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Journal of Physics B Atomic Molecular and Optical Physics

Quantum Otto engine powered by two-spin Heisenberg chain with Zeeman energy and symmetric cross spin

L. Mashhor, Mahmoud Youssef Abd‐Rabbou, K A Dib, Mahmoud Abdel‐Aty, A.‐S. F. Obada

Published Nov 19, 2025• 3 citations
Publisher

Abstract

Abstract This paper proposes a theoretical model for a heat engine operating on the Otto cycle, employing a two-qubit Heisenberg chain as its working substance. This system is subjected to an external, time-dependent homogeneous magnetic field and a symmetric cross-spin interaction. The interaction is configured to occur along two distinct orientations, contingent upon the direction of Zeeman energy and symmetric interaction: either exclusively along the X -direction or exclusively along the Z -direction. Furthermore, the thermal reservoirs integral to the Otto engine are considered to engage with the working substance via two discrete modes: a localized interaction or a collective interaction. The two qubits exhibit weak coupling to a non-equilibrium thermal environment during the isochoric heating and cooling strokes, thereby validating the application of a Markovian model as a suitable approximation for describing the time evolution of the working substance. This study investigates the influence of various system parameters on the thermodynamic quantities and the resultant power output. A principal finding is that refrigeration functionality is the predominant operational characteristic when the system engages in collective interaction with the reservoirs. Conversely, localized interactions facilitate dual operational modes, with the sign of the Zeeman energy determining the function as either a refrigerator or a heat engine. Significantly, positive power output is achieved in the engine regime, and we find that the choice of interaction axis acts as a powerful amplification mechanism for the thermodynamic output, while the system-environment coupling scheme proves to be the most decisive factor in determining the machine’s fundamental purpose.

DOI
10.1088/1361-6455/ae216b

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Abstract This paper proposes a theoretical model for a heat engine operating on the Otto cycle, employing a two-qubit Heisenberg chain as its working substance. This system is subjected to an external, time-dependent homogeneous magnetic field and a symmetric cross-spin interaction. The interaction is configured to occur along two distinct orientations, contingent upon the direction of Zeeman energy and symmetric interaction: either exclusively along the X -direction or exclusively along the Z -direction. Furthermore, the thermal reservoirs integral to the Otto engine are considered to engage with the working substance via two discrete modes: a localized interaction or a collective interaction. The two qubits exhibit weak coupling to a non-equilibrium thermal environment during the isochoric heating and cooling strokes, thereby validating the application of a Markovian model as a suitable approximation for describing the time evolution of the working substance. This study investigates the influence of various system parameters on the thermodynamic quantities and the resultant power output. A principal finding is that refrigeration functionality is the predominant operational characteristic when the system engages in collective interaction with the reservoirs. Conversely, localized interactions facilitate dual operational modes, with the sign of the Zeeman energy determining the function as either a refrigerator or a heat engine. Significantly, positive power output is achieved in the engine regime, and we find that the choice of interaction axis acts as a powerful amplification mechanism for the thermodynamic output, while the system-environment coupling scheme proves to be the most decisive factor in determining the machine’s fundamental purpose.
Quantum Otto and Carnot engines have recently been receiving attention due to their ability to achieve high efficiencies and powers based on the laws of quantum mechanics. This paper discusses the theory, progress, and possible applications of quantum Otto and Carnot engines, such as energy production, cooling, and nanoscale technologies. In particular, we investigate a two-spin Heisenberg system that works as a substance in quantum Otto and Carnot cycles while exposed to an external magnetic field with both Dzyaloshinsky-Moriya and dipole-dipole interactions. The four stages of engine cycles are subject to analysis with respect to the heat exchanges that occur between the hot and cold reservoirs, alongside the work done during each stage. The operating conditions of the heat engine, refrigerator, thermal accelerator, and heater are all achieved. Moreover, our results demonstrate that the laws of thermodynamics are strictly upheld and the Carnot cycle produces more useful work than that of the Otto cycle.
We study a quantum Otto heat engine whose working substance is an anisotropic two-qubit Heisenberg XYZ model. Independent local magnetic fields are used to control each spin individually. The influence of the longitudinal coupling, anisotropy, transverse coupling, and local fields on the net work output and efficiency is systematically examined. Reducing the longitudinal coupling is found to markedly improve both the maximum work and the peak efficiency. The engine performance reaches an optimum at a particular value of the anisotropy parameter. A local work analysis clarifies how work is produced during the cycle. Because of the asymmetric local fields and the intrinsic spin-spin interaction, the two qubits play markedly different thermodynamic roles; the interaction term itself contributes crucially to the total work. We further analyze the variation of quantum entanglement, quantified by concurrence, along the cycle. The results indicate that a pronounced change in entanglement between the hot and cold isomagnetic strokes is closely correlated with the efficiency enhancement. This work offers new insight into the operating principles and control of quantum Otto heat engines.
Abstract We study a four-stroke Otto engine whose working fluid is a quantum Ising chain. The thermodynamic cycle consists in sweeps of the transverse magnetic field occurring in thermal isolation, alternated by thermalisation strokes with reservoirs at different temperatures. The system–environment coupling is modelled in a thermodynamically consistent way by means of a nonlocal Lindblad master equation. We show that the engine may operate in four different operation modes, depending on the various parameters, in particular it can act as a heat engine and as a refrigerator. We detect an enhancement of the thermodynamic performance as the critical point is crossed, and investigate it in detail.
We construct a special four-level entangled quantum Otto heat engine based on the two-qubit Heisenberg XX model, in which we assume that all the energy gaps are changed in the same ratio in the two quantum adiabatic processes. Hence during the whole cycle, the relative coupling constant κ = J / B is fixed, where J and B are the coupling constant and the external magnetic field, respectively. The dependence of the basic thermodynamical quantities on the two entanglements at the end of two quantum isochoric processes with different relative coupling constants κ is studied. Our results show that in the weak coupling region, i.e. κ < 1, the heat engine can be operated in both areas where c 1 < c 2 and c 1 > c 2 , whereas when κ ⩾ 1, it only operates under the condition c 1 < c 2 . Here c 1 and c 2 are entanglements of the working substance when it comes into contact with hot and cold baths, respectively. Moreover, we find that the maximal work output for fixed κ increases with the relative coupling constant.
Abstract This study investigates the quantum heat correlations associated with the quantum Otto machine, considering the discrete sides of the Lipkin-Meshkov-Glick model as the working medium in the presence of a magnetic field and a symmetric cross interaction. The eigenenergy and occupation probabilities of two-sided and three-sided spin interactions are determined at thermal equilibrium. The results reveal symmetrical heat correlations around the coupling of the symmetric cross interaction, regardless of whether the working medium adopts anisotropic XY, Ising model, or mixed ferromagnetism. The work done by two or three sides of the mixed ferromagnetic working substance exhibits symmetry but with different maximum bounds. Furthermore, the efficiency of the two-sided mixed ferromagnetism model improves as the exchange parameter increases, while the maximum efficiency of the anisotropic XY model is lower compared to the efficiency of the Ising model and mixed ferromagnetism. It is also highlighted that a quantum heat engine or refrigerator can be generated by controlling the system’s anisotropy parameter using a three-sided spin interaction.
We study quantum Otto thermal machines with a two-spin working system coupled by anisotropic interaction. Depending on the choice of different parameters, the quantum Otto cycle can function as different thermal machines, including a heat engine, refrigerator, accelerator, and heater. We aim to investigate how the anisotropy plays a fundamental role in the performance of the quantum Otto engine (QOE) operating in different timescales. We find that while the engine's efficiency increases with the increase in anisotropy for the quasistatic operation, quantum internal friction and incomplete thermalization degrade the performance in a finite-time cycle. Further, we study the quantum heat engine (QHE) with one of the spins (local spin) as the working system. We show that the efficiency of such an engine can surpass the standard quantum Otto limit, along with maximum power, thanks to the anisotropy. This can be attributed to quantum interference effects. We demonstrate that the enhanced performance of a local-spin QHE originates from the same interference effects, as in a measurement-based QOE for their finite-time operation.