Carnot Limit Research Articles

Quantum thermal machines with single nonequilibrium environments

We propose a scheme for a quantum thermal machine made by atoms interacting with a single nonequilibrium electromagnetic field. The field is produced by a simple configuration of macroscopic objects held at thermal equilibrium at different temperatures. We show that these machines can deliver all thermodynamic tasks (cooling, heating, and population inversion) by establishing quantum coherence with the body on which they act. Remarkably, this system allows these machines to reach efficiencies at maximum power very close to the Carnot limit, which is much more than in existing models. Our findings offer a paradigm for efficient quantum energy flux management, and can be relevant for both experimental and technological purposes.

Vibrational cooling and thermoelectric response of nanoelectromechanical systems

Cooling a nanomechanical system by applying an electron current through the nanomechanical structure is investigated in the context of the general theory of thermoelectrics. This allows the authors to discuss the efficiency of such phonon refrigerators and compare it with the fundamental Carnot limit. The results should provide guidance for the experimental implementation of the vibrational cooling mechanism based on the application of a current.

Proposal for a phase-coherent thermoelectric transistor

Identifying materials and devices which offer efficient thermoelectric effects at low temperature is a major obstacle for the development of thermal management strategies for low-temperature electronic systems. Superconductors cannot offer a solution since their near perfect electron-hole symmetry leads to a negligible thermoelectric response; however, here we demonstrate theoretically a superconducting thermoelectric transistor which offers unparalleled figures of merit of up to ∼45 and Seebeck coefficients as large as a few mV/K at sub-Kelvin temperatures. The device is also phase-tunable meaning its thermoelectric response for power generation can be precisely controlled with a small magnetic field. Our concept is based on a superconductor-normal metal-superconductor interferometer in which the normal metal weak-link is tunnel coupled to a ferromagnetic insulator and a Zeeman split superconductor. Upon application of an external magnetic flux, the interferometer enables phase-coherent manipulation of thermoelectric properties whilst offering efficiencies which approach the Carnot limit.

Self-contained n-qubit quantum refrigerator

Brunner et al. [Phys. Rev. E 85 (2012) 05111] have claimed that, "essentially only the smallest machines can approach Carnot efficiency". We have verified this claim by raising self-contained four-qubit quantum refrigerator, and we have shown that according to concepts of virtual qubit, it can reach the maximum efficiency in other words Carnot efficiency. But its efficiency, such as self-contained three-qubit quantum refrigerator is not universal. We also investigated a special case of self-contained four-qubit quantum refrigerator, in other words self-contained four-qubit quantum refrigerator with two hot baths in the same temperature. We demonstrated that its efficiency has the form as efficiency of a self-contained three-qubit quantum refrigerator. In other words, from the perspective of efficiency, this particular model is equivalent to self-contained three-qubit quantum refrigerator. We also demonstrated the efficiency of this particular model in the Carnot limit that is independent from details of system model, but only depends on the environmental temperatures. Also, we raised a system that consists of n-qubit which acts as a refrigerator. According to self-contained four-qubit quantum refrigerator, we also investigated a special case of self-contained n-qubit quantum refrigerator — a self-contained n-qubit quantum refrigerator with (n - 2) baths in the same temperature. We considered the three different special situations of the n-qubit refrigerator and demonstrated their efficiency in three different situations which has the form as efficiency of self-contained three-qubit quantum refrigerator. In this special situations, (n - 2) qubits are in thermal contact with isothermal heat baths.

Entanglement enhances cooling in microscopic quantum refrigerators.

Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.

Predicted Very Large Thermoelectric Effect in Ferromagnet-Superconductor Junctions in the Presence of a Spin-Splitting Magnetic Field

We show that a huge thermoelectric effect can be observed by contacting a superconductor whose density of states is spin split by a Zeeman field with a ferromagnet with a nonzero polarization. The resulting thermopower exceeds kB/e by a large factor, and the thermoelectric figure of merit ZT can far exceed unity, leading to heat engine efficiencies close to the Carnot limit. We also show that spin-polarized currents can be generated in the superconductor by applying a temperature bias.

Nanoscale Heat Engine Beyond the Carnot Limit

We consider a quantum Otto cycle for a time-dependent harmonic oscillator coupled to a squeezed thermal reservoir. We show that the efficiency at maximum power increases with the degree of squeezing, surpassing the standard Carnot limit and approaching unity exponentially for large squeezing parameters. We further propose an experimental scheme to implement such a model system by using a single trapped ion in a linear Paul trap with special geometry. Our analytical investigations are supported by MonteCarlo simulations that demonstrate the feasibility of our proposal. For realistic trap parameters, an increase of the efficiency at maximum power of up to a factor of 4 is reached, largely exceeding the Carnot bound.

Efficiency and dissipation in a two-terminal thermoelectric junction, emphasizing small dissipation

The efficiency and cooling power of a two-terminal thermoelectric refrigerator are analyzed near the limit of vanishing dissipation (ideal system), where the optimal efficiency is the Carnot one, but the cooling power vanishes. This limit, where transport occurs only via a single sharp electronic energy, has been referred to as "strong coupling" or "the best thermoelectric." Confining the discussion to the linear-response regime, it is found that "parasitic" effects that make the system deviate from the ideal limit, and reduce the efficiency from the Carnot limit, are crucial for the usefulness of the device. Among these parasitics, there are: parallel phonon conduction, finite width of the electrons' transport band, and more than a single energy transport channel. In terms of a small parameter characterizing the deviation from the ideal limit, the efficiency and power grow linearly, and the dissipation quadratically. The results are generalized to the case of broken time-reversal symmetry, and the major nontrivial changes are discussed. Finally, the recent universal relation between the thermopower and the asymmetry of the dissipation between the two terminals is briefly discussed, including the small dissipation limit.

Hot Carriers in Quantum Wells for Photovoltaic Efficiency Enhancement

In a hot carrier solar cell, the steady-state carrier population is hot relative to the surrounding lattice. This requires an absorber material which restricts carrier-phonon interaction and, therefore, reduces entropic loss during thermalization. The limiting efficiency of these devices approaches 85%: the Carnot limit for a solar energy collector. A spectroscopic analysis of GaAsP/InGaAs quantum well structures shows that carrier cooling in single quantum well samples is dominated by the rate of radiative recombination, leading to unprecedented carrier cooling lifetime (τ = 5.8 ±0.1 ns). This exceptional lifetime arises due to state saturation, frustrating the carrier scattering processes. A steady-state carrier population temperature >100 K above the lattice temperature is measured under illumination equivalent to 10 000 Suns. We calculate the projected efficiency >40% for a device with these characteristics, amounting to a 3% efficiency enhancement over equivalent single-junction devices.

Thermomagnetic energy harvesting with first order phase change materials

Two cycles of thermomagnetic generation have been compared, one with a conventional ferromagnetic material and one using a Heusler alloy undergoing a first order phase transformation. The two have been analytically compared in terms of overall thermal-to-magnetic energy conversion efficiency. In addition, a state-space model of a thermomagnetic generator has been developed and analyzed in order to compare the performance of the two in terms of response to decreased thermal difference and changes in plate separation. Both analytical calculations and simulation indicated a large difference in operational behavior between the two materials, with the Heusler alloy's behavior being characterized by latent heat and large changes in magnetism, and the ferromagnet being characterized by a smaller heat input and more gradual magnetic change. The theoretical energy conversion efficiency of the Heusler alloy was calculated to be 0.2% under an external field of 3kOe, increasing to 0.8% under a field of 15kOe. These values corresponded to 15.9% and 63.8% of the Carnot limit, respectively, and compare favorably with the conversion efficiencies of ferromagnetic materials previously used in thermomagnetic generation.

Breaking the Carnot limit without violating the second law: A thermodynamic analysis of off-resonant quantum light generation

The Carnot limit, formulated in 1824, represents the maximal efficiency of a classical heat engine. In this work we present a thermodynamical analysis of a light amplifier based on a three-level atom coupled off-resonantly to a single quantized cavity mode and to two heat reservoirs with positive temperatures. Based on standard work and heat flow equilibrium, we show that for a cavity blue-detuned with respect to the atomic resonance, the system can surpass the Carnot limit. Nevertheless, the second law of thermodynamics is still obeyed, as the total entropy always increases. By analyzing a semiclassical version of the model, we derive a formula for the critical frequency for which the Carnot limit is broken and a formula for the amplifier efficiency which agrees with its quantum counterpart. In the semiclassical regime, however, the second law is not satisfied and hence it does not offer a physically acceptable description of the system. Finally, we show that breaking the Carnot limit occurs also in a blue-detuned quantum amplifier with output coupling, which represents a realistic model of a laser or maser.

A high-efficiency solar Rankine engine with isothermal expansion

Though the principle of the solar Rankine cycle is well known, with several examples reported in the literature, there is yet a scarcity of engines that could be efficiently applied in small-scale (<100 KW) applications. Hence, this paper presents a variant of the engine that uses an isothermal expansion to achieve a theoretical efficiency close to the Carnot limit. Generation of steam inside the power cylinder obviates the need for an external boiler. The device is suitable for slow-moving applications and is of particular interest for driving a batch-desalination process. Preliminary experiments have shown cycle efficiency of 16%, and a high work ratio of 0.997. ©The Author 2013. Published by Oxford University Press. All rights reserved.

Performance analysis of an interacting quantum dot thermoelectric setup

We analyze the nanocaloritronic performance of an interacting quantum dot that is subject to an applied bias and an applied temperature gradient. It is now well known that, in the absence of phonon contribution, a weakly coupled non-interacting quantum dot can operate at thermoelectric efficiencies approaching the Carnot limit. However, it has also been recently pointed out that such peak efficiencies can only be achieved when operated in the reversible limit, with a vanishing current and hence a vanishing power output. In this paper, we point out three fundamental results affecting the thermoelectric performance due to the inclusion of Coulomb interactions: a) The reversible operating point carries zero efficiency, b) operation at finite power output is possible even at peak efficiencies approaching the Carnot value, and c) the evaluated trends of the the maximum efficiency deviate considerably from the conventional {\it{figure of merit}} $zT$ based result. Finally, we also analyze our system for thermoelectric operation at maximum power output.

The Mean State of Axisymmetric Hurricanes in Statistical Equilibrium

Abstract Numerical experiments are performed to determine the mean state of an axisymmetric hurricane in statistical equilibrium. Most earlier studies used a damping scheme on the temperature field as a parameterization of radiative cooling, which the authors demonstrate yields storms that have little convection outside the eyewall and do not achieve statistical equilibrium. Here the effects of infrared radiation are explicitly simulated, which permits the storm to achieve radiative–convective equilibrium. Beginning from a state of rest, a storm spontaneously develops with maximum surface wind speeds in excess of 100 m s−1 by day 10. This transient “superintense” storm weakens and is replaced by an equilibrium storm that lasts over 400 days with a time-mean maximum wind speed that compares closely with a diagnostic estimate of potential intensity (PI). The main assumptions of PI theory are found to be consistent with the properties of the equilibrium storm, but the thermodynamic cycle does not resemble a Carnot cycle, with an implied efficiency of about half that of the Carnot limit. Maximum radiative cooling is found in the midtroposphere outside the storm, where convective clouds detrain into the dry layer of storm-outflow subsidence, producing a large vertical gradient in water vapor and cloud water. Sensitivity experiments reveal that the results are robust to changes in the prestorm thermodynamic sounding, ambient rotation, horizontal turbulent mixing, and details in the radiative heating field. Subject to the assumptions in this study, it can be concluded that 1) the undisturbed tropical atmosphere is unstable to axisymmetric hurricanes, 2) PI theory accurately bounds time-mean storm intensity (but not transient fluctuations), and 3) equilibrium storm intensity is insensitive to turbulent mixing in the radial direction.

Increasing thermoelectric efficiency: dynamical models unveil microscopic mechanisms

Dynamical nonlinear systems provide a new approach to the old problem of increasing the efficiency of thermoelectric machines. In this review, we discuss stylized models of classical dynamics, including non-interacting complex molecules in an ergodic billiard, a disordered hard-point gas and an abstract thermoelectric machine. The main focus will be on the physical mechanisms, unveiled by these dynamical models, which lead to high thermoelectric efficiency approaching the Carnot limit.

Constrained maximal power in small engines

Efficiency at maximum power is studied for two simple engines (three- and five-state systems). This quantity is found to be sensitive to the variable with respect to which the maximization is implemented. It can be wildly different from the well-known Curzon-Ahlborn bound (one minus the square root of the temperature ratio), or can be even closer than previously realized. It is shown that when the power is optimized with respect to a maximum number of variables the Curzon-Ahlborn bound is a lower bound, accurate at high temperatures, but a rather poor estimate when the cold reservoir temperature approaches zero (at which point the Carnot limit is achieved).

Pyroelectric response of ferroelectric nanowires: Size effect and electric energy harvesting

The size effect on pyroelectric response of ferroelectric nanowires is analyzed. The pyroelectric coefficient strongly increases with the wire radius decrease and diverges at critical radius Rcr corresponding to the size-driven transition into paraelectric phase. Size-driven enhancement of pyroelectric coupling leads to the giant pyroelectric current and voltage generation by the polarized ferroelectric nanoparticles in response to the temperature fluctuation. The maximum efficiency of the pyroelectric energy harvesting and bolometric detection is derived, and is shown to approach the Carnot limit for low temperatures.

Thermodynamic performance assessment of an ammonia–water Rankine cycle for power and heat production

In this paper, an ammonia–water based Rankine cycle is thermodynamically analyzed for renewable-based power production, e.g. solar, geothermal, biomass, oceanic-thermal, and nuclear as well as industrial waste heat. Due to the nature of the ammonia–water mixture, changes in its concentration allow thermodynamic cycles to adapt to fluctuations in renewable energy sources, which is an important advantage with respect to other working fluids. The non-linearity of the working fluid’s behaviour imposes that each cycle must be optimized based upon several parameters. A model has been developed to optimize the thermodynamic cycle for maximum power output and carry out a parametric study. The lowest temperature state of the system is fixed, and three other parameters are variables of study, namely, maximum system temperature, ammonia concentration and energy ratio, which is a newly introduced parameter. Energy ratio indicates the relative position of the expansion state and is defined in terms of enthalpies. The study is conducted over a concentration range of 0–0.5, the maximum temperature studied varies between 75 °C and 350 °C for extreme cases, and the energy ratio from saturated liquid to superheated vapour. As a result, the optimal expansion energy ratio is predicted. The cycle efficiencies are drastically affected by the concentrations and temperatures. Depending on the source temperature, the cycle energy efficiency varies between 5% and 35% representing up to 65% of the Carnot limit. The optimal energy ratio has been determined for several concentrations and reported graphically.

Stochastic Pumping of Heat: Approaching the Carnot Efficiency

Random noise can generate a unidirectional heat current across asymmetric nano-objects in the absence (or against) a temperature gradient. We present a minimal model for a molecular-level stochastic heat pump that may operate arbitrarily close to the Carnot efficiency. The model consists a fluctuating molecular unit coupled to two solids characterized by distinct phonon spectral properties. Heat pumping persists for a broad range of system and bath parameters. Furthermore, by filtering the reservoirs' phonons the pump efficiency can approach the Carnot limit.

Concept study for a high-efficiency nanowire based thermoelectric

Materials capable of highly efficient, direct thermal-to-electric energy conversion wouldhave substantial economic potential. Theory predicts that thermoelectric efficienciesapproaching the Carnot limit can be achieved at low temperatures in one-dimensionalconductors that contain an energy filter such as a double-barrier resonant tunnellingstructure. The recent advances in growth techniques suggest that such devices can now berealized in heterostructured, semiconductor nanowires. Here we propose specific structuralparameters for InAs/InP nanowires that may allow the experimental observation ofnear-Carnot efficient thermoelectric energy conversion in a single nanowire at lowtemperature.