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A quantum heat engine (QHE) model by considering as working substance two spins (spin-1, spin-$\frac{1}{2}$) is proposed. It consists of using different Heisenberg models with the Dzyaloshinskii-Moriya (DM) interaction in the presence of magnetic field $B$. The proposed model contains four stroke two isochoric and two others adiabatic. A comparison of different models such that $XXX$, $XXZ$ and $XYZ$ is examined for various thermodynamics quantities, especially the efficiency $\eta$ and work $W$. Finally, discussion and interpretation all results are given in the last section.

In this paper, the effects of identical particles and energy-level degeneracy on the work output of the quantum Otto and Stirling heat engines are studied. For quantum Otto heat engine, we find the effects of degeneracy in the ground state and in the excited state are same in the high-temperature limitation while the work done by a system with n-fold degeneracy in the excited state (ground state) is n ($1∕n$) times the one without degeneracy in the single-particle case. Moreover, the effects of the identical two-level systems with degeneracy in the ground state or excited state as working substances are discussed. The results of such problem for the Stirling and Carnot heat engines are similar. By analytical derivations in two limit conditions, we conclude that for the cycles which are composed of the quantum adiabatic process, isochoric process and isothermal process have similar results.

The two-level quantum heat engines have been studied extensively. Before that, the optimization of most heat engines was mainly concentrated in non-degenerate cases. We consider the level degeneracy, then calculate the maximum operation time and the irreversible dissipation coefficient of the two-level system under the scheme of linear tuned levels. In the high-temperature limit, we find that the level degeneracy affects the maximum power of the two-level heat engine. Especially in the case of the same degeneracy of the ground state and the excited state, the influence is the greatest. In addition, we also show that the degeneracy does not affect the efficiency at maximum power and the consistent relation of the two-level Carnot-like heat engine.

A device — referred to as a photonic quantum heat engine — was reported in Nature Photonics [J. Kim, S. Oh, D. Yang, J. Kim, M. Lee and K. An, A photonic quantum engine driven by superradiance, Nat. Photon. 16 (2022) 707–711] with an efficiency of $98\pm 4$%. Moreover, in a related News & Views contribution in the same issue [M. Kim, M. Scully and A. Svidzinsky, A supercharged photonic quantum heat engine, Nat. Photon. 16 (2022) 669–670], this device was reported to exceed the Carnot limit, an extraordinary claim. As Carl Sagan once remarked, “Extraordinary claims require extraordinary evidence.” Here, we outline the fundamental lack of empirical evidence that would be required to support such a claim, show that the actual efficiency of the device is $\sim$ 0% and bring to attention critical aspects of the operating physics of the device.

The four-level entangled quantum heat engine (QHE) is analyzed in the various Heisenberg models for a two-qubit. The QHE is examined for the XX, XXX and XXZ Heisenberg models by introducing a parameter x which controls the strength of the exchange parameter J_z = xJ along the z-axis with respect to the ones along the x- and y-axes, i.e. J_x = J_y = J, respectively. It is assumed that the two-qubit is entangled and in contact with two heat reservoirs at different temperatures and under the effect of a constant magnetic field. The concurrences (C) are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency of the QHE are derived. The contour, i.e. the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are calculated and some interesting features are found.