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JURNAL ILMU FISIKA | UNIVERSITAS ANDALAS

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

Shofiyah Shofiyah, Trengginas Eka Putra Sutantyo, Zulfi Abdullah

Published Apr 24, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.25077/jif.18.2.117-128.2026

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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.
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 propose two algorithmic quantum Otto refrigerators (AQOR) in which the standard isochoric cooling stroke is replaced by two distinct heat-bath algorithmic cooling (HBAC) protocols based on the partner-pairing algorithm (PPA). For each protocol, we derive closed-form expressions for the target qubit's asymptotic polarization and explicitly incorporate the work performed by HBAC into the coefficient of performance (COP). We further quantify the thermodynamic cost of the HBAC stroke and Landauer's bound for both protocols. Our analytical COP curves reveal parameter regimes where the AQOR surpasses the conventional Otto refrigerator. Furthermore, we show that, by tuning the auxiliary qubit's transition frequency and adjusting external control parameters, both protocols achieve enhanced COP and extend the operational window across a wider range of bath temperature differences. Therefore, the AQORs present a tradeoff between achieving high performance in specific regimes and maintaining enhanced applicability. These results demonstrate that algorithmic cooling can be seamlessly integrated into Otto cycles to realize quantum thermal machines with improved practicality on near-term hardware.
The derivation of general performance benchmarks is important in the design of highly optimized heat engines and refrigerators. To obtain them, one may model phenomenologically the leading sources of irreversibility ending up with results that are model independent, but limited in scope. Alternatively, one can take a simple physical system realizing a thermodynamic cycle and assess its optimal operation from a complete microscopic description. We follow this approach in order to derive the coefficient of performance at maximum cooling rate for any endoreversible quantum refrigerator. At striking variance with the universality of the optimal efficiency of heat engines, we find that the cooling performance at maximum power is crucially determined by the details of the specific system-bath interaction mechanism. A closed analytical benchmark is found for endoreversible refrigerators weakly coupled to unstructured bosonic heat baths: an ubiquitous case study in quantum thermodynamics.
Abstract Finite-time cycle period for a quantum Otto machine implies that either an adiabatic stroke or an isochoric process proceeds in finite time duration. The quantum Otto refrigerators under consideration consist of two adiabatic strokes, where the system (isolated from the heat reservoir) undergoes finite-time unitary transformation, and two isochoric steps, where the system may not reach thermal equilibrium even at the respective ends of the two stages due to finite-time interaction intervals. Using two-time projective measurement method, we find the probability distribution functions of both coefficient of performance and cooling load, which are dependent on the time duration along each process. With these distributions we find the analytical expressions for the performance parameters as well as their fluctuations. We then numerically determine the performance and fluctuations for the refrigerator operating with a two-level system employed in a recent experimental implementation. Our results clarify the role of finite-time durations of four processes on the performance and fluctuations of the quantum Otto refrigerators.
The study of nanoscopic thermal devices attracts an increasing attention, not only because of their key role in understanding the emergence of thermodynamics from quantum theory, but also for the potential use of quantum-mechanical thermal cycles, especially refrigerators, in quantum technologies. This thesis, is devoted to the performance optimization of autonomous (heat-driven) refrigerators. For a quantum refrigerator, one has a full microscopic description of the simple system serving as a working medium, and of its interaction with the external heat baths. This enables a consistent `finite-time? thermodynamic analysis, not relying on any phenomenological assumptions about the leading sources of irreversibility, and allows to establish arguably general performance bounds, essential to benchmark the operation of realistic devices. In particular, tight and model-independent upper bounds for the coefficient of performance at maximum power, are derived here for a class of strongly coupled refrigerators, and seen to hold more generally for other types of heat and power-driven cycles. Remarkably, these ultimate limitations only depend on the particulars of the system-baths interaction at the interface with the object to be cooled. Strategies might be then defined so as to saturate those limits: It is shown how the working medium of the refrigerator may be, for instance, scaled up into a parallel multi-stage configuration, resembling that of macroscopic multi-effect absorption chillers, as a means to increase its cooling power. Similarly, by applying reservoir engineering techniques on selected transitions between the energy states of the working medium, one can mimic exploitable non-equilibrium fluctuations in the baths, capable of boosting the overall power and COP beyond what would be otherwise allowed by the second law of thermodynamics. In this way, heat-driven chillers could be set to compete on a equal footing with the best power-driven refrigerators.