Search

We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent work fluctuations, average work, and thermodynamic efficiency are explicitly obtained for a complete cycle operating with an analytically solvable two-level system. The effects of the irreversibility originating from finite-time cycle operation on the thermodynamic efficiency, work fluctuations, and relative power fluctuations are discussed.

A three-terminal refrigerator based on resonant-tunneling quantum wells is proposed. With the help of the Landauer formula, the expressions for the cooling rate and the coefficient of performance (COP) are derived. The working regions of the refrigerator are determined and the three-dimensional projection graphs of the cooling rate and the COP varying with the positions of the two energy levels are plotted. Moreover, the influence of the bias voltage, the asymmetric factor, and the temperature difference on the optimal performance parameters is analyzed in detail. Finally, the performance characteristics of the refrigerator in the case of negative temperature difference are discussed.

A quantum Otto engine using two-interacting spins as its working medium is analyzed within framework of stochastic thermodynamics. The time-dependent power fluctuations and average power are explicitly derived for a complete cycle of engine operation. We find that the efficiency and power fluctuations are affected significantly by interparticle interactions, but both of them become interaction-independent under maximal power via optimizing the external control parameter. The behavior of the efficiency at maximum power is further explained by analyzing the optimal protocol of the engine.

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.

We investigate the finite-power performance of quantum heat engines working in the linear response regime where the temperature gradient is small. The engine cycles with working substances of ideal harmonic systems consist of two heat transfer and two adiabatic processes, such as the Carnot cycle, Otto cycle, and Brayton cycle. By analyzing the optimal protocol under maximum power we derive the explicitly analytic expression for the irreversible entropy production, which becomes the low dissipation form in the long duration limit. Assuming the engine to be endoreversible, we derive the universal expression for the efficiency at maximum power, which agrees well with that obtained from the phenomenological heat transfer laws holding in the classical thermodynamics. Through appropriate identification of the thermodynamic fluxes and forces that a linear relation connects, we find that the quantum engines under consideration are tightly coupled, and the universality of efficiency at maximum power is confirmed at the linear order in the temperature gradient.

We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures β_{h} and β_{c}(>β_{h}) with (k_{B}≡1)β=1/T. We derive the analytical expressions for work, efficiency, power, and power fluctuations, in which the squeezing parameter is involved. By optimizing the power output with respect to two frequencies, we derive the efficiency at maximum power as η_{mp}=(η_{C}^{gen})^{2}/[η_{C}^{gen}-(1-η_{C}^{gen})ln(1-η_{C}^{gen})], where the generalized Carnot efficiency η_{C}^{gen} in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter γ: η_{C}^{gen}=1-β_{h}/[β_{c}cosh(2γ)]. Within the context of irreversible thermodynamics, we demonstrate that the expression of efficiency at maximum power satisfies a general form derived from nonlinear steady state heat engines. We show that, the power fluctuations are considerably increased, although the engine efficiency is enhanced by squeezing.

In this paper, the model of a three-terminal quantum dot heat engine consists of two quantum dots with a single energy level, a cavity and two electron reservoirs is established. According to Landauer formula the expressions for the heat current, the output power and the efficiency are derived analytically. The performance characteristic curves of the output power versus the efficiency are plotted by numerical calculation. Moreover, the optimal performance parameters are determined. Then we optimize the output power and the efficiency respectively, the influence of the width of energy level and the heat leak on performance of the three-terminal thermoelectric heat engine is discussed. Lastly, the variation of the corresponding efficiency at the maximum power output with the Carnot efficiency between two reservoirs is discussed and the corresponding efficiency is compared with Carnot efficiency and CA efficiency. It is shown that this three-terminal heat engine is irreversible due to the existence of the width of energy level and the heat leak. Thus the curve of the power output versus the efficiency is a loop-shaped one. And due to the heat leak, the characteristics of the efficiency and the width of energy level is a non-monotone curve. The efficiency at the maximum power will be greater than the CA efficiency when the heat leak and the width of energy level are not taken into account.

We propose a quantum-mechanical Brayton engine model that works between two superposed states, employing a single particle confined in an arbitrary power-law trap as the working substance. Applying the superposition principle, we obtain the explicit expressions of the power and efficiency, and find that the efficiency at maximum power is bounded from above by the function: η+ = θ/(θ + 1), with θ being a potential-dependent exponent.

We study the minimally nonlinear irreversible heat engines in which the time-reversal symmetry for the systems may be broken. The expressions for the power and the efficiency are derived, in which the effects of the nonlinear terms due to dissipations are included. We show that, as within the linear responses, the minimally nonlinear irreversible heat engines can enable attainment of Carnot efficiency at positive power. We also find that the Curzon-Ahlborn limit imposed on the efficiency at maximum power can be overcome if the time-reversal symmetry is broken.

We study the performance of a cyclic heat engine which uses a small system with a finite number of ultracold atoms as its working substance and works between two heat reservoirs at constant temperatures T h and T c (

We analyze general models of quantum heat engines operating a cycle of two adiabatic and two isothermal processes. We use the quantum master equation for a system to describe heat transfer current during a thermodynamic process in contact with a heat reservoir, with no use of phenomenological thermal conduction. We apply the endoreversibility description to such engine models working in the linear response regime and derive expressions of the efficiency and the power. By analyzing the entropy production rate along a single cycle, we identify the thermodynamic flux and force that a linear relation connects. From maximizing the power output, we find that such heat engines satisfy the tight-coupling condition and the efficiency at maximum power agrees with the Curzon-Ahlborn efficiency known as the upper bound in the linear response regime.

We derive an exact recursive scheme to determine exactly the microcanonical partition function of a finite Bose system. Such a recursive approach is identical to that previously obtained within the context of counting statistics. Within the exact microcanonical ensemble, we study microcanonical finite-size scaling behaviors of condensate fraction and specific heat around the critical energy ϵ c for the finite ideal Bose system. We show that the microcanonical scaling functions governing the various critical behaviors are universal in the ideal Bose-Einstein condensates.

The performance in finite time of a quantum-mechanical Brayton engine cycle is discussed, without introduction of temperature. The engine model consists of two quantum isoenergetic and two quantum isobaric processes, and works with a single particle in a harmonic trap. Directly employing the finite-time thermodynamics, the efficiency at maximum power output is determined. Extending the harmonic trap to a power-law trap, we find that the efficiency at maximum power is independent of any parameter involved in the model, but depends on the confinement of the trapping potential.

A model of thermionic heat engine with the energy selective electron mechanism is studied. Analytical expressions of the power output and efficiency of this device are derived at low temperature, where the chemical potentials of the reservoirs are assumed to be constant. After discussing the impact of the energy spectrum width of the energy selective electron mechanism, we find two bounds ( η ± ) of efficiency at maximum power exist naturally. When the energy spectrum width increases gradually from zero and then to the semi-infinite case with the infinite upper limit, the efficiency at maximum power decreases monotonously from the upper bound η + to the lower bound η − at a given temperature ratio of the cold and hot reservoirs. The two bound are given by numerical simulation and by an analytical expression respectively. These results may provide some guidance for the application of the practical energy selective electron heat engines.

Based on a two-qubit Heisenberg XY model, we construct a four-level entangled quantum heat engine (QHE). It is an interesting quantum Otto cycle where the exchange constant is fixed and only the magnetic field is varied during the adiabatic steps. The expressions for several thermodynamic quantities such as the heat transferred, the work and the efficiency are derived. Moreover, the influence of the entanglement on the thermodynamic quantities is investigated numerically. Several interesting features of the variation of the heat transferred, the work and the efficiency with the concurrences of the thermal entanglement of different thermal equilibrium states are obtained. Finally, we discussed the maximum efficiency of the QHE.

Based on a two-qubit isotropic Heisenberg XXX model with a constant external magnetic field, we construct a four-level entangled quantum heat engine (QHE). The expressions for several thermodynamic quantities such as the heat transferred, the work and efficiency are derived. Moreover, the influence of the entanglement on the thermodynamic quantities is investigated analytically and numerically. Several interesting features of the variation of the heat transferred, the work and the efficiency with the concurrences of the thermal entanglement of different thermal equilibrium states are obtained.

Within an exact canonical-ensemble treatment, we investigate the thermodynamics for a finite number of ideal bosons confined in a three-dimensional quartic trap. We calculate several physical quantities including the specific heat C N , chemical potential μ, condensate fraction 〈n 0〉/N, root-mean-square fluctuations δn 0 of the condensate population, and transition temperature T c . We discuss the particle-number dependence of T c through proposing three T c definitions, which are compared with ones derived in the grand canonical ensemble.

Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number N of particles trapped in a d-dimensional quartic potential. We find that the presence and nature of phase transition depend on the dimensionality of the quartic potential. Proposing three different definitions of transition temperature, we discuss either N or d dependence of transition temperature for the ideal Bose condensate in the d-dimensional quartic potential.

Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number of particles confined in a three-dimensional quartic trap. We show that the phase transition of an ideal Bose gas in the three-dimensional quartic trap is of third order for finite particle numbers, quite different from the fact that the phase transition is of first order in the thermodynamic limit. We discuss the effects of finite particle numbers on the nature of the phase transitions, and determine the dependence of transition temperature on particle number.

In a recent paper [A. Sisman, I. Muller, Phys. Lett. A 320 (2004) 360] the thermodynamic properties of ideal gases confined in a narrow box were examined theoretically. The so-called “thermosize effects” similar to thermoelectric effects, such as Seebeck-like thermosize effect, Peltier-like thermosize effect and Thomson-like thermosize effect, were analyzed. Like the thermoelectric generator, based on the thermosize effects we have established a model of micro/nano scaled ideal gas heat engine cycle which includes two isothermal and two isobaric processes. The expressions of power output and efficiency of this cycle in the two cases of reversible and irreversible heat exchange are derived and the optimal performance characteristics of the heat engine is discussed by some numerical example. The results obtained here will provide theoretical guidance for the design of micro/nano scaled device.

A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are discussed in brief.

An irreversible cycle model of a quantum heat engine with internal friction is established, which is composed of two adiabatic and two isomagnetic field processes. The working substance of the cycle consists of an ensemble of many non-interacting spin-1/2 systems. Based on a quantum master equation and semi-group approach, the general performance characteristics of the heat engine are investigated. The general expressions for several important parameters, such as the efficiency, power output, and rate of the entropy production, are derived. The performance of the cycle is optimized with respect to the temperatures of the working substance. By numerical solutions, the maximum power output and the corresponding parameters are calculated. The optimal regions of efficiency, temperatures of the working substance, and cycle period are determined. Moreover, the performance of the heat engine in the frictionless case is obtained, which is different from that in the friction case. Finally, the results obtained are generalized to the performance optimization of the heat engine working with spin-J systems.

We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures T(h) and T(c)(

We propose a quantum absorption refrigerator driven by photons. The model uses a four-level system as its working substance and couples simultaneously to hot, cold, and solar heat reservoirs. Explicit expressions for the cooling power ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{Q}}_{c}$ and coefficient of performance (COP) ${\ensuremath{\eta}}_{\text{COP}}$ are derived, with the purpose of revealing and optimizing the performance of the device. Our model runs most efficiently under the tight coupling condition, and it is consistent with the third law of thermodynamics in the limit $T\ensuremath{\rightarrow}0$.

The irreversible model of a quantum refrigeration cycle composed of two adiabatic and two isomagnetic field processes is established. The working substance in the cycle consists of many noninteracting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semi-group approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. It is found that the coefficient of performance of this cycle is close analogues of that of classical Carnot cycle. Some performance characteristics curves between the cooling rate and the maximum “temperature” ratio of the working substances are plotted. Further, at high temperatures the optimal relations of the cooling rate and the maximum cooling rate are analyzed in detail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of the quantum refrigerator using spin- J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot and Ericsson refrigeration cycles are derived analogously.

We consider the efficiency at maximum power of a quantum Otto engine, which uses a spin or a harmonic system as its working substance and works between two heat reservoirs at constant temperatures ${T}_{h}$ and ${T}_{c}$ $(l{T}_{h})$. Although the behavior of spin-$1/2$ system differs substantially from that of the harmonic system in that they obey two typical quantum statistics, the efficiencies at maximum power based on these two different kinds of quantum systems are bounded from the upper side by the same expression ${\ensuremath{\eta}}_{\mathrm{mp}}\ensuremath{\le}{\ensuremath{\eta}}_{+}\ensuremath{\equiv}{\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})ln(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$ with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$ as the Carnot efficiency. This expression ${\ensuremath{\eta}}_{\mathrm{mp}}$ possesses the same universality of the CA efficiency ${\ensuremath{\eta}}_{\mathrm{CA}}=1\ensuremath{-}\sqrt{1\ensuremath{-}{\ensuremath{\eta}}_{C}}$ at small relative temperature difference. Within the context of irreversible thermodynamics, we calculate the Onsager coefficients and show that the value of ${\ensuremath{\eta}}_{\mathrm{CA}}$ is indeed the upper bound of EMP for an Otto engine working in the linear-response regime.

The performance of the Ericsson refrigeration cycle using an ideal Fermi gas as the working substance, which is simply referred to as the Fermi Ericsson refrigeration cycle, is examined, based on the equation of state of an ideal Fermi gas. The inherent regenerative losses and the coefficient of performance (COP) of the cycle are calculated. Three special cases are discussed in detail. It is found that under the conditions of low and high temperatures, the COP of the cycle is only a function of temperature, while under other conditions, the COP of the cycle is not only a function of temperature, but also is dependent on the pressures and other parameters. The results obtained here may reveal the general performance characteristics of the Fermi Ericsson refrigeration cycle.

The influence of quantum degeneracy on the performance of a Stirling refrigeration cycle is investigated, based on the equation of state of an ideal Fermi gas. The inherent regenerative losses and the coefficient of performance (COP) of the cycle are calculated. It is found that, under the condition of strong gas degeneracy, the COP of the cycle in the first approximation is a function only of the temperatures of the heat reservoirs, while under other conditions, the COPs of the cycle depend on the temperatures of the heat reservoirs and other parameters of the cycle. The results obtained here reveal the general performance characteristics of a Stirling refrigeration cycle having a Fermi gas as its working substance.

We study the coefficient of performance (COP) and its bounds for a Carnot-like refrigerator working between two heat reservoirs at constant temperatures ${T}_{h}$ and ${T}_{c}$, under two optimization criteria $\ensuremath{\chi}$ and $\ensuremath{\Omega}$. In view of the fact that an ``adiabatic'' process usually takes finite time and is nonisentropic, the nonadiabatic dissipation and the finite time required for the adiabatic processes are taken into account by assuming low dissipation. For given optimization criteria, we find that the lower and upper bounds of the COP are the same as the corresponding ones obtained from the previous idealized models where any adiabatic process is undergone instantaneously with constant entropy. To describe some particular models with very fast adiabatic transitions, we also consider the influence of the nonadiabatic dissipation on the bounds of the COP, under the assumption that the irreversible entropy production in the adiabatic process is constant and independent of time. Our theoretical predictions match the observed COPs of real refrigerators more closely than the ones derived in the previous models, providing a strong argument in favor of our approach.

We consider the finite-time operation of a quantum heat engine whose working substance is composed of a two-level atomic system. The engine cycle, consisting of two quantum adiabatic and two quantum isochoric (constant-frequency) processes and working between two heat reservoirs at temperatures T(h) and T(c)(

A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ε(CA)=(1/√[1-τ])-1. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ε(CA) and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.

In this paper, we propose a pair of symmetric three-terminal refrigerator models with a hot cavity connected to two colder reservoirs via ideal tunneling quantum dots. The cooling of the refrigerators is achieved by investing thermal power from a hot reservoir and electric power from an applied voltage. Based on the model proposed, we numerically analyze the performance of the refrigerators with different half width of energy levels, and particularly discuss the coefficient of performance for zero applied voltage in the limit of a small half level width. Finally, we optimize with half width of energy levels and get the optimal region of the refrigerators.

本文研究了一种由周期性非均匀线性温场所驱动的布朗制冷机性能特征. 利用布朗粒子的动力学方程——Langevin equation, 获得了稳态时布朗制冷机的粒子流、制冷率和制冷系数的解析表达式. 通过数值计算分析了势垒高度、非对称性、外力和温比等参数对制冷机性能的影响. 在最大品质因子条件下, 对制冷机性能参数进行优化, 画出了优化的制冷系数和制冷率随温比的演化曲线. 研究表明: 在准静态极限下, 制冷系数趋于用等效温度给出的卡诺制冷系数, 制冷率趋于零; 制冷系数随制冷率增加而减少; 优化的制冷系数随温比减小而下降, 而对应的制冷率却相反; 相比于在分段均匀温度场中, 非均匀线性温度场将导致制冷系数的提高.

We generalize the quantum heat engine (QHE) model which was first proposed by Bender et al. [J. Phys. A 33, 4427 (2000)] to the case in which an ideal Fermi gas with an arbitrary number N of particles in a box trap is used as the working substance. Besides two quantum adiabatic processes, the engine model contains two isoenergetic processes, during which the particles are coupled to energy baths at a high constant energy E(h) and a low constant energy E(c), respectively. Directly employing the finite-time thermodynamics, we find that the power output is enhanced by increasing particle number N (or decreasing minimum trap size L(A)) for given L(A) (or N), without reduction in the efficiency. By use of global optimization, the efficiency at possible maximum power output (EPMP) is found to be universal and independent of any parameter contained in the engine model. For an engine model with any particle-number N, the efficiency at maximum power output (EMP) can be determined under the condition that it should be closest to the EPMP. Moreover, we extend the heat engine to a more general multilevel engine model with an arbitrary 1D power-law potential. Comparison between our engine model and the Carnot cycle shows that, under the same conditions, the efficiency η = 1 - E(c)/E(h) of the engine cycle is bounded from above the Carnot value η(c) =1 - T(c)/T(h).

We establish a quantum Otto engine (QOE) of a two-level atom, which is confined in a one-dimensional (1D) harmonic trap and is coupled to single-mode radiation fields. Besides two adiabatic processes, the QOE cycle consists of two isochoric processes, along one of which the two-level atom as the working substance interacts with a single-mode radiation field. Based on the semigroup approach, we derive the time for completing any adiabatic process and then present a performance analysis of the heat engine model. Furthermore, we generalize the results to the performance optimization for a QOE of a single two-level atom trapped in a 1D power-law potential. Our result shows that the efficiency at maximum power output is dependent on the trap exponent $\ensuremath{\theta}$ but is independent of the energy spectrum index $\ensuremath{\sigma}$.

Based on counting statistics and Bogoliubov theory, we present a recurrence relation for the microcanonical partition function for a weakly interacting Bose gas with a finite number of particles in a cubic box. According to this microcanonical partition function, we calculate numerically the distribution function, condensate fraction, and condensate fluctuations for a finite and isolated Bose-Einstein condensate. For ideal and weakly interacting Bose gases, we compare the condensate fluctuations with those in the canonical ensemble. The present approach yields an accurate account of the condensate fluctuations for temperatures close to the critical region. We emphasize that the interactions between excited atoms turn out to be important for moderate temperatures.

We present a performance analysis of a two-state heat engine model working with a single-mode radiation field in a cavity. The heat engine cycle consists of two adiabatic and two isoenergetic processes. Assuming the wall of the potential moves at a very slow speed, we determine the optimization region and the positive work condition of the heat engine model. Furthermore, we generalize the results to the performance optimization for a two-state heat engine with a one-dimensional power-law potential. Based on the generalized model with an arbitrary one-dimensional potential, we obtain the expression of efficiency as $\ensuremath{\eta}=1\ensuremath{-}\frac{{E}_{C}}{{E}_{H}}$, with ${E}_{H}$ (${E}_{C}$) denoting the expectation value of the system Hamiltonian along the isoenergetic process at high (low) energy. This expression is an analog of the classical thermodynamical result of Carnot, ${\ensuremath{\eta}}_{c}=1\ensuremath{-}\frac{{T}_{C}}{{T}_{H}}$, with ${T}_{H}$ (${T}_{C}$) being the temperature along the isothermal process at high (low) temperature. We prove that under the same conditions, the efficiency $\ensuremath{\eta}=1\ensuremath{-}\frac{{E}_{C}}{{E}_{H}}$ is bounded from above the Carnot efficiency, ${\ensuremath{\eta}}_{c}=1\ensuremath{-}\frac{{T}_{C}}{{T}_{H}}$, and even quantum dynamics is reversible.

We study a Feynman-like thermal Brownian motor, in which the asymmetric corrugated cylinder as the ratchet is coupled with a corrugated plate by the noncontact Casimir interaction between them. The source of driving of the system is the thermal fluctuations and its dynamic evolution is described by a set of Langevin equations. Further, the mean velocity and thermal efficiency of the motor in the overdamped limit are studied in detail as a function of the temperature of the baths, external load applied, magnitude of the Casimir interaction, and other relevant parameters by the numerical stimulation. The transport properties attained here and the essential roles of the Casimir interaction can be explicitly demonstrated by designing a Casimir Brownian motor with present nanotechnology.

We present an approach to the energetics of a diode based on the Langevin equation for an ideal $RC$ circuit and establish a simple model consisting of two diodes switched in the same directions located in two heat reservoirs with different temperatures. We calculate the thermoelectric voltage and the efficiency of the diode system as a fluctuation rectifier and show the efficiency is always smaller than the Carnot value, thus, indicating the irreversible mode of operation. The Carnot efficiency is achieved only when the diode works as the normal resistor.

The simple system of two two-level identical atoms couple to single-mode optical cavity in the resonance case is studied for investigating the thermal entanglement. It is interesting to see that the critical temperature is only dependent on the coefficient of atom-atom dipole-dipole interaction. Based on the mode, we construct and investigate a entangled quantum Otto engine (QOE). Expressions for several important performance parameters such as the heat transferred, the work done in a cycle, and the efficiency of the entangled QOE in zero G are derived in terms of thermal concurrence. Some intriguing features and their qualitative explanations are given. Furthermore, the validity of the second law of thermodynamics is confirmed in the entangled QOE. The results obtained here have general significance and will be helpful to understand deeply the performance of an entangled QOE.

Based on quantum thermodynamic processes, we make a quantum-mechanical (QM) extension of the typical heat engine cycles, such as the Carnot, Brayton, Otto, Diesel cycles, etc., with no introduction of the concept of temperature. When these QM engine cycles are implemented by an ideal gas confined in an arbitrary power-law trap, a relation between the quantum adiabatic exponent and trap exponent is found. The differences and similarities between the efficiency of a given QM engine cycle and its classical counterpart are revealed and discussed.