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.
Comments
28 pages, 8 figures. All numerical calculations, symbolic verifications, and figure generation were performed using open-source Python libraries (NumPy, SciPy, Matplotlib). No proprietary commercial software was used in the production of this work. The complete Python source code is available from the corresponding author upon reasonable request
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.
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.
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.
We investigate the energetic and thermodynamic performance of an interacting two-qubit system serving as both a quantum battery and a quantum Otto heat engine. The working medium is described by an anisotropic Heisenberg Hamiltonian supplemented by a dipolar interaction, a symmetric spin--orbit interaction, and an external magnetic field. Within a unified microscopic framework, we first analyze a coherent unitary charging protocol and characterize the resulting energy-storage performance through the ergotropy, anti-ergotropy, charging power, storage capacity, and ℓ1-norm of quantum coherence. We investigate the effects of the dipolar interaction, temperature, and magnetic field on these quantities. We then employ the same working medium in a quantum Otto cycle and study the absorbed and released heat, net work, and thermodynamic efficiency as functions of the magnetic-field modulation, dipolar interaction, and temperature bias. A direct comparison between the two protocols reveals a pronounced contrast in their response to the dipolar interaction. In the investigated parameter regime, increasing the dipolar interaction substantially enhances the maximum ergotropy and storage capacity of the quantum battery, whereas the maximum work extracted per Otto cycle decreases. The Otto efficiency exhibits a nonmonotonic dependence on the dipolar interaction while remaining below the Carnot bound. These results demonstrate that an enhancement of quantum energy-storage capability does not necessarily imply an enhancement of heat-to-work conversion. Our findings highlight the complementary nature of quantum batteries and quantum heat engines and show how microscopic spin interactions can
be used to control different forms of quantum energy conversion within
the same physical platform.
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.
We investigate a quantum heat engine with a working substance of two particles, one with a spin-1/2 and the other with an arbitrary spin (spin s), coupled by Heisenberg exchange interaction, and subject to an external magnetic field. The engine operates in a quantum Otto cycle. Work harvested in the cycle and its efficiency are calculated using quantum thermodynamical definitions. It is found that the engine has higher efficiencies at higher spins and can harvest work at higher exchange interaction strengths. The role of exchange coupling and spin s on the work output and the thermal efficiency is studied in detail. In addition, the engine operation is analyzed from the perspective of local work and efficiency. We develop a general formalism to explore local thermodynamics applicable to any coupled bipartite system. Our general framework allows for examination of local thermodynamics even when global parameters of the system are varied in thermodynamic cycles. The generalized definitions of local and cooperative work are introduced by using mean field Hamiltonians. The general conditions for which the global work is not equal to the sum of the local works are given in terms of the covariance of the subsystems. Our coupled spin quantum Otto engine is used as an example of the general formalism.
Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.