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Nuclear Physics B

Quantum Stirling cycle with spin-chain-star working fluid

Salwa L. Alkhayyat, M. D. Alsulami, Hanaa Abu-Zinadah, Eied Mahmoud Khalil

Published Jul 27, 2026• 0 citations
Publisher

Abstract

We investigate a quasi-static quantum Stirling cycle employing a spin-chain-star working fluid, comprising a central ancilla coupled to multiple Heisenberg chains via anisotropic exchange. A unitary transformation reduces the many-body thermodynamics to exact diagonalisation within a Hilbert space of dimension two to the power of the chain number plus one. We evaluate purely transverse, isotropic in-plane, and fully anisotropic configurations. The cycle exhibits tunable heat engine, refrigerator, and quantum accelerator regimes governed by ancilla frequency and coupling strength disparities. The transverse configuration demonstrates superior engine performance approaching the Carnot limit, corroborated by a closed-form partition function that permits the engine-refrigerator boundary to be evaluated exactly at arbitrary chain number. Conversely, the fully anisotropic architecture undergoes a genuine many-body crossover from engine to refrigerator with escalating chain multiplicity, driven by collective coupling amplification. Regenerator functionality proves non-ideal, rendering the cycle irreversible. Perfect regeneration emerges only along a precise quantum resonance locus where isochoric heat exchanges balance. Deviating from this condition exacerbates thermal imbalance with increasing system size, constituting the primary irreversibility source. Finally, kinematic coherence maximizes during cold-bath compression and amplifies with anisotropy and chain number. Originating from Hamiltonian basis rotation rather than non-equilibrium dynamics, this coherence remains dissociated from thermodynamic efficacy.

DOI
10.1016/j.nuclphysb.2026.117606

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We investigate a quasi-static quantum Stirling cycle employing a spin-chain-star working fluid, comprising a central ancilla coupled to multiple Heisenberg chains via anisotropic exchange. A unitary transformation reduces the many-body thermodynamics to exact diagonalisation within a Hilbert space of dimension two to the power of the chain number plus one. We evaluate purely transverse, isotropic in-plane, and fully anisotropic configurations. The cycle exhibits tunable heat engine, refrigerator, and quantum accelerator regimes governed by ancilla frequency and coupling strength disparities. The transverse configuration demonstrates superior engine performance approaching the Carnot limit, corroborated by a closed-form partition function that permits the engine-refrigerator boundary to be evaluated exactly at arbitrary chain number. Conversely, the fully anisotropic architecture undergoes a genuine many-body crossover from engine to refrigerator with escalating chain multiplicity, driven by collective coupling amplification. Regenerator functionality proves non-ideal, rendering the cycle irreversible. Perfect regeneration emerges only along a precise quantum resonance locus where isochoric heat exchanges balance. Deviating from this condition exacerbates thermal imbalance with increasing system size, constituting the primary irreversibility source. Finally, kinematic coherence maximizes during cold-bath compression and amplifies with anisotropy and chain number. Originating from Hamiltonian basis rotation rather than non-equilibrium dynamics, this coherence remains dissociated from thermodynamic efficacy.
Abstract We study the thermodynamic performance of a finite-time non-regenerative quantum Stirling-like cycle used as a heat engine. We consider specifically the case in which the working substance (WS) is a two-level system (TLS). The Stirling cycle is made of two isochoric transformations separated by a compression and an expansion stroke during which the WS is in contact with a thermal reservoir. To describe these two strokes we derive a non-Markovian master equation which allows to study the real-time dynamics of a driven open quantum system with arbitrary fast driving. Following the real-time dynamics of the WS using this master equation, the endpoints of the isotherms can deviate from the equilibrium thermal states. The role of this deviation in the performance of the heat engine is addressed. We found that the finite-time dynamics and thermodynamics of the cycle depend non-trivially on the different time scales at play. In particular, driving the WS at a time scale comparable to the resonance time of the bath enhances the performance of the cycle and allows for an efficiency higher than the efficiency of the quasistatic cycle, but still below the Carnot bound. However, by adding thermalization of the WS with the baths at the end of compression/expansion processes one recovers the conventional scenario in which efficiency decreases by speeding up the processes. In addition, the performance of the cycle is dependent on the compression/expansion speeds asymmetrically, which suggests new freedom in optimizing quantum heat engines. The maximum output power and the maximum efficiency are obtained almost simultaneously when the real-time endpoints of the compression/expansion processes are considered instead of the equilibrium thermal endpoint states. However, the net extractable work always declines by speeding up the drive.
We investigate a quantum thermal machine composed of two qubits coupled through a Raman-induced exchange interaction and driven by inhomogeneous transition frequencies. The system is analyzed within Carnot, Otto, and Stirling thermodynamic cycles, including the Stirling cycle with and without regeneration. We identify the conditions under which the device operates as a heat engine, refrigerator, thermal accelerator, or heater. Efficiency maps and operational-mode diagrams reveal well-defined boundaries in parameter space, governed by the frequency ratio r=ωˉ/ωr=\barω/ωr=ωˉ/ω, the coupling strength ggg, and the thermal gradient between reservoirs. The Carnot cycle exhibits sharp transitions between engine and refrigerator regimes, while the Otto cycle displays a richer structure with the coexistence of all operational modes. The Stirling cycle shows enhanced versatility and performance, particularly when assisted by a regenerator, where near-ideal efficiencies are achieved. Overall, the Raman-type interaction introduces a controllable left-right asymmetry that enables nontrivial manipulation of thermodynamic behavior through frequency tuning.
Abstract This study investigates a theoretical model of a Quantum Otto Cycle (QOC) that utilizes a working fluid spin‐chain‐star model. The system consists of a central atom interacting with multiple Heisenberg spin chains. Employing unitary transformations, the spin‐chain‐star system is transformed into a spin‐star model. The work done and heat transferred for three distinct working fluid configurations: the , , and cases are discussed. The efficiency of the heat engine is examined, and a comparative study between the efficiencies of the three configurations is presented. The study assumes two interaction scenarios for the central atom: either with a single chain (resulting in a two‐qubit system after transformation) or with three Heisenberg chains. The results demonstrate that increasing the ratio between the central atom's frequency in the hot bath and the cold bath leads to an enhancement in positive work performed for the and cases. In the case, the magnitude of this enhancement exhibits a dependence on the system's temperature. The QOC employing the configuration working fluid exhibits superior efficiency compared to the other two configurations. Moreover, increasing the central atom's relative frequency improves efficiency for all three cases.
We compute the efficiency of the reversible Stirling engine, with and without regeneration, for a broad class of working substances including Van der Waals fluids, quantum ideal gases (Bose and Fermi), Bose-Einstein condensates, thermal conformal field theories (CFTs), and holographic CFTs. Regeneration acts as an internal heat recycling mechanism that enhances efficiency by reducing the net heat exchange with external reservoirs. For regenerative Stirling cycles, we identify a general sufficient condition for attaining Carnot efficiency: at fixed conserved charges, the fixed-volume heat capacity is independent of volume. This ensures that, at each temperature along the isochores, the heat released during cooling equals the heat absorbed during heating. An ideal regenerator can therefore store and return this heat reversibly, returning to its initial thermodynamic state with no net change in energy or entropy. While this condition is satisfied for classical ideal gases and Van der Waals fluids, it is violated for quantum ideal gases and CFT working substances. For thermal CFT states dual to AdS-Schwarzschild and AdS-Reissner-Nordstrom black holes, we obtain exact expressions for the Stirling efficiency. In the fixed-potential ensemble, both the regenerative and non-regenerative efficiencies approach the Carnot value in the large-potential limit. Regeneration reduces the leading deviation from the Carnot value, although both efficiencies have corrections of the same asymptotic order.
This study investigates the anisotropic effects on a system of three qubits with chain and ring topology, described by the antiferromagnetic Heisenberg XXX model subjected to a homogeneous magnetic field. We explore the Stirling and Otto cycles and find that easy-axis anisotropy significantly enhances engine efficiency across all cases. At low temperatures, the ring configuration outperforms the chain on both work and efficiency during the Stirling cycle. Additionally, in both topologies, the Stirling cycle achieves Carnot efficiency with finite work at quantum critical points. In contrast, the quasistatic Otto engine also reaches Carnot efficiency at these points but yields no useful work. Notably, the Stirling cycle exhibits all thermal operational regimes-engine, refrigerator, heater, and accelerator-unlike the quasistatic Otto cycle, which functions only as an engine or refrigerator.
We propose a quantum heat engine based on a two-component Fermi gas with s-wave contact interaction, operating across the BCS-BEC crossover. The work is extracted from the statistical properties of the gas, which are controlled by the interaction, rather than relying solely on compression and expansion stages. Using the functional renormalization group formalism, we obtain the equation of state in a non-perturbative form along the crossover, encompassing the superfluid-normal phase transition. The cycle combines isentropic density strokes, isochoric thermalization, and isothermal interaction sweeps. This construction makes it possible to integrate features of both Otto and Carnot cycles, in which the system simultaneously saturates both efficiency limits without the net work vanishing. In the absence of density variations, the cycle reduces to a statistical Stirling-like engine, in which the work generated arises exclusively from the interaction, achieving efficiencies up to 38%38\%38%. A pronounced asymmetry emerges through the crossover, giving rise to distinct operating regimes depending on the trajectory followed in the phase diagram. Consequently, the same architecture can be tuned to function as an engine, refrigerator, accelerator, or heater. These findings highlight pairing correlations as a versatile thermodynamic resource for quantum heat machines.