.022108], where the role of a hot reservoir in a four-stroke cycle was replaced by a quantum measurement apparatus, the other steps being two quantum adiabatic strokes and thermalization with a cold reservoir. We propose a five-stroke cycle, where an ergotropy extracting stroke is introduced following the measurement stroke, and study the effect of measurements of different spin components on the performance of the machine. For measurements along z-z directions, we find two possible occupation distributions that yield an active state and the ergotropic stroke improves the performance of the engine over the four-stroke cycle. Further, the three-stroke engine (without the adiabatic strokes) yields the same performance as the five-stroke engine. For arbitrary working medium and nonselective measurements, we prove that the total work output of a five-stroke engine is equal to the sum of the work outputs of the corresponding four-stroke and three-stroke engines. For measurement directions other than z-z, there may be many possible orderings of the postmeasurement probabilities that yield an active state. However, as we illustrate, for specific cases (e.g., x-x), a definite ordering may be obtained with the projective measurements. Thus we find that the five-stroke engine exploiting ergotropy outperforms both its four-stroke as well as three-stroke counterparts.
Abstract In this work, we introduce a three-stroke quantum engine with a single-qubit working substance whose cycle consists of two strokes arise due to performing two distinct general quantum measurements and it is completed by thermalization through contact with a finite temperature thermal reservoir. It is demonstrated that energy is imported into the engine by first measurement channel and work (useful energy) is extracted from it, in a frictionless isentropic manner, by the second measurement channel. It is particularly shown that the engine is capable to have perfect efficiency. In continuation, we equip the engine cycle with two additional adiabatic strokes. As illustrated, the presence of adiabatic strokes in the cycle provide an improved lower bound for the parametrized efficiency range of the engine.
The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or more baths at different temperatures and continuously driven. To this end, we investigate parametrically driven quantum harmonic oscillators coupled to heat baths via a collision model. Using a thermodynamically consistent local master equation, we derive the heat flows and power of the working device, which can operate as an engine, refrigerator, or accelerator, and analyze the instantaneous and average efficiencies and coefficients of performance. Studying the regimes of both slow and fast driving of the system, we find that an increased driving frequency can lead to a change of functioning to a dissipator. Finally, we investigate the effect of squeezing one of the thermal baths: it leads to an apparent higher efficiency compared to the corresponding Carnot value of an equilibrium bath with the same temperature and to sustained entanglement between the working substance oscillators in the limit cycle.
Finite-time quantum heat engines (QHEs) typically extract less work than their quasistatic counterparts because fast driving generates coherences and non-adiabatic transitions during the work strokes, a phenomenon commonly referred to as quantum friction. Quantum lubrication denotes a broad class of strategies that use auxiliary systems or controls to mitigate this loss. In this work, we introduce a lubrication protocol based on the quantum Zeno dynamics (QZD). By coupling the working medium to an auxiliary lubricant system and frequently monitoring the lubricant, we confine the joint evolution to a Zeno subspace and obtain an effective shortcut to adiabaticity during the work strokes of a QHE running an Otto cycle. In the ideal Zeno limit, the protocol reproduces the transitionless dynamics required to preserve populations in the instantaneous energy basis and recover the Otto efficiency at finite stroke duration. We also analyze several implementation-dependent thermodynamic costs, including switching, driving, monitoring, and imperfect thermalization, in order to assess how these costs constrain the practical gains in efficiency and power. Our results identify QZD as a conceptually distinct route to quantum lubrication and highlight quantum heat engines as a useful setting in which to study the interplay between strong coupling, measurement, and quantum thermodynamic control.