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We investigate the thermodynamics and fluctuations of a finite-time quantum Otto engine alter- natively driven by a hot-squeezed and a cold thermal reservoir. We show that reservoir squeezing significantly enhances the performance by increasing the thermodynamic efficiency and the power and enables higher stability by decreasing the relative power fluctuations and speeding up the convergence of quantum efficiency to its most probable value. We also demonstrate the counterintuitive result that the efficiency can be larger than the Otto limit in the finite-time operation. Experimental demonstration of this quantum heat engine can be available, based on a single-electron spin pertaining to a trapped ^{40}Ca^{+} ion [D. von Lindenfels et al., Phys. Rev. Lett. 123, 080602 (2019)0031-900710.1103/PhysRevLett.123.080602]. We provide a general framework for reliably studying the finite-time nanoengine in finite-time operation which accounts for quantum friction and coherence, deriving important insights into the thermodynamic behaviors beyond the classical thermal machines.

We present a quantum Otto engine model alternatively driven by a hot and a cold heat reservoir and consisting of two isochoric and two adiabatic strokes, where the adiabatic expansion or compression is realized by adiabatically changing the shape of the potential. Here, we show that such an adiabatic deformation may alter operation mode and enhance machine performance by increasing output work and efficiency, even with the advantage of decreasing work fluctuations. If the heat engine in the sudden limit operates under maximal power by optimizing the control parameter, the efficiency shows certain universal behavior, η*=ηC/2+ηC2/8+O(ηC3), where ηC=1−βhr/βcr is the Carnot efficiency, with βhr(βcr) being the inverse temperature of the hot (cold) reservoir. However, such efficiency under maximal power can be produced by our machine model in the regimes where the machine without adiabatic deformation can only operate as a heater or a refrigerator.

Abstract 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 (

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 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 propose an Otto heat engine that undergoes processes involving a special class of feedback and analyze theoretically its response. We use stochastic thermodynamics to determine the performance characteristics of the heat engine and indicate the possibility that its maximum efficiency can surpass the Carnot value. The analytical expression for efficiency at maximum power, including the effects resulting from feedback, reduces to that previously derived based on an engine without feedback. [ABSTRACT FROM AUTHOR]

Theoretical thermoelectric nanophysics models of low-dimensional electronic heat engine and refrigerator devices, comprising two-dimensional hot and cold reservoirs and an interconnecting filtered electron transport mechanism have been established. The models were used to numerically simulate and evaluate the thermoelectric performance and energy conversion efficiencies of these low-dimensional devices, based on three different types of electron transport momentum-dependent filters, referred to herein as kx, ky, and kr filters. Assuming the Fermi-Dirac distribution of electrons, expressions for key thermoelectric performance parameters were derived for the resonant transport processes, in which the transmission of electrons has been approximated as a Lorentzian resonance function. Optimizations were carried out and the corresponding optimized design parameters have been determined, including but not limited to the universal theoretical upper bound of the efficiency at maximum power for heat engines, and the maximum coefficient of performance for refrigerators. From the results, it was determined that kr filter delivers the best thermoelectric performance, followed by the kx filter, and then the ky filter. For refrigerators with any one of three filters, an optimum range for the full width at half maximum of the transport resonance was found to be <2kBT. [ABSTRACT FROM AUTHOR]

The effects of the irreversibility and the compression ratio of the two isochoric processes on the performance of the Bose-Otto engine and optimization of some important performance parameters are discussed on the basis of the thermodynamic properties of ideal Bose gas. The evaluation and determination of the optimal operating regions including those for the power output, efficiency, and the temperatures of the cyclic working substance at two important state points are also discussed.

The quantum boundary effect of gas particles is considered as a working substance of cycle in order to calculate the work output (W) and efficiency ([eta]) of a Carnot cycle in micro-/nanoscale. The studies have shown that under the quantum boundary effect conditions, the work output cycle has depended sensitively on the surface area of the system and is not predicted by the classical approximate result, while the efficiency of cycle is independent of the surface area of the system and equals the Carnot efficiency.

The cycle model of a micro-/nanothermosize refrigerator composed of two isothermal and two isobaric processes is described, which is based on the so-called thermosize effects similar to thermoelectric effects. The results have provided theoretical guidance for designing of a micro-/nanoscaled refrigerator.

In this paper, the energy selective electron (ESE) refrigerator with an ideal energy filter based on resonant tunneling is established. It consists of two infinitely large electron reservoirs with different temperatures and chemical potentials, and electrons can be exchanged between the two reservoirs through the ideal energy filter. According to Landauer formula and the assumption of being coupled tightly with the electron current, the expressions for the heat flux, the cooling rate and the coefficient of performance (COP) are derived analytically. The performance characteristic curves such as the cooling rate versus coefficient of performance, the cooling rate and coefficient of performance versus the position of energy level are plotted by numerical calculation. The optimal regions of the cooling rate and the COP are determined. Moreover, we optimize the cooling rate and the COP respectively with respect to the position of energy level. The influence of the width of energy level on performance of the ESE refrigerator is discussed. Finally, based on the optimization criterion χ = γ ⋅ ...C for refrigerator, i.e. the product of the COP times the cooling rate, the optimal performance of the ESE refrigerator is discussed in detail. [ABSTRACT FROM AUTHOR]

We investigate the efficiency at the maximum power output (EMP) of an irreversible Carnot engine performing finite-time cycles between two reservoirs at constant temperatures Th, and Tc (

We study the efficiency at maximum power, &eegr;m, of irreversible quantum Camot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th and Tc., respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), &eegr;m becomes identical to the Carnot efficiency &eegr;c = 1 -- Tc/Th- For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabais are included, the efficiency &eegr;m at maximum power output is bounded from above by &eegr;c/(2 -- &eegr;c) and from below by &eegr;c/2. In the case of symmetric dissipation, the Curzon-Ahlbom efficiency &eegr;CA = 1 - √Tc/Th is recovered under the condition that the time allocation between the adiabais and the contact time with the reservoir satisfy a certain relation. [ABSTRACT FROM AUTHOR]

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 η = 1 - EC/EH, with EH (EC) 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, ηc = 1 - TC/TH, with TH (TC) being the temperature along the isothermal process at high (low) temperature. We prove that under the same conditions, the efficiency η = 1 - EC/EH is bounded from above the Carnot efficiency, ηc = 1 - TC/TH, and even quantum dynamics is reversible. [ABSTRACT FROM AUTHOR]

Based on counting statistics and Bogoliubov theory, we present a recurrence relation for the microcanonical partition function for a wealdy 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. [ABSTRACT FROM AUTHOR]

A general irreversible cycle model of a magnetic Ericsson refrigerator is established. The irreversibilities in the cycle model result from the finite-rate heat transfer between the working substance and the external heat reservoirs, the inherent regenerative loss, the additional regenerative loss due to thermal resistances, and the heat leak loss between the external heat reservoirs. The cycle model is used to optimize the performance of the magnetic Ericsson refrigeration cycle. The fundamental optimum relation between the cooling rate and the coefficient of performance of the cycle is derived. The maximum coefficient of performance, maximum cooling rate and other relevant important parameters are calculated. The optimal operating region of the cycle is determined. The results obtained here are very general and will be helpful for the optimal design and operation of the magnetic Ericsson refrigerators. [ABSTRACT FROM AUTHOR]

Analyzes the thermodynamic properties of the dielectric materials based on the Curie law, Curie-Weiss law and other relations between the electrical polarization and the electric field strength. Specific heat at constant polarization as only a function of temperature; Heat absorbed from low temperature reservoir; Regenerative characteristics.

The irreversibilities resulting from the finite-rate heat transfer between the working substance and the external heat reservoirs and the regenerative losses in regenerative processes are considered in the cycle model of a magnetic Ericsson refrigerator. The fundamental optimum relations between the cooling rate and the coefficient of performance and between the power input and the coefficient of performance are derived, based on a class of heat-transfer laws and the Curie law. The general characteristic curves of the cycle are presented. The effect of the different forms of the regenerative time and heat-transfer laws on the performance of the cycle is discussed in detail. The results obtained here will be useful to further understand the general optimum performance of real magnetic Ericsson refrigerators. [ABSTRACT FROM AUTHOR]

We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures βh and βc(>βh) with (kB≡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 ηmp=(ηgenC)2/[ηgenC-(1-ηgenC)ln(1-ηgenC)], where the generalized Carnot efficiency ηgenC in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter γ: ηgenC=1-βh/[βccosh(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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 Th and Tc (

A two-level atomic system as a working substance is used to set up a refrigerator consisting of two quantum adiabatic and two isochoric processes (two constant-frequency processes ωa and ωb with ωa < ωb), during which the two-level system is in contact with two heat reservoirs at temperatures Th, and Tc(

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 Th and Tc(

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 Eh and a low constant energy Ec, 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 LA) for given LA (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 ID power-law potential. Comparison between our engine model and the Carnot cycle shows that, under the same conditions, the efficiency η = 1 -- Ec&frac;Eh of the engine cycle is bounded from above the Carnot value ηc = 1 -- Tc&frac;Th. [ABSTRACT FROM AUTHOR]

We establish a quantum Otto engine (QOE) of a two-level atom, which is confined in a one-dimensional (ID) 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 9 but is independent of the energy spectrum index &sgr;. [ABSTRACT FROM AUTHOR]

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 Th and Tc(< Th). respectively, and it is tuned slowly along a protocol to realize an adiabatic process. To illustrate the performance in finite time of the quantum heat engine, we adopt the semigroup approach to model the thermal relaxation dynamics along the two isochoric processes, and we find the upper bound of efficiency at maximum power (EMP) η* to be a function of the Carnot efficiency ηc(=1 - Tc/Th): η* ≲ η+ ≡ ηc²/[ηc - (1 - ηc)ln(l - ηc)], identical to those previously derived from ideal (noninteracting) microscopic, mesoscopic, and macroscopic systems. [ABSTRACT FROM AUTHOR]

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 Qc, and coefficient of performance (COP)ηcop 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 → 0. [ABSTRACT FROM AUTHOR]

We study the thermodynamic performance of a nanosized photoelectric refrigerator consisting of three coupled single-level quantum dots embedded between two reservoirs at different temperatures. Based on the quantum master equation, we derive expressions for the cooling power and coefficient of performance (COP) of the refrigerator and plot the characteristic curves between the cooling power and the COP. We analyze the optimal performance parameters under conditions of maximum cooling power and maximum COP, and we discuss the influence of the energy level difference and the temperature ratio on the optimal performance parameters in detail. [ABSTRACT FROM AUTHOR]

We study the coefficient of performance (COP) and its bounds for a Carnot-like refrigerator working between two heat reservoirs at constant temperatures Th, and Tc, under two optimization criteria X and Ω. 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. [ABSTRACT FROM AUTHOR]