Reversible quantum brownian heat engines for electrons

Thermodynamics of a continuously monitored double-quantum-dot heat engine in the repeated interactions framework

Understanding the thermodynamic role of measurement in quantum mechanical systems is a burgeoning field of study. In this article, we study a double quantum dot (DQD) connected to two macroscopic fermionic thermal reservoirs. We assume that the DQD is continuously monitored by a quantum point contact (QPC), which serves as a charge detector. Starting from a minimalist microscopic model for the QPC and reservoirs, we show that the local master equation of the DQD can alternatively be derived in the framework of repeated interactions and that this framework guarantees a thermodynamically consistent description of the DQD and its environment (including the QPC). We analyze the effect of the measurement strength and identify a regime in which particle transport through the DQD is both assisted and stabilized by dephasing. We also find that in this regime the entropic cost of driving the particle current with fixed relative fluctuations through the DQD is reduced. We thus conclude that under continuous measurement a more constant particle current may be achieved at a fixed entropic cost.

Four-Objective Optimizations of a Single Resonance Energy Selective Electron Refrigerator

According to the established model of a single resonance energy selective electron refrigerator with heat leakage in the previous literature, this paper performs multi-objective optimization with finite-time thermodynamic theory and NSGA-II algorithm. Cooling load (R¯), coefficient of performance (ε), ecological function (ECO¯), and figure of merit (χ¯) of the ESER are taken as objective functions. Energy boundary (E′/kB) and resonance width (ΔE/kB) are regarded as optimization variables and their optimal intervals are obtained. The optimal solutions of quadru-, tri-, bi-, and single-objective optimizations are obtained by selecting the minimum deviation indices with three approaches of TOPSIS, LINMAP, and Shannon Entropy; the smaller the value of deviation index, the better the result. The results show that values of E′/kB and ΔE/kB are closely related to the values of the four optimization objectives; selecting the appropriate values of the system can design the system for optimal performance. The deviation indices are 0.0812 with LINMAP and TOPSIS approaches for four-objective optimization (ECO¯−R¯−ε−χ¯), while the deviation indices are 0.1085, 0.8455, 0.1865, and 0.1780 for four single-objective optimizations of maximum ECO¯, R¯, ε, and χ¯, respectively. Compared with single-objective optimization, four-objective optimization can better take different optimization objectives into account by choosing appropriate decision-making approaches. The optimal values of E′/kB and ΔE/kB range mainly from 12 to 13, and 1.5 to 2.5, respectively, for the four-objective optimization.

Non-equilibrium thermoelectric transport across normal metal-quantum dot-superconductor hybrid system within the Coulomb blockade regime

A detailed investigation of the non-equilibrium steady-state electric and thermoelectric transport properties of a quantum dot (QD) coupled to the normal metallic and s-wave superconducting reservoirs (N-QD-S) are provided within the Coulomb blockade regime. Using non-equilibrium Keldysh Green's function formalism, initially, various model parameter dependences of thermoelectric transport properties are analysed within the linear response regime. It is observed that the single-particle tunnelling close to the superconducting gap edge can generate a relatively large thermopower and figure of merit. Moreover, the Andreev tunnelling plays a significant role in the suppression of thermopower and figure of merit within the gap region. Further, within the non-linear regime, we discuss two different situations, i.e., the finite voltage biasing between isothermal reservoirs and the finite thermal gradient in the context of thermoelectric heat engine. In the former case, it is shown that the sub-gap Andreev heat current can become finite beyond the linear response regime and play a vital role in asymmetric heat dissipation and thermal rectification effect for low voltage biasing. The rectification of heat current is enhanced for strong on-dot Coulomb interaction and at low background thermal energy. In the latter case, we study the variation of thermovoltage, thermopower, maximum power output, and corresponding efficiency with the applied thermal gradient. These results illustrate that hybrid superconductor-QD nanostructures are promising candidates for the low-temperature thermal applications.

Universal Bounds on Fluctuations in Continuous Thermal Machines

We study bounds on ratios of fluctuations in steady-state time-reversal energy conversion devices. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.

Thermoelectricity of near-resonant tunnel junctions and their relation to Carnot efficiency

We present a conceptual study motivated by electrical and thermoelectrical measurements on various near-resonant tunnel junctions. The squeezable nano junction technique allows the quasi-synchronous measurement of conductance G, I(V) characteristics and Seebeck coefficient S. Correlations between G and S are uncovered, in particular boundaries for S(G). We find the simplest and consistent description of the observed phenomena in the framework of the single level resonant tunneling model within which measuring I(V) and S suffice for determining all model parameters. We can further employ the model for assigning thermoelectric efficiencies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}η without measuring the heat flow. Within the ensemble of thermoelectric data, junctions with assigned \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}η close to the Carnot limit can be identified. These insights allow providing design rules for optimized thermoelectric efficiency in nanoscale junctions.

Experimental Test of the 1/τ-Scaling Entropy Generation in Finite-Time Thermodynamics

The finite-time dynamics, apart from its fundamental importance in nonequilibrium thermodynamics, is of great significance in designing heat engine cycles. We build an experimental apparatus to test the predicted long-time 1/τ scaling of the irreversible entropy generation in the finite-time (τ) thermodynamic process by compressing dry air in a temperature-controlled water bath. We present the first direct experimental validation of the scaling, utilized in many finite-time thermodynamic models at the long-time regime. The experimental data also demonstrate a clear deviation from the scaling at the short-time regime. We show the optimal control scheme to minimize the irreversible entropy generation in finite-time process. Such optimization shall bring new insight to the practical design of heat engine cycles.

Analog of a Quantum Heat Engine Using a Single-Spin Qubit

A quantum two-level system with periodically modulated energy splitting could provide a minimal universal quantum heat machine. We present the experimental realization and the theoretical description of such a two-level system as an impurity electron spin in a silicon tunnel field-effect transistor. In the incoherent regime, the system can behave analogously to either an Otto heat engine or a refrigerator. The coherent regime could be described as a superposition of those two regimes, producing specific interference fringes in the observed source-drain current.

Power, efficiency, and fluctuations in steady-state heat engines

We consider the quality factor Q, which quantifies the trade-off between power, efficiency, and fluctuations in steady-state heat engines modeled by dynamical systems. We show that the nonlinear scattering theory, in both classical and quantum mechanics, sets the bound Q=3/8 when approaching the Carnot efficiency. On the other hand, interacting, nonintegrable, and momentum-conserving systems can achieve the value Q=1/2, which is the universal upper bound in linear response. This result shows that interactions are necessary to achieve the optimal performance of a steady-state heat engine.

Experimental Realization of a Quantum Dot Energy Harvester

We demonstrate experimentally an autonomous nanoscale energy harvester that utilizes the physics of resonant tunneling quantum dots. Gate-defined quantum dots on GaAs/AlGaAs high-electron-mobility transistors are placed on either side of a hot-electron reservoir. The discrete energy levels of the quantum dots are tuned to be aligned with low energy electrons on one side and high energy electrons on the other side of the hot reservoir. The quantum dots thus act as energy filters and allow for the conversion of heat from the cavity into electrical power. Our energy harvester, measured at an estimated base temperature of 75 mK in a He^{3}/He^{4} dilution refrigerator, can generate a thermal power of 0.13 fW for a temperature difference across each dot of about 67 mK.

Simple scheme for extracting work with a single bath

We propose a simple protocol exploiting the thermalization of a storage bipartite system S to extract work from a resource system R. The protocol is based on a recent work definition involving only a single bath. A general description of the protocol is provided without specifying the characteristics of S. We quantify both the extracted work and the ideal efficiency of the process, also giving maximum bounds for them. Then, we apply the protocol to two cases: two interacting qubits and the Rabi model. In both cases, for very strong couplings, an extraction of work comparable with the bare energies of the subsystems of S is obtained and its peak is reached for finite values of the bath temperature, T. We finally show, in the Rabi model at T=0, how to transfer the work stored in S to an external device, permitting thus a cyclic implementation of the whole work-extraction protocol. Our proposal makes use of simple operations not needing fine control.

Quantum self-contained refrigerator in terms of the cavity quantum electrodynamics in the weak internal-coupling regime

We present two schemes to implement the self-contained refrigerator in the framework of the cavity quantum electrodynamics. The considered refrigerators are composed of three interacting microcavities (or two microcavities simultaneously interacting with one three-level atom) separately coupling to a thermal bath with a certain temperature. Despite the local master equation employed, the proposed analytic procedure shows the perfect thermodynamical consistency. It is also demonstrated that the heat is stably extracted from the lowest temperature bath with a fixed efficiency only determined by the intrinsic properties of the refrigerators, i.e., the frequency ratio of the two cavities in contact with the two higher temperature baths. These two schemes indicate that the system with the weak internal coupling in the infinite dimensional Hilbert space can be used to realize the quantum self-contained refrigerator on the principle completely the same as the original self-contained refrigerator.

A quantum-dot heat engine operating close to the thermodynamic efficiency limits

Cyclical heat engines are a paradigm of classical thermodynamics, but are impractical for miniaturization because they rely on moving parts. A more recent concept is particle-exchange (PE) heat engines, which uses energy filtering to control a thermally driven particle flow between two heat reservoirs^1,2. As they do not require moving parts and can be realized in solid-state materials, they are suitable for low-power applications and miniaturization. It was predicted that PE engines could reach the same thermodynamically ideal efficiency limits as those accessible to cyclical engines^3-6, but this prediction has not been verified experimentally. Here, we demonstrate a PE heat engine based on a quantum dot (QD) embedded into a semiconductor nanowire. We directly measure the engine's steady-state electric power output and combine it with the calculated electronic heat flow to determine the electronic efficiency η. We find that at the maximum power conditions, η is in agreement with the Curzon-Ahlborn efficiency^6-9 and that the overall maximum η is in excess of 70% of the Carnot efficiency while maintaining a finite power output. Our results demonstrate that thermoelectric power conversion can, in principle, be achieved close to the thermodynamic limits, with direct relevance for future hot-carrier photovoltaics¹⁰, on-chip coolers or energy harvesters for quantum technologies.

Thermodynamic Bound on Heat-to-Power Conversion

In systems described by the scattering theory, there is an upper bound, lower than Carnot, on the efficiency of steady-state heat-to-work conversion at a given output power. We show that interacting systems can overcome such bound and saturate, in the thermodynamic limit, the much more favorable linear-response bound. This result is rooted in the possibility for interacting systems to achieve the Carnot efficiency at the thermodynamic limit without delta-energy filtering, so that large efficiencies can be obtained without greatly reducing power.

Thermodynamic Bounds on Precision in Ballistic Multiterminal Transport

For classical ballistic transport in a multiterminal geometry, we derive a universal trade-off relation between total dissipation and the precision, at which particles are extracted from individual reservoirs. Remarkably, this bound becomes significantly weaker in the presence of a magnetic field breaking time-reversal symmetry. By working out an explicit model for chiral transport enforced by a strong magnetic field, we show that our bounds are tight. Beyond the classical regime, we find that, in quantum systems far from equilibrium, the correlated exchange of particles makes it possible to exponentially reduce the thermodynamic cost of precision.

Thermionic cooling devices based on resonant-tunneling AlGaAs/GaAs heterostructure

We study by means of full quantum simulations the operating principle and performance of a semiconductor heterostructure refrigerator combining resonant tunneling filtering and thermionic emission. Our model takes into account the coupling between the electric and thermal currents by self-consistently solving the transport equations within the non-equilibrium Green's function framework and the heat equation. We show that the device can achieve relatively high cooling power values, while in the considered implementation, the maximum lattice temperature drop is severely limited by the thermal conductivity of the constituting materials. In such an out-of-equilibrium structure, we then emphasize the significant deviation of the phonon temperature from its electronic counterpart which can vary over several hundred Kelvin. The interplay between those two temperatures and the impact on the electrochemical potential is also discussed. Finally, viable options toward an optimization of the device are proposed.

Nonlinear effects for three-terminal heat engine and refrigerator

The three-terminal heat device that consists of an electronic cavity and couples to a heat bath is studied both as a heat engine and as a refrigerator. We investigate the characteristic performance in the linear and nonlinear regime for both setups. It is our focus here to analyze how the efficiency of the heat engine and coefficient of performance of the refrigerator are affected by the nonlinear transport. With such considerations, the maximum efficiency and power are then optimized for various energy levels, temperatures and other parameters.

Heating without heat: Thermodynamics of passive energy filters between finite systems

Passive filters allowing the exchange of particles in a narrow band of energy are currently used in microrefrigerators and energy transducers. In this Rapid Communication, we analyze their thermal properties using linear irreversible thermodynamics and kinetic theory, and discuss a striking phenomenon: the possibility of simultaneously increasing or decreasing the temperatures of two systems without any supply of energy. This occurs when the filter induces a flow of particles whose energy is between the average energies of the two systems. Here we show that this selective transfer of particles does not need the action of any sort of Maxwell demon and can be carried out by passive filters without compromising the second law of thermodynamics. This phenomenon allows us to design cycles between two reservoirs at temperatures T_{1}<T_{2} that are able to reach temperatures below T_{1} or above T_{2}.

Non-linear effects and thermoelectric efficiency of quantum dot-based single-electron transistors

By means of advanced numerical simulation, the thermoelectric properties of a Si-quantum dot-based single-electron transistor operating in sequential tunneling regime are investigated in terms of figure of merit, efficiency and power. By taking into account the phonon-induced collisional broadening of energy levels in the quantum dot, both heat and electrical currents are computed in a voltage range beyond the linear response. Using our homemade code consisting in a 3D Poisson-Schrödinger solver and the resolution of the Master equation, the Seebeck coefficient at low bias voltage appears to be material independent and nearly independent on the level broadening, which makes this device promising for metrology applications as a nanoscale standard of Seebeck coefficient. Besides, at higher voltage bias, the non-linear characteristics of the heat current are shown to be related to the multi-level effects. Finally, when considering only the electronic contribution to the thermal conductance, the single-electron transistor operating in generator regime is shown to exhibit very good efficiency at maximum power.

Enabling the self-contained refrigerator to work beyond its limits by filtering the reservoirs

In this paper, we study the quantum self-contained refrigerator [Linden et al., Phys. Rev. Lett. 105, 130401 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.130401] in the strong internal coupling regime with engineered reservoirs. We find that if some modes of the three thermal reservoirs can be properly filtered out, the efficiency and the working domain of the refrigerator can be improved in contrast to the those in the weak internal coupling regime, which indicates one advantage of the strong internal coupling. In addition, we find that the background natural vacuum reservoir could cause the filtered refrigerator to stop working and the background natural thermal reservoir could greatly reduce the cooling efficiency.

Single-nanowire, low-bandgap hot carrier solar cells with tunable open-circuit voltage

Compared to traditional pn-junction photovoltaics, hot carrier solar cells offer potentially higher efficiency by extracting work from the kinetic energy of photogenerated 'hot carriers' before they cool to the lattice temperature. Hot carrier solar cells have been demonstrated in high-bandgap ferroelectric insulators and GaAs/AlGaAs heterostructures, but so far not in low-bandgap materials, where the potential efficiency gain is highest. Recently, a high open-circuit voltage was demonstrated in an illuminated wurtzite InAs nanowire with a low bandgap of 0.39 eV, and was interpreted in terms of a photothermoelectric effect. Here, we point out that this device is a hot carrier solar cell and discuss its performance in those terms. In the demonstrated devices, InP heterostructures are used as energy filters in order to thermoelectrically harvest the energy of hot electrons photogenerated in InAs absorber segments. The obtained photovoltage depends on the heterostructure design of the energy filter and is therefore tunable. By using a high-resistance, thermionic barrier, an open-circuit voltage is obtained that is in excess of the Shockley-Queisser limit. These results provide generalizable insight into how to realize high voltage hot carrier solar cells in low-bandgap materials, and therefore are a step towards the demonstration of higher efficiency hot carrier solar cells.

Route towards the optimization at given power of thermoelectric heat engines with broken time-reversal symmetry

We investigate the performance at a given power of a thermoelectric heat engine with broken time-reversal symmetry, and derive analytically the efficiency at a given power of a thermoelectric generator within linear irreversible thermodynamics. A universal bound on the efficiency of the thermoelectric heat engine is achieved under a strong constraint on the Onsager coefficients, and some interesting features are further revealed. Our results demonstrate that there exists a trade-off between efficiency and power output, and the efficiency at a given power may surpass the Curzon-Ahlborn limit due to broken time-reversal symmetry. Moreover, optimal efficiency at a given power can be achieved, which indicates that broken time-reversal symmetry offers physically allowed ways to optimize the performance of heat engines. Our study may contribute to the interesting guidelines for optimizing actual engines.

Efficiency versus speed in quantum heat engines: Rigorous constraint from Lieb-Robinson bound

A long-standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investgated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with quantum heat engines. In a first step, employing the Lieb-Robinson bound we establish an inequality on the change in a local observable caused by an operation far from support of the local observable. This inequality provides a rigorous characterization of the following intuitive picture that most of the energy emitted from the engine to the cold bath remains near the engine when the cyclic process is finished. Using this description, we prove an upper bound on efficiency with the aid of quantum information geometry. Our result generally excludes the possibility of a process with finite speed at the Carnot efficiency in quantum heat engines. In particular, the obtained constraint covers engines evolving with non-Markovian dynamics, which almost all previous studies on this topic fail to address.

Bipolar Photothermoelectric Effect Across Energy Filters in Single Nanowires

The photothermoelectric (PTE) effect uses nonuniform absorption of light to produce a voltage via the Seebeck effect and is of interest for optical sensing and solar-to-electric energy conversion. However, the utility of PTE devices reported to date has been limited by the need to use a tightly focused laser spot to achieve the required, nonuniform illumination and by their dependence upon the Seebeck coefficients of the constituent materials, which exhibit limited tunability and, generally, low values. Here, we use InAs/InP heterostructure nanowires to overcome these limitations: first, we use naturally occurring absorption "hot spots" at wave mode maxima within the nanowire to achieve sharp boundaries between heated and unheated subwavelength regions of high and low absorption, allowing us to use global illumination; second, we employ carrier energy-filtering heterostructures to achieve a high Seebeck coefficient that is tunable by heterostructure design. Using these methods, we demonstrate PTE voltages of hundreds of millivolts at room temperature from a globally illuminated nanowire device. Furthermore, we find PTE currents and voltages that change polarity as a function of the wavelength of illumination due to spatial shifting of subwavelength absorption hot spots. These results indicate the feasibility of designing new types of PTE-based photodetectors, photothermoelectrics, and hot-carrier solar cells using nanowires.

Stationary engines in and beyond the linear response regime at the Carnot efficiency

The condition for stationary engines to attain the Carnot efficiency in and beyond the linear response regime is investigated. We find that this condition for finite-size engines is significantly different from that for macroscopic engines in the thermodynamic limit. For the case of finite-size engines, the tight-coupling condition in the linear response regime directly implies the attainability of the Carnot efficiency beyond the linear response regime. As opposed to this, for the case of macroscopic engines in the thermodynamic limit, there are three types of mechanisms to attain the Carnot efficiency. One mechanism allows engines to attain the Carnot efficiency only in the linear response limit, while the other two mechanisms enable engines to attain the Carnot efficiency beyond the linear response regime. These three mechanisms are classified by introducing a tight-coupling window.

Implementation of transmission functions for an optimized three-terminal quantum dot heat engine

We consider two modifications of a recently proposed three-terminal quantum dot heat engine. First, we investigate the necessity of the thermalization assumption, namely that electrons are always thermalized by inelastic processes when traveling across the cavity where the heat is supplied. Second, we analyze various arrangements of tunneling-coupled quantum dots in order to implement a transmission function that is superior to the Lorentzian transmission function of a single quantum dot. We show that the maximum power of the heat engine can be improved by about a factor of two, even for a small number of dots, by choosing an optimal structure.

Quantum thermal machines driven by vacuum forces

We propose a quantum thermal machine composed of two nanomechanical resonators (two membranes suspended over a trench in a substrate) placed a few μm from each other. The quantum thermodynamical cycle is powered by the Casimir interaction between the resonators and the working fluid is the polariton resulting from the mixture of the flexural (out-of-plane) vibrations. With the help of piezoelectric cells, we select and sweep the polariton frequency cyclically. We calculate the performance of the proposed quantum thermal machines and show that high efficiencies are achieved thanks to (i) the strong coupling between the resonators and (ii) the large difference between the membrane stiffnesses. Our findings can be of particular importance for applications in nanomechanical technologies where a sensitive control of temperature is needed.

Closed-loop approach to thermodynamics

We present the closed-loop approach to linear nonequilibrium thermodynamics considering a generic heat engine dissipatively connected to two temperature baths. The system is usually quite generally characterized by two parameters: the output power P and the conversion efficiency η, to which we add a third one, the working frequency ω. We establish that a detailed understanding of the effects of the dissipative coupling on the energy conversion process requires only knowing two quantities: the system's feedback factor β and its open-loop gain A_{0}, which product A_{0}β characterizes the interplay between the efficiency, the output power, and the operating rate of the system. By raising the abstract hermodynamic analysis to a higher level, the feedback loop approach provides a versatile and economical, hence fairly efficient, tool for the study of any conversion engine operation for which a feedback factor can be defined.

Efficiency at maximum power of thermochemical engines with near-independent particles

Two-reservoir thermochemical engines are established by using near-independent particles (including Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein particles) as the working substance. Particle and heat fluxes can be formed based on the temperature and chemical potential gradients between two different reservoirs. A rectangular-type energy filter with width Γ is introduced for each engine to weaken the coupling between the particle and heat fluxes. The efficiency at maximum power of each particle system decreases monotonously from an upper bound η(+) to a lower bound η(-) when Γ increases from 0 to ∞. It is found that the η(+) values for all three systems are bounded by η(C)/2 ≤ η(+) ≤ η(C)/(2-η(C)) due to strong coupling, where η(C) is the Carnot efficiency. For the Bose-Einstein system, it is found that the upper bound is approximated by the Curzon-Ahlborn efficiency: η(CA)=1-sqrt[1-η(C)]. When Γ → ∞, the intrinsic maximum powers are proportional to the square of the temperature difference of the two reservoirs for all three systems, and the corresponding lower bounds of efficiency at maximum power can be simplified in the same form of η(-)=η(C)/[1+a(0)(2-η(C))].

Optimal performance of periodically driven, stochastic heat engines under limited control

We consider the performance of periodically driven stochastic heat engines in the linear response regime. Reaching the theoretical bounds for efficiency and efficiency at maximum power typically requires full control over the design and the driving of the system. We develop a framework which allows us to quantify the role that limited control over the system has on the performance. Specifically, we show that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency. In particular, we show that reaching Carnot efficiency (and, hence, Curzon-Ahlborn efficiency at maximum power) requires to have control over the amplitude of the full Hamiltonian of the system. Since the kinetic energy cannot be controlled by an external parameter, heat engines based on underdamped dynamics can typically not reach Carnot efficiency. We illustrate our general theory with a paradigmatic case study of a heat engine consisting of an underdamped charged particle in a modulated two-dimensional harmonic trap in the presence of a magnetic field.

Universality of efficiency at unified trade-off optimization

We calculate the efficiency at the unified trade-off optimization criterion (the so-called maximum Ω criterion) representing a compromise between the useful energy and the lost energy of heat engines operating between two reservoirs at different temperatures and chemical potentials, and demonstrate that the linear coefficient 3/4 and quadratic coefficient 1/32 of the efficiency at maximum Ω are universal for heat engines under strong coupling and symmetry conditions. It is further proved that the conclusions obtained here also apply to the ecological optimization criterion.

Thermal electron-tunneling devices as coolers and amplifiers

Nanoscale thermal systems that are associated with a pair of electron reservoirs have been previously studied. In particular, devices that adjust electron tunnels relatively to reservoirs' chemical potentials enjoy the novelty and the potential. Since only two reservoirs and one tunnel exist, however, designers need external aids to complete a cycle, rendering their models non-spontaneous. Here we design thermal conversion devices that are operated among three electron reservoirs connected by energy-filtering tunnels and also referred to as thermal electron-tunneling devices. They are driven by one of electron reservoirs rather than the external power input, and are equivalent to those coupling systems consisting of forward and reverse Carnot cycles with energy selective electron functions. These previously-unreported electronic devices can be used as coolers and thermal amplifiers and may be called as thermal transistors. The electron and energy fluxes of devices are capable of being manipulated in the same or oppsite directions at our disposal. The proposed model can open a new field in the application of nano-devices.

Attainability of Carnot efficiency with autonomous engines

The maximum efficiency of autonomous engines with a finite chemical potential difference is investigated. We show that, without a particular type of singularity, autonomous engines cannot attain the Carnot efficiency. This singularity is realized in two ways: single particle transports and the thermodynamic limit. We demonstrate that both of these ways actually lead to the Carnot efficiency in concrete setups. Our results clearly illustrate that the singularity plays a crucial role in the maximum efficiency of autonomous engines.

Thermodynamics of the mesoscopic thermoelectric heat engine beyond the linear-response regime

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriately in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the same formalism as that of the cyclic engine, we find the following two interesting results within the Landauer-Büttiker formalism: the efficiency of the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only if the transmission probability is finite at a specific energy and zero otherwise; the unitarity of the transmission probability guarantees the second law of thermodynamics, invalidating Benenti et al.'s argument in the linear-response regime that one could obtain a finite power with the Carnot efficiency under a broken time-reversal symmetry [Phys. Rev. Lett. 106, 230602 (2011)]. These results demonstrate how quantum mechanics constrains thermodynamics.

Thermoelectricity of interacting particles: a numerical approach

A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case of a one-dimensional gas with (screened) Coulomb interparticle interaction. Numerical simulations up to N>10^{4} particles confirm the general theoretical arguments for momentum-conserving systems and show that the thermoelectric figure of merit increases linearly with the system size.

Three-terminal quantum-dot refrigerators

Based on two capacitively coupled quantum dots in the Coulomb-blockade regime, a model of three-terminal quantum-dot refrigerators is proposed. With the help of the master equation, the transport properties of steady-state charge current and energy flow between two quantum dots and thermal reservoirs are revealed. It is expounded that such a structure can be used to construct a refrigerator by controlling the voltage bias and temperature ratio. The thermodynamic performance characteristics of the refrigerator are analyzed, including the cooling power, coefficient of performance (COP), maximum cooling power, and maximum COP. Moreover, the optimal regions of main performance parameters are determined. The influence of dissipative tunnel processes on the optimal performance is discussed in detail. Finally, the performance characteristics of the refrigerators operated in two different cases are compared.

Quantum thermodynamics: a nonequilibrium Green's function approach

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.

Thermoelectric energy harvesting with quantum dots

We review recent theoretical work on thermoelectric energy harvesting in multi-terminal quantum-dot setups. We first discuss several examples of nanoscale heat engines based on Coulomb-coupled conductors. In particular, we focus on quantum dots in the Coulomb-blockade regime, chaotic cavities and resonant tunneling through quantum dots and wells. We then turn toward quantum-dot heat engines that are driven by bosonic degrees of freedom such as phonons, magnons and microwave photons. These systems provide interesting connections to spin caloritronics and circuit quantum electrodynamics.

Bound on thermoelectric power in a magnetic field within linear response

For thermoelectric power generation in a multiterminal geometry, strong numerical evidence for a universal bound as a function of the magnetic-field induced asymmetry of the nondiagonal Onsager coefficients is presented. This bound implies, inter alia, that the power vanishes at least linearly when the maximal efficiency is approached. In particular, this result rules out that Carnot efficiency can be reached at finite power, which an analysis based on the second law only would, in principle, allow.

Re-examining the self-contained quantum refrigerator in the strong-coupling regime

We revisit the self-contained quantum refrigerator in the strong-internal-coupling regime by employing the quantum optical master equation. It is shown that strong internal coupling reduces the cooling ability of the refrigerator. In contrast to the weak-coupling case, strong internal coupling could lead to quite different and even converse thermodynamic behaviors.

Revisiting Feynman's ratchet with thermoelectric transport theory

We show how the formalism used for thermoelectric transport may be adapted to Smoluchowski's seminal thought experiment, also known as Feynman's ratchet and pawl system. Our analysis rests on the notion of useful flux, which for a thermoelectric system is the electrical current and for Feynman's ratchet is the effective jump frequency. Our approach yields original insight into the derivation and analysis of the system's properties. In particular we define an entropy per tooth in analogy with the entropy per carrier or Seebeck coefficient, and we derive the analog to Kelvin's second relation for Feynman's ratchet. Owing to the formal similarity between the heat fluxes balance equations for a thermoelectric generator (TEG) and those for Feynman's ratchet, we introduce a distribution parameter γ that quantifies the amount of heat that flows through the cold and hot sides of both heat engines. While it is well established that γ = 1/2 for a TEG, it is equal to 1 for Feynman's ratchet. This implies that no heat may be rejected in the cold reservoir for the latter case. Further, the analysis of the efficiency at maximum power shows that the so-called Feynman efficiency corresponds to that of an exoreversible engine, with γ = 1. Then, turning to the nonlinear regime, we generalize the approach based on the convection picture and introduce two different types of resistance to distinguish the dynamical behavior of the considered system from its ability to dissipate energy. We finally put forth the strong similarity between the original Feynman ratchet and a mesoscopic thermoelectric generator with a single conducting channel.

Hybrid microwave-cavity heat engine

We propose and analyze the use of hybrid microwave cavities as quantum heat engines. A possible realization consists of two macroscopically separated quantum-dot conductors coupled capacitively to the fundamental mode of a microwave cavity. We demonstrate that an electrical current can be induced in one conductor through cavity-mediated processes by heating up the other conductor. The heat engine can reach Carnot efficiency with optimal conversion of heat to work. When the system delivers the maximum power, the efficiency can be a large fraction of the Carnot efficiency. The heat engine functions even with moderate electronic relaxation and dephasing in the quantum dots. We provide detailed estimates for the electrical current and output power using realistic parameters.

Performance characteristics and optimal analysis of a nanosized quantum dot photoelectric refrigerator

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.

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors

We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

Strong bounds on Onsager coefficients and efficiency for three-terminal thermoelectric transport in a magnetic field

For thermoelectric transport in the presence of a magnetic field that breaks time-reversal symmetry, a strong bound on the Onsager coefficients is derived within a general setup using three terminals. Asymmetric Onsager coefficients lead to a maximum efficiency substantially smaller than the Carnot efficiency reaching only η(C)/4 in the limit of strong asymmetry. Related bounds are derived for efficiency at maximum power, which can become larger than the Curzon-Ahlborn value η(C)/2, and for a cooling device. Our approach reveals that in the presence of reversible currents the standard analysis based on the positivity of entropy production is incomplete without considering the role of current conservation explicitly.

Conservation laws and thermodynamic efficiencies

We show that generic systems with a single relevant conserved quantity reach the Carnot efficiency in the thermodynamic limit. Such a general result is illustrated by means of a diatomic chain of hard-point elastically colliding particles where the total momentum is the only relevant conserved quantity.

Scattering theory of nonlinear thermoelectric transport

We investigate nonlinear transport properties of quantum conductors in response to both electrical and thermal driving forces. Within the scattering approach, we determine the nonequilibrium screening potential of a generic mesoscopic system and find that its response is dictated by particle and entropic injectivities which describe the charge and entropy transfer during transport. We illustrate our model analyzing the voltage and thermal rectification of a resonant tunneling barrier. Importantly, we discuss interaction induced contributions to the thermopower in the presence of large temperature differences.