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

Journal of Physics Conference Series

Performance of 3D quantum Otto engine with partial thermalization

Trengginas Eka Putra Sutantyo, Zahara Zettira, Ade Fahriza, Zulfi Abdullah

Published Mar 1, 2024• 2 citations
Publisher

Abstract

Abstract We investigate the phenomenon of partial thermalization in the context of the efficiency at maximum power (EMP) for a quantum Otto engine. This engine utilizes Bose-Einstein Condensation in a cubic potential. The occurrence of partial thermalization is observed during a finite-time isochoric process, preventing the system from reaching an equilibrium state with the reservoirs and leaving it in a state of residual coherence. The engine’s performance can be evaluated based on its power output and EMP. The cubic potential is employed to induce energy excitation during the expansion and compression phases. The total energy is determined by the work done over a complete cycle. Utilizing Fourier’s law for heat conduction, we have determined that the power output is explicitly influenced by the duration of the heating and cooling strokes as well as the engine’s efficiency. Specifically, a longer stroke time and higher efficiency result in reduced power output. To calculate EMP, we optimize power by varying the compression ratio (κ), and we have found that EMP is also influenced by the isochoric heating and cooling processes. When varying the duration of the isochoric process, EMP shows a slight decrease as isochoric time increases due to entropy production. However, significant improvements in the EMP of the Otto Engine can be achieved by extending the cooling stroke time beyond the heating stroke time.

DOI
10.1088/1742-6596/2734/1/012031

Related papers

Efficiency at maximum power of a heat engine working with a two-level atomic system

Rui Wang, Jianhui Wang, Jizhou He +1 more

We consider the finite-time operation of a quantum heat engine whose working substance is composed of a two-level atomic system. The engine cycle, consisting of two quantum adiabatic and two quantum isochoric (constant-frequency) processes and working between two heat reservoirs at temperatures ${T}_{h}$ and ${T}_{c}$$(<$${T}_{h})$, is a quantum version of the classical Otto cycle. By optimizing the power output with respect to two frequencies, we obtain the efficiency at maximum power output (EMP) and analyze numerically the effects of the times taken for two adiabatic and two isochoric processes on the EMP. In the absence of internally dissipative friction, we find that the EMP is bounded from the upper side by a function of the Carnot efficiency ${\ensuremath{\eta}}_{C}$, ${\ensuremath{\eta}}_{+}={\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})\mathrm{ln}(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$, with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$. This analytic expression is confirmed by our exact numerical result and is identical to the one derived in an engine model based on a mesoscopic or macroscopic system. If the internal friction is included, we find that the EMP decreases as the friction coefficient increases.

Physical Review E•Apr 23, 2013•78 citations

Finite-time performance of a single-ion quantum Otto engine

Suman Chand, Shubhrangshu Dasgupta, Asoka Biswas

We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.

arXiv:2106.06700•Physical review. E•Mar 24, 2021•35 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

Thermodynamic Analysis of an Endoreversible Bosonic Quantum Otto Refrigerator under Partial Thermalization

Shofiyah Shofiyah, Trengginas Eka Putra Sutantyo, Zulfi Abdullah

Quantum refrigerators (QRs) are pivotal in exploring thermodynamic behavior at microscopic scales. This study investigates a quantum Otto refrigerator using a bosonic gas confined in a cubic potential, operating under finite-time thermalization. We derive key thermodynamic quantities analytically, including the coefficient of performance (COP), cooling power, entropy, and cooling rate. Additionally, we investigate how partial thermalization during the isochoric heating and cooling stages influences overall system performance. The findings reveal a trade-off between COP and cooling power, emphasizing the importance of thermalization duration. Notably, by extending the cooling time relative to heating, the COP can be significantly improved, offering a practical approach to optimizing QR performance under realistic conditions.

JURNAL ILMU FISIKA | UNIVERSITAS ANDALAS•Apr 24, 2026•0 citations

Performance Analysis Of A Bosonic Quantum Otto Refrigerator In A Three-Dimensional Cubic Potential

Shofiyah Shofiyah

This thesis studies a finite-time quantum Otto refrigerator with an ideal Bose gas confined in a three-dimensional cubic trap. Finite thermal contact times with the hot and cold reservoirs lead to partial thermalization during the isovolume processes, causing deviations from the quasistatic regime. The effects of trap volume ratio \kappa and thermalization time on the system performance are analyzed. The results show that the coefficient of performance (COP) decreases monotonically with increasing \kappa, due to enhanced work input associated with spectral deformation during the isentropic processes, while heat extraction from the cold reservoir remains limited. A clear trade-off between the cooling rate and COP is observed, where higher efficiency is achieved at the expense of cooling power. Entropy production analysis indicates that near-reversible operation occurs when the heating and cooling durations are comparable, whereas prolonged heating increases irreversibility and degrades performance. These findings highlight the important role of trap geometry and partial thermalization in determining the performance of finite-time quantum refrigeration systems.

•Feb 3, 2026•0 citations

Feedback-driven quantum Otto-like engines

Dehua Liu, Yingying Hong, Shaolin Luo +3 more

An analytical study of a feedback-driven quantum engine based on a two-level system is presented. This engine is similar to a quantum Otto engine but substitutes the quantum isochoric process with a feedback-driven operation based on a measured observable $A(\ensuremath{\theta})$, whose eigenstates are coherent superpositions of energy eigenstates. Projective measurements control the feedback operations, while work extraction or heat absorption occurs during driven operations. We derive the general time-dependent efficiency, power, and power fluctuations. Quantum coherence is examined through three mechanisms: (i) coherence associated with $\ensuremath{\theta}\ensuremath{\ne}0$, (ii) residual coherence after incomplete thermalization, and (iii) coherence generated by the interaction between the system and a coherent laser pulse on resonance. We investigate how the parameter $\ensuremath{\theta}$, quantum coherence, and timing of unitary and feedback-driven strokes influence engine performance. We demonstrate that quantum coherence can significantly enhance power output and efficiency while reducing fluctuations through optimal cycle parameter adjustments.

Physical Review A•Jan 3, 2025•6 citations
Abstract We investigate the phenomenon of partial thermalization in the context of the efficiency at maximum power (EMP) for a quantum Otto engine. This engine utilizes Bose-Einstein Condensation in a cubic potential. The occurrence of partial thermalization is observed during a finite-time isochoric process, preventing the system from reaching an equilibrium state with the reservoirs and leaving it in a state of residual coherence. The engine’s performance can be evaluated based on its power output and EMP. The cubic potential is employed to induce energy excitation during the expansion and compression phases. The total energy is determined by the work done over a complete cycle. Utilizing Fourier’s law for heat conduction, we have determined that the power output is explicitly influenced by the duration of the heating and cooling strokes as well as the engine’s efficiency. Specifically, a longer stroke time and higher efficiency result in reduced power output. To calculate EMP, we optimize power by varying the compression ratio (κ), and we have found that EMP is also influenced by the isochoric heating and cooling processes. When varying the duration of the isochoric process, EMP shows a slight decrease as isochoric time increases due to entropy production. However, significant improvements in the EMP of the Otto Engine can be achieved by extending the cooling stroke time beyond the heating stroke time.
We consider the finite-time operation of a quantum heat engine whose working substance is composed of a two-level atomic system. The engine cycle, consisting of two quantum adiabatic and two quantum isochoric (constant-frequency) processes and working between two heat reservoirs at temperatures Th{T}_{h}Th​ and Tc{T}_{c}Tc​(<(<(<Th){T}_{h})Th​), is a quantum version of the classical Otto cycle. By optimizing the power output with respect to two frequencies, we obtain the efficiency at maximum power output (EMP) and analyze numerically the effects of the times taken for two adiabatic and two isochoric processes on the EMP. In the absence of internally dissipative friction, we find that the EMP is bounded from the upper side by a function of the Carnot efficiency ${\ensuremath{\eta}}_{C}$, ${\ensuremath{\eta}}_{+}={\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})\mathrm{ln}(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$, with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$. This analytic expression is confirmed by our exact numerical result and is identical to the one derived in an engine model based on a mesoscopic or macroscopic system. If the internal friction is included, we find that the EMP decreases as the friction coefficient increases.
We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite duration of each stroke affects the engine performance. We show that partial thermalization can in fact enhance the efficiency of the engine, due to the residual coherence, whereas faster expansion and compression strokes increase the inner friction and therefore reduce the efficiency.
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.
Quantum refrigerators (QRs) are pivotal in exploring thermodynamic behavior at microscopic scales. This study investigates a quantum Otto refrigerator using a bosonic gas confined in a cubic potential, operating under finite-time thermalization. We derive key thermodynamic quantities analytically, including the coefficient of performance (COP), cooling power, entropy, and cooling rate. Additionally, we investigate how partial thermalization during the isochoric heating and cooling stages influences overall system performance. The findings reveal a trade-off between COP and cooling power, emphasizing the importance of thermalization duration. Notably, by extending the cooling time relative to heating, the COP can be significantly improved, offering a practical approach to optimizing QR performance under realistic conditions.
This thesis studies a finite-time quantum Otto refrigerator with an ideal Bose gas confined in a three-dimensional cubic trap. Finite thermal contact times with the hot and cold reservoirs lead to partial thermalization during the isovolume processes, causing deviations from the quasistatic regime. The effects of trap volume ratio \kappa and thermalization time on the system performance are analyzed. The results show that the coefficient of performance (COP) decreases monotonically with increasing \kappa, due to enhanced work input associated with spectral deformation during the isentropic processes, while heat extraction from the cold reservoir remains limited. A clear trade-off between the cooling rate and COP is observed, where higher efficiency is achieved at the expense of cooling power. Entropy production analysis indicates that near-reversible operation occurs when the heating and cooling durations are comparable, whereas prolonged heating increases irreversibility and degrades performance. These findings highlight the important role of trap geometry and partial thermalization in determining the performance of finite-time quantum refrigeration systems.
An analytical study of a feedback-driven quantum engine based on a two-level system is presented. This engine is similar to a quantum Otto engine but substitutes the quantum isochoric process with a feedback-driven operation based on a measured observable $A(\ensuremath{\theta})$, whose eigenstates are coherent superpositions of energy eigenstates. Projective measurements control the feedback operations, while work extraction or heat absorption occurs during driven operations. We derive the general time-dependent efficiency, power, and power fluctuations. Quantum coherence is examined through three mechanisms: (i) coherence associated with $\ensuremath{\theta}\ensuremath{\ne}0$, (ii) residual coherence after incomplete thermalization, and (iii) coherence generated by the interaction between the system and a coherent laser pulse on resonance. We investigate how the parameter $\ensuremath{\theta}$, quantum coherence, and timing of unitary and feedback-driven strokes influence engine performance. We demonstrate that quantum coherence can significantly enhance power output and efficiency while reducing fluctuations through optimal cycle parameter adjustments.