Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2609.30132

Collective thermalization, work reliability, and resource bounds in a population-inverted Dicke Otto engine

Cler T. Garcez, Gabriella G. Damas, Norton G. de Almeida, G. D. de Moraes Neto

quant-phSubmitted Sep 24, 2026• Announced Sep 25, 2026• 1 citation
arXivHTMLPDF

Abstract

Population inversion and collective relaxation can both enhance the performance of a quantum heat engine, but through distinct mechanisms. We study a quantum Otto engine whose working medium is a symmetric collective spin of $N$ two-level constituents. For commuting work strokes and collective reservoir coupling, the dynamics reduces exactly to a finite birth--death process on the Dicke ladder, allowing a unified treatment of stationary operation, work fluctuations, and finite-time relaxation. In the complete-reset limit, passive work per cycle saturates with system size, whereas population inversion yields work that grows linearly with $N$. The work reliability shows the same linear scaling, exceeding the square-root behavior of $N$ independent engines. This enhancement originates from a macroscopic polarization displacement between hot and cold states, while collective coupling instead accelerates the finite-time dynamics through Dicke transition rates. For matched passive and inverted hot states, the extra gross work equals the Otto efficiency times the ergotropy of the inverted state. Charging the corresponding reversible excess state-formation cost removes this advantage, showing that the enhanced output converts a pre-existing active-state resource rather than generating a free thermodynamic gain. Exact finite-contact trajectory statistics further quantify how collective kinetics, fluctuations, correlations, and resource accounting remain linked away from complete reset.

Related papers

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

Gabriella G. Damas, Norton G. de Almeida, Gao Xianlong +1 more

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.

quant-pharXiv:2605.01719•Advanced Quantum Technologies•May 5, 2026•0 citations

Finite-size reliability of homothetic quantum Otto engines

Gabriella G. Damas, Clebson Cruz, Norton G. de Almeida +2 more

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.

quant-pharXiv:2607.29050•Aug 3, 2026•0 citations

Finite-time quantum Otto engine with a squeezed thermal bath: Role of quantum coherence and squeezing in the performance and fluctuations

Xiao Ping Yang, Dehua Liu, Jizhou He +2 more

We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cycle, which are dependent on the time duration along each process. With these, we derive the analytical expressions for the thermodynamic quantities of the two-level heat engine, such as total work, thermodynamic efficiency, entropy production, and work fluctuations, in which effects of coherence, squeezing, inner friction and finite-time heat exchange are included. We then numerically determine the thermodynamic quantities and the fluctuations using the parameters employed in the experimental implementation. Our results clarify the role of coherence and squeezing in the performance and fluctuations in the quantum Otto engines.

arXiv:2205.13290•May 26, 2022•2 citations

Thermodynamics and fluctuations in finite-time quantum heat engines under reservoir squeezing

Yang Xiao, Dehua Liu, Jizhou He +4 more

We investigate the thermodynamics and fluctuations of a finite-time quantum Otto engine alter- natively driven by a hot-squeezed and a cold thermal reservoir. We show that reservoir squeezing significantly enhances the performance by increasing the thermodynamic efficiency and the power and enables higher stability by decreasing the relative power fluctuations and speeding up the convergence of quantum efficiency to its most probable value. We also demonstrate the counterintuitive result that the efficiency can be larger than the Otto limit in the finite-time operation. Experimental demonstration of this quantum heat engine can be available, based on a single-electron spin pertaining to a trapped $^{40}\mathrm{Ca}^{+}$ ion [D. von Lindenfels et al., Phys. Rev. Lett. 123, 080602 (2019)]. We provide a general framework for reliably studying the finite-time nanoengine in finite-time operation which accounts for quantum friction and coherence, deriving important insights into the thermodynamic behaviors beyond the classical thermal machines.

Physical Review Research•Nov 27, 2023•24 citations

Entropy Production in Quantum Heat Engines with Squeezed Reservoirs

Pavol Berger, Natalia Zizka, Andrej Molnar

Squeezed thermal reservoirs have been proposed as a route to boosting the efficiency and power of quantum heat engines beyond the standard Carnot bound, since squeezing injects an effective negative entropy that can, in principle, be converted into extra work. What remains poorly quantified is the entropy-production cost that driving a working qubit against a squeezed bath actually incurs once finite-time operation and reservoir decoherence are taken into account. We simulate a quantum Otto-cycle heat engine built from a two-level working system coupled alternately to a hot reservoir at temperature 4.2 K, squeezed with squeezing parameter r ranging from 0 to 1.2, and an unsqueezed cold reservoir at 0.8 K, integrating the Lindblad master equation across 42 combinations of squeezing parameter and cycle duration between 0.05 and 2.0 (in units of the inverse qubit gap). At r = 0, mean entropy production per cycle was 0.223 k_B, consistent with standard finite-time Otto-cycle behaviour, but rose to 0.361 k_B at r = 1.2, a 62% increase, even as extractable work per cycle increased by 41%, from 0.184 to 0.259 (in units of the qubit gap). The ratio of work output to entropy production, an effective thermodynamic figure of merit, was therefore not monotonic in squeezing: it peaked at r = 0.6, where work per unit entropy produced reached 0.98, 15% above the unsqueezed value of 0.85, before declining at higher squeezing as entropy production began to outpace the marginal work gain. Power output at the maximum-power cycle duration increased with squeezing across the full range tested, from 0.31 (gap units) at r = 0 to 0.52 at r = 1.2, a 68% gain, but efficiency at maximum power fell from 0.41 to 0.33 over the same range, a trade-off traced out in detail in Table 1. A decomposition of total entropy production attributed 58-71% to hot-bath coupling across all squeezing values, with the squeezed-bath contribution alone rising from undefined at r = 0 to 34% of hot-bath entropy production at r = 1.2, while coherence generated during the unitary strokes accounted for a comparatively stable 12-18% regardless of squeezing strength. These results indicate that reservoir squeezing in quantum heat engines delivers a genuine power and work advantage but at a non-negligible and squeezing-dependent entropy cost, with an intermediate squeezing level offering the best entropy-normalized performance rather than the strongest squeezing tested, a finding directly relevant to the design of squeezed-bath quantum thermal devices operating under realistic decoherence.

•Jun 15, 2026•0 citations

Finite-Resource Contacts in Collective Quantum Engines: Exact Dynamics, Resource Reconstruction, and Identifiability

Attar Ali

The same quantum channel can hide different resource costs \[\boxed{C_{\mathrm{loc}}=\varepsilon(\mu_M-\mu_0)+k_{\mathrm B}T_0\left[\sum_{j=1}^{M}h(q-\mu_j+\mu_{j-1})-Mh(q)\right].}\] Two finite supply devices can implement exactly the same complete quantum channel while depleting different amounts of locally recoverable free energy. Even perfect endpoint process tomography need not determine that supply cost. This paper proves an explicit counterexample, then identifies the extra records that reconstruct the resource without fitting a relaxation rate: the intermediate mean excitation numbers, together with independently known preparation and energy scales. For a qubit contact with fixed population contraction \(\Lambda\), prepared supply population \(q\), initial system population \(p_0\), and \(M\) contacts, write \(\Delta=(q-p_0)(1-\Lambda)\). The full dynamically attainable resource interval is \[C_{\min}=\varepsilon\Delta+k_{\mathrm B}T_0[h(q-\Delta)-h(q)],\qquad C_{\max}=\varepsilon\Delta+Mk_{\mathrm B}T_0[h(q-\Delta/M)-h(q)].\] Both endpoints are constructively attainable when idle contacts are allowed. Every intermediate value occurs with the same complete reduced channel. The paper supplies the realizing contact angles, the refinement limit, an explicit correction for outgoing-unit coherence, and finite-error bounds that include uncertain energy and temperature scales. The collective extension gives the exact Dicke collision kernel, a controlled weak-collision limit, finite-contact parameter identification, and a stationary Otto-cycle resource balance. The reconstruction archive independently builds the joint unitary, partial traces, full reduced superoperators and a second Markov propagator. It reproduces the published collective-engine benchmark and includes all numerical cases, code, plot data and checksums. Scientific status. These are conditional mathematical theorems with reproducible synthetic verification. They extend the QTT physical-contact program by separating endpoint selection from resource selection. The chosen exchange contact has a matched conventional quantum realization. The work neither reports a laboratory detection nor claims an engine-specific axiom-only value of its coupling. Its operational advance is an explicit resource-selection criterion and a reconstruction that requires no coupling fit. Dependencies: QTT Physical Contact Selection and Predictive Transfer and Completed-Event Transport and Quantum Coherence. Independent benchmark: Garcez and colleagues, collective Dicke Otto engine. Corpus Tree. The PDF is the main paper and default preview. The ZIP contains the complete editable and executable reconstruction package.

•Sep 29, 2026•0 citations
Population inversion and collective relaxation can both enhance the performance of a quantum heat engine, but through distinct mechanisms. We study a quantum Otto engine whose working medium is a symmetric collective spin of NNN two-level constituents. For commuting work strokes and collective reservoir coupling, the dynamics reduces exactly to a finite birth--death process on the Dicke ladder, allowing a unified treatment of stationary operation, work fluctuations, and finite-time relaxation. In the complete-reset limit, passive work per cycle saturates with system size, whereas population inversion yields work that grows linearly with NNN. The work reliability shows the same linear scaling, exceeding the square-root behavior of NNN independent engines. This enhancement originates from a macroscopic polarization displacement between hot and cold states, while collective coupling instead accelerates the finite-time dynamics through Dicke transition rates. For matched passive and inverted hot states, the extra gross work equals the Otto efficiency times the ergotropy of the inverted state. Charging the corresponding reversible excess state-formation cost removes this advantage, showing that the enhanced output converts a pre-existing active-state resource rather than generating a free thermodynamic gain. Exact finite-contact trajectory statistics further quantify how collective kinetics, fluctuations, correlations, and resource accounting remain linked away from complete reset.
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.
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-NNN 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-NNN 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 NNN 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.
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cycle, which are dependent on the time duration along each process. With these, we derive the analytical expressions for the thermodynamic quantities of the two-level heat engine, such as total work, thermodynamic efficiency, entropy production, and work fluctuations, in which effects of coherence, squeezing, inner friction and finite-time heat exchange are included. We then numerically determine the thermodynamic quantities and the fluctuations using the parameters employed in the experimental implementation. Our results clarify the role of coherence and squeezing in the performance and fluctuations in the quantum Otto engines.
We investigate the thermodynamics and fluctuations of a finite-time quantum Otto engine alter- natively driven by a hot-squeezed and a cold thermal reservoir. We show that reservoir squeezing significantly enhances the performance by increasing the thermodynamic efficiency and the power and enables higher stability by decreasing the relative power fluctuations and speeding up the convergence of quantum efficiency to its most probable value. We also demonstrate the counterintuitive result that the efficiency can be larger than the Otto limit in the finite-time operation. Experimental demonstration of this quantum heat engine can be available, based on a single-electron spin pertaining to a trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion [D. von Lindenfels et al., Phys. Rev. Lett. 123, 080602 (2019)]. We provide a general framework for reliably studying the finite-time nanoengine in finite-time operation which accounts for quantum friction and coherence, deriving important insights into the thermodynamic behaviors beyond the classical thermal machines.
Squeezed thermal reservoirs have been proposed as a route to boosting the efficiency and power of quantum heat engines beyond the standard Carnot bound, since squeezing injects an effective negative entropy that can, in principle, be converted into extra work. What remains poorly quantified is the entropy-production cost that driving a working qubit against a squeezed bath actually incurs once finite-time operation and reservoir decoherence are taken into account. We simulate a quantum Otto-cycle heat engine built from a two-level working system coupled alternately to a hot reservoir at temperature 4.2 K, squeezed with squeezing parameter r ranging from 0 to 1.2, and an unsqueezed cold reservoir at 0.8 K, integrating the Lindblad master equation across 42 combinations of squeezing parameter and cycle duration between 0.05 and 2.0 (in units of the inverse qubit gap). At r = 0, mean entropy production per cycle was 0.223 k_B, consistent with standard finite-time Otto-cycle behaviour, but rose to 0.361 k_B at r = 1.2, a 62% increase, even as extractable work per cycle increased by 41%, from 0.184 to 0.259 (in units of the qubit gap). The ratio of work output to entropy production, an effective thermodynamic figure of merit, was therefore not monotonic in squeezing: it peaked at r = 0.6, where work per unit entropy produced reached 0.98, 15% above the unsqueezed value of 0.85, before declining at higher squeezing as entropy production began to outpace the marginal work gain. Power output at the maximum-power cycle duration increased with squeezing across the full range tested, from 0.31 (gap units) at r = 0 to 0.52 at r = 1.2, a 68% gain, but efficiency at maximum power fell from 0.41 to 0.33 over the same range, a trade-off traced out in detail in Table 1. A decomposition of total entropy production attributed 58-71% to hot-bath coupling across all squeezing values, with the squeezed-bath contribution alone rising from undefined at r = 0 to 34% of hot-bath entropy production at r = 1.2, while coherence generated during the unitary strokes accounted for a comparatively stable 12-18% regardless of squeezing strength. These results indicate that reservoir squeezing in quantum heat engines delivers a genuine power and work advantage but at a non-negligible and squeezing-dependent entropy cost, with an intermediate squeezing level offering the best entropy-normalized performance rather than the strongest squeezing tested, a finding directly relevant to the design of squeezed-bath quantum thermal devices operating under realistic decoherence.
The same quantum channel can hide different resource costs Cloc=ε(μM−μ0)+kBT0[∑j=1Mh(q−μj+μj−1)−Mh(q)].\boxed{C_{\mathrm{loc}}=\varepsilon(\mu_M-\mu_0)+k_{\mathrm B}T_0\left[\sum_{j=1}^{M}h(q-\mu_j+\mu_{j-1})-Mh(q)\right].}Cloc​=ε(μM​−μ0​)+kB​T0​[j=1∑M​h(q−μj​+μj−1​)−Mh(q)].​ Two finite supply devices can implement exactly the same complete quantum channel while depleting different amounts of locally recoverable free energy. Even perfect endpoint process tomography need not determine that supply cost. This paper proves an explicit counterexample, then identifies the extra records that reconstruct the resource without fitting a relaxation rate: the intermediate mean excitation numbers, together with independently known preparation and energy scales. For a qubit contact with fixed population contraction Λ\LambdaΛ, prepared supply population qqq, initial system population p0p_0p0​, and MMM contacts, write Δ=(q−p0)(1−Λ)\Delta=(q-p_0)(1-\Lambda)Δ=(q−p0​)(1−Λ). The full dynamically attainable resource interval is Cmin⁡=εΔ+kBT0[h(q−Δ)−h(q)],Cmax⁡=εΔ+MkBT0[h(q−Δ/M)−h(q)].C_{\min}=\varepsilon\Delta+k_{\mathrm B}T_0[h(q-\Delta)-h(q)],\qquad C_{\max}=\varepsilon\Delta+Mk_{\mathrm B}T_0[h(q-\Delta/M)-h(q)].Cmin​=εΔ+kB​T0​[h(q−Δ)−h(q)],Cmax​=εΔ+MkB​T0​[h(q−Δ/M)−h(q)]. Both endpoints are constructively attainable when idle contacts are allowed. Every intermediate value occurs with the same complete reduced channel. The paper supplies the realizing contact angles, the refinement limit, an explicit correction for outgoing-unit coherence, and finite-error bounds that include uncertain energy and temperature scales. The collective extension gives the exact Dicke collision kernel, a controlled weak-collision limit, finite-contact parameter identification, and a stationary Otto-cycle resource balance. The reconstruction archive independently builds the joint unitary, partial traces, full reduced superoperators and a second Markov propagator. It reproduces the published collective-engine benchmark and includes all numerical cases, code, plot data and checksums. Scientific status. These are conditional mathematical theorems with reproducible synthetic verification. They extend the QTT physical-contact program by separating endpoint selection from resource selection. The chosen exchange contact has a matched conventional quantum realization. The work neither reports a laboratory detection nor claims an engine-specific axiom-only value of its coupling. Its operational advance is an explicit resource-selection criterion and a reconstruction that requires no coupling fit. Dependencies: QTT Physical Contact Selection and Predictive Transfer and Completed-Event Transport and Quantum Coherence. Independent benchmark: Garcez and colleagues, collective Dicke Otto engine. Corpus Tree. The PDF is the main paper and default preview. The ZIP contains the complete editable and executable reconstruction package.