The continuous introduction of renewable electricity and increased consumption through electrification of the transport and heating sector challenges grid stability. This study investigates load shifting through demand side management as …
The continuous introduction of renewable electricity and increased consumption through electrification of the transport and heating sector challenges grid stability. This study investigates load shifting through demand side management as a solution. We present a four-month experimental study of a low-complexity, hierarchical Model Predictive Control approach for demand side management in a near-zero emission occupied single-family house in Denmark. The control algorithm uses a price signal, weather forecast, a single-zone building model, and a non-linear heat pump efficiency model to generate a space-heating schedule. The weather-compensated, commercial heat pump is made to act smart grid-ready through outdoor temperature input override to enable heat boosting and forced stops to accommodate the heating schedule. The cost reduction from the controller ranged from 2-33% depending on the chosen comfort level. The experiment demonstrates that load shifting is feasible and cost-effective, even without energy storage, and that the current price scheme provides an incentive for Danish end-consumers to shift heating loads. However, issues related to controlling the heat pump through input-manipulation were identified, and the authors propose a more promising path forward involving coordination with manufacturers and regulators to make commercial heat pumps truly smart grid-ready.
The continuous introduction of renewable electricity and increased consumption through electrification of the transport and heating sector challenges grid stability. This study investigates load shifting through demand side management as …
The continuous introduction of renewable electricity and increased consumption through electrification of the transport and heating sector challenges grid stability. This study investigates load shifting through demand side management as a solution. We present a four-month experimental study of a low-complexity, hierarchical Model Predictive Control approach for demand side management in a near-zero emission occupied single-family house in Denmark. The control algorithm uses a price signal, weather forecast, a single-zone building model, and a non-linear heat pump efficiency model to generate a space-heating schedule. The weather-compensated, commercial heat pump is made to act smart grid-ready through outdoor temperature input override to enable heat boosting and forced stops to accommodate the heating schedule. The cost reduction from the controller ranged from 2-33% depending on the chosen comfort level. The experiment demonstrates that load shifting is feasible and cost-effective, even without energy storage, and that the current price scheme provides an incentive for Danish end-consumers to shift heating loads. However, issues related to controlling the heat pump through input-manipulation were identified, and the authors propose a more promising path forward involving coordination with manufacturers and regulators to make commercial heat pumps truly smart grid-ready.
Markovian master equations provide a versatile tool for describing open quantum systems when memory effects of the environment may be neglected. As these equations are of an approximate nature, they …
Markovian master equations provide a versatile tool for describing open quantum systems when memory effects of the environment may be neglected. As these equations are of an approximate nature, they often do not respect the laws of thermodynamics when no secular approximation is performed in their derivation. Here we introduce a Markovian master equation that is thermodynamically consistent and provides an accurate description whenever memory effects can be neglected. The thermodynamic consistency is obtained through a rescaled Hamiltonian for the thermodynamic bookkeeping, exploiting the fact that a Markovian description implies a limited resolution for heat. Our results enable a thermodynamically consistent description of a variety of systems where the secular approximation breaks down.
Nanoscale heat engines are subject to large fluctuations which affect their precision. The Thermodynamic Uncertainty Relation (TUR) provides a trade-off between output power, fluctuations and entropic cost. This trade-off may …
Nanoscale heat engines are subject to large fluctuations which affect their precision. The Thermodynamic Uncertainty Relation (TUR) provides a trade-off between output power, fluctuations and entropic cost. This trade-off may be overcome by systems exhibiting quantum coherence. This letter provides a study of the TUR in a prototypical quantum heat engine, the Scovil & Schulz-DuBois maser. Comparison with a classical reference system allows us to determine the effect of quantum coherence on the performance of the heat engine. We identify analytically regions where coherence suppresses fluctuations, implying a quantum advantage, as well as regions where fluctuations are enhanced by coherence. This quantum effect cannot be anticipated from the off-diagonal elements of the density matrix. Because the fluctuations are not encoded in the steady state alone, TUR violations are a consequence of coherence that goes beyond steady-state coherence. While the system violates the conventional TUR, it adheres a recent formulation of a quantum TUR. We further show that parameters where the engine operates close to the conventional limit are prevalent and TUR violations in the quantum model not uncommon.
The ignition of Quantum Cascade Lasers can occur from a state of oscillating fie ld domains. Here, the interplay between lasing and the kinetics of traveling dom ain boundaries provides …
The ignition of Quantum Cascade Lasers can occur from a state of oscillating fie ld domains. Here, the interplay between lasing and the kinetics of traveling dom ain boundaries provides complex oscillation scenarios. We analyze our numerical findings in detail for a device operating at terahertz frequencies and manifest chaotic evolution by positive Lyapunov exponents. This shows that these importan t devices can exhibit chaotic behavior even without periodic driving, which need s to be taken into account in their design.
Entropy production is a key concept of thermodynamics and allows one to analyze the operation of engines. For the Scovil-Schulz-DuBois heat engine, the archetypal three-level thermal maser coupled to thermal …
Entropy production is a key concept of thermodynamics and allows one to analyze the operation of engines. For the Scovil-Schulz-DuBois heat engine, the archetypal three-level thermal maser coupled to thermal baths, it was argued that the common definition of heat flow may provide negative entropy production for certain parameters [E. Boukobza and D. J. Tannor, Phys. Rev. Lett. 98, 240601 (2007)]. Here, we show that this can be cured, if corrections for detuning are properly applied to the energies used for the bath transitions. This method can be used more generally for the thermodynamical analysis of optical transitions where the modes of the light field are detuned from the transition energy.
Abstract The electron kinetics in nanowire-based hot-carrier solar cells is studied, where both relaxation and extraction are considered concurrently. Our kinetics is formulated in the many-particle basis of the interacting …
Abstract The electron kinetics in nanowire-based hot-carrier solar cells is studied, where both relaxation and extraction are considered concurrently. Our kinetics is formulated in the many-particle basis of the interacting system. Detailed comparison with simplified calculations based on product states shows that this includes the Coulomb interaction both in lowest and higher orders. While relaxation rates of 1 ps are obtained, if lowest order processes are available, timescales of tens of ps arise if these are not allowed for particular designs and initial conditions. Based on these calculations we quantify the second order effects and discuss the extraction efficiency, which remains low unless an energy filter by resonant tunnelling is applied.
The electron kinetics in nanowire-based hot-carrier solar cells is studied, where both relaxation and extraction are considered concurrently. Our kinetics is formulated in the many-particle basis of the interacting system. …
The electron kinetics in nanowire-based hot-carrier solar cells is studied, where both relaxation and extraction are considered concurrently. Our kinetics is formulated in the many-particle basis of the interacting system. Detailed comparison with simplified calculations based on product states shows that this includes the Coulomb interaction both in lowest and higher orders. While relaxation rates of 1 ps are obtained, if lowest order processes are available, timescales of tens of ps arise if these are not allowed for particular designs and initial conditions. Based on these calculations we discuss the extraction efficiency, which remains low unless an energy filter by resonant tunnelling is applied.
The electron kinetics in nanowire-based hot-carrier solar cells is studied, where both relaxation and extraction are considered concurrently. Our kinetics is formulated in the many-particle basis of the interacting system. …
The electron kinetics in nanowire-based hot-carrier solar cells is studied, where both relaxation and extraction are considered concurrently. Our kinetics is formulated in the many-particle basis of the interacting system. Detailed comparison with simplified calculations based on product states shows that this includes the Coulomb interaction both in lowest and higher orders. While relaxation rates of 1 ps are obtained, if lowest order processes are available, timescales of tens of ps arise if these are not allowed for particular designs and initial conditions. Based on these calculations we quantify the second order effects and discuss the extraction efficiency, which remains low unless an energy filter by resonant tunnelling is applied.
The electron kinetics in nanowire-based hot-carrier solar cells is studied, where both relaxation and extraction are considered concurrently. Our kinetics is formulated in the many-particle basis of the interacting system. …
The electron kinetics in nanowire-based hot-carrier solar cells is studied, where both relaxation and extraction are considered concurrently. Our kinetics is formulated in the many-particle basis of the interacting system. Detailed comparison with simplified calculations based on product states shows that this includes the Coulomb interaction both in lowest and higher orders. While relaxation rates of 1 ps are obtained, if lowest order processes are available, timescales of tens of ps arise if these are not allowed for particular designs and initial conditions. Based on these calculations we quantify the second order effects and discuss the extraction efficiency, which remains low unless an energy filter by resonant tunnelling is applied.
A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which …
A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular approximation. This allows for the treatment of systems, where coherences are generated by the bath couplings while avoiding the negative occupations occurring in the Bloch-Wangsness-Redfield kinetic equations. The versatility and accuracy of the approach is verified by its application to three entirely different physical systems: (i) electric transport through a double-dot system coupled to electronic reservoirs, (ii) exciton kinetics in coupled chromophores in the presence of a heat bath, and (iii) the simulation of quantum cascade lasers, where the coherent electron transport is established by scattering with phonons and impurities.
We examine the so-called thermodynamic uncertainty relation (TUR), a cost-precision trade-off relationship in transport systems. Based on the fluctuation symmetry, we derive a condition on the validity of the TUR …
We examine the so-called thermodynamic uncertainty relation (TUR), a cost-precision trade-off relationship in transport systems. Based on the fluctuation symmetry, we derive a condition on the validity of the TUR for general nonequilibrium (classical and quantum) systems. We find that the first non-zero contribution to the TUR beyond equilibrium, given in terms of nonlinear transport coefficients, can be positive or negative, thus affirming or violating the TUR depending on the details of the system. We exemplify our results for noninteracting quantum systems by deriving the thermodynamic uncertainty relation in the language of the transmission function. We demonstrate that quantum coherent systems that do not follow a population Markovian master equation, e.g. by supporting high order tunneling processes or relying on coherences, violate the TUR.
Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed …
Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed and open systems driven out of equilibrium by an external time-dependent force, and for open systems maintained in a nonequilibrium steady-state by nonequilibrium boundary conditions, are derived from a unified approach. Applications to fermion and boson transport in quantum junctions are discussed. Quantum master equations and Green's functions techniques for computing the energy and particle statistics are presented.
One of the fundamental questions in quantum thermodynamics concerns the decomposition of energetic changes into heat and work. Contrary to classical engines, the entropy change of the piston cannot be …
One of the fundamental questions in quantum thermodynamics concerns the decomposition of energetic changes into heat and work. Contrary to classical engines, the entropy change of the piston cannot be neglected in the quantum domain. As a consequence, different concepts of work arise, depending on the desired task and the implied capabilities of the agent using the work generated by the engine. Each work quantifier---from ergotropy to non-equilibrium free energy---has well defined operational interpretations. We analyse these work quantifiers for a heat-pumped three-level maser and derive the respective engine efficiencies. In the classical limit of strong maser intensities the engine efficiency converges towards the Scovil--Schulz-DuBois maser efficiency, irrespective of the work quantifier.
Multiple exciton generation (MEG) is a process in which more than one electron hole pair is generated per absorbed photon. It allows us to increase the efficiency of solar energy …
Multiple exciton generation (MEG) is a process in which more than one electron hole pair is generated per absorbed photon. It allows us to increase the efficiency of solar energy harvesting. Experimental studies have shown the multiple exciton generation yield of 1.2 in isolated colloidal quantum dots. However real photoelectric devices require the extraction of electron hole pairs to electric contacts. We provide a systematic study of the corresponding quantum coherent processes including extraction and injection and show that a proper design of extraction and injection rates enhances the yield significantly up to values around 1.6.
Heat and work for quantum systems governed by dissipative master equations with a time-dependent driving field were introduced in the pioneering work of Alicki [J. Phys. A 12, L103 (1979)]. …
Heat and work for quantum systems governed by dissipative master equations with a time-dependent driving field were introduced in the pioneering work of Alicki [J. Phys. A 12, L103 (1979)]. Alicki's work was in the Schr\"odinger picture; here we extend these definitions to the Heisenberg and interaction pictures. We show that, in order to avoid consistency problems, the full time derivatives in the definitions for heat flux and power (work flux) should be replaced by partial time derivatives. We also present an alternative approach to the partitioning of the energy flux which differs from that of Alicki in that the instantaneous interaction energy with the external field is not included directly. We then proceed to generalize Alicki's definition of power by replacing the original system and its external driving field with a larger, bipartite system, governed by a time-independent Hamiltonian. Using the definition of heat flux and the generalized definition of power, we derive the first law of thermodynamics in differential form, for both the full bipartite system and the partially traced subsystems. Although the second law (Clausius formulation) is satisfied for the full bipartite system, we find that in general there is no rigorous formulation of the second law for the partially traced subsystem unless certain additional requirements are met. Once these requirements are satisfied, however, both the Carnot and the Clausius formulations of the second law are satisfied. We illustrate this thermodynamic analysis on both the simple Jaynes-Cummings model and an extended dissipative Jaynes-Cummings model, which is a model for a quantum amplifier.
Fluctuations of thermodynamic observables, such as heat and work, contain relevant information on the underlying physical process. These fluctuations are however not taken into account in the traditional laws of …
Fluctuations of thermodynamic observables, such as heat and work, contain relevant information on the underlying physical process. These fluctuations are however not taken into account in the traditional laws of thermodynamics. While the second law is extended to fluctuating systems by the celebrated fluctuation theorems, the first law is generally believed to hold even in the presence of fluctuations. Here we show that in the presence of quantum fluctuations, also the first law of thermodynamics may break down. This happens because quantum mechanics imposes constraints on the knowledge of heat and work. To illustrate our results, we provide a detailed case-study of work and heat fluctuations in a quantum heat engine based on a circuit QED architecture. We find probabilistic violations of the first law and show that they are closely connected to quantum signatures related to negative quasi-probabilities. Our results imply that in the presence of quantum fluctuations, the first law of thermodynamics may not be applicable to individual experimental runs.
We study the exciton dynamics in an optically excited nanocrystal quantum dot. Multiple exciton formation is more efficient in nanocrystal quantum dots compared to bulk semiconductors due to enhanced Coulomb …
We study the exciton dynamics in an optically excited nanocrystal quantum dot. Multiple exciton formation is more efficient in nanocrystal quantum dots compared to bulk semiconductors due to enhanced Coulomb interactions and the absence of conservation of momentum. The formation of multiple excitons is dependent on different excitation parameters and the dissipation. We study this process within a Lindblad quantum rate equation using the full many-particle states. We optically excite the system by creating a single high energy exciton ESX in resonance to a double exciton EDX. With Coulomb electron-electron interaction, the population can be transferred from the single exciton to the double exciton state by impact ionisation (inverse Auger process). The ratio between the recombination processes and the absorbed photons provide the yield of the structure. We observe a quantum yield of comparable value to experiment assuming typical experimental conditions for a 4 nm PbS quantum dot.
Recent experimental progress has made it possible to detect in real-time single electrons tunneling through Coulomb blockade nanostructures, thereby allowing for precise measurements of the statistical distribution of the number …
Recent experimental progress has made it possible to detect in real-time single electrons tunneling through Coulomb blockade nanostructures, thereby allowing for precise measurements of the statistical distribution of the number of transferred charges, the so-called full counting statistics. These experimental advances call for a solid theoretical platform for equally accurate calculations of distribution functions and their cumulants. Here we develop a general framework for calculating zero-frequency current cumulants of arbitrary orders for transport through nanostructures with strong Coulomb interactions. Our recursive method can treat systems with many states as well as non-Markovian dynamics. We illustrate our approach with three examples of current experimental relevance: bunching transport through a two-level quantum dot, transport through a nano-electromechanical system with dynamical Franck-Condon blockade, and transport through coherently coupled quantum dots embedded in a dissipative environment. We discuss properties of high-order cumulants as well as possible subtleties associated with non-Markovian dynamics.
Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler …
Using the parametrically driven harmonic oscillator as a working example, we study two different Markovian approaches to the quantum dynamics of a periodically driven system with dissipation. In the simpler approach, the driving enters the master equation for the reduced density operator only in the Hamiltonian term. An improved master equation is achieved by treating the entire driven system within the Floquet formalism and coupling it to the reservoir as a whole. The different ensuing evolution equations are compared in various representations, particularly as Fokker-Planck equations for the Wigner function. On all levels of approximation, these evolution equations retain the periodicity of the driving, so that their solutions have Floquet form and represent eigenfunctions of a nonunitary propagator over a single period of the driving. We discuss asymptotic states in the long-time limit as well as the conservative and the high-temperature limits. Numerical results obtained within the different Markov approximations are compared with the exact path-integral solution. The application of the improved Floquet-Markov scheme becomes increasingly important when considering stronger driving and lower temperatures.
We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially …
We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially described by a canonical equilibrium distribution. Whereas the total entropy of system plus reservoirs is conserved, we show that the system entropy production is always positive and is a direct measure of the system-reservoir correlations and/or entanglements. Using an exactly solvable quantum model, we illustrate our novel interpretation of the Second Law in a microscopically reversible finite-size setting, with strong coupling between system and reservoirs. With this model, we also explicitly show the approach of our exact formulation to the standard description of irreversibility in the limit of a large reservoir.
Practical methods to extract the generalized dimension Dq and the largest Lyapunov exponent from experimental data are proposed and tested on examples. The measured values agree well with known values. …
Practical methods to extract the generalized dimension Dq and the largest Lyapunov exponent from experimental data are proposed and tested on examples. The measured values agree well with known values. In applications to chaotic signals, convergence of dimension is investigated for varying the delay time and the embedding dimension.
We present a first-principles derivation of the Markovian semi-group master equation without invoking the rotating wave approximation (RWA). Instead we use a time coarse-graining approach which leaves us with a …
We present a first-principles derivation of the Markovian semi-group master equation without invoking the rotating wave approximation (RWA). Instead we use a time coarse-graining approach which leaves us with a free timescale parameter, which we can optimize. Comparing this approach to the standard RWA-based Markovian master equation, we find that significantly better agreement is possible using the coarse-graining approach, for a three-level model coupled to a bath of oscillators, whose exact dynamics we can solve for at zero temperature. The model has the important feature that the RWA has a non-trivial effect on the dynamics of the populations. We show that the two different master equations can exhibit strong qualitative differences for the population of the energy eigenstates even for such a simple model. The RWA-based master equation misses an important feature which the coarse-graining based scheme does not. By optimizing the coarse-graining timescale the latter scheme can be made to approach the exact solution much more closely than the RWA-based master equation.
We formulate the general approach based on the Lindblad equation to calculate the full counting statistics of work and heat produced by driven quantum systems weakly coupled with a Markovian …
We formulate the general approach based on the Lindblad equation to calculate the full counting statistics of work and heat produced by driven quantum systems weakly coupled with a Markovian thermal bath. The approach can be applied to a wide class of dissipative quantum systems driven by an arbitrary force protocol. We show the validity of general fluctuation relations and consider several generic examples. The possibilities of using calorimetric measurements to test the presence of coherence and entanglement in the open quantum systems are discussed.
In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation …
In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the approximations under which the phenomenological model correctly describes the dynamics of the atom-cavity system. Some examples wherein the phenomenological and the microscopic master equations give rise to different predictions are discussed in detail.
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined …
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power, can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones like molecular motors, and heat engines like thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Heat engines should ideally have large power output, operate close to Carnot efficiency and show constancy, i.e., exhibit only small fluctuations in this output. For steady-state heat engines, driven by …
Heat engines should ideally have large power output, operate close to Carnot efficiency and show constancy, i.e., exhibit only small fluctuations in this output. For steady-state heat engines, driven by a constant temperature difference between the two heat baths, we prove that out of these three requirements only two are compatible. Constancy enters quantitatively the conventional trade-off between power and efficiency. Thus, we rationalize and unify recent suggestions for overcoming this simple trade-off. Our universal bound is illustrated for a paradigmatic model of a quantum dot solar cell and for a Brownian gyrator delivering mechanical work against an external force.
An extension of the planar Smale–Birkhoff homoclinic theorem to the case of a heteroclinic saddle connection containing a finite number of fixed points is presented. This extension is used to …
An extension of the planar Smale–Birkhoff homoclinic theorem to the case of a heteroclinic saddle connection containing a finite number of fixed points is presented. This extension is used to find chaotic dynamics present in certain time-periodic perturbations of planar fluid models. Specifically, the Kelvin–Stuart cat's eye flow is studied, a model for a vortex pattern found in shear layers. A flow on the two-torus with Hamiltonian $H_0 = (2\pi )^{ - 1} \sin (2\pi x_1 )\cos (2\pi x_2 )$ is studied, as well as the evolution equations for an elliptical vortex in a three-dimensional strain flow.
An efficient molecular motor would deliver cargo to the target site at a high speed and in a punctual manner while consuming a minimal amount of energy. According to a …
An efficient molecular motor would deliver cargo to the target site at a high speed and in a punctual manner while consuming a minimal amount of energy. According to a recently formulated thermodynamic principle, referred to as the thermodynamic uncertainty relation, the travel distance of a motor and its variance are, however, constrained by the free energy being consumed. Here we use the principle underlying the uncertainty relation to quantify the transport efficiency of molecular motors for varying ATP concentration ([ATP]) and applied load (f). Our analyses of experimental data find that transport efficiencies of the motors studied here are semioptimized under the cellular condition. The efficiency is significantly deteriorated for a kinesin-1 mutant that has a longer neck-linker, which underscores the importance of molecular structure. It is remarkable to recognize that, among many possible directions for optimization, biological motors have evolved to optimize the transport efficiency in particular.
We consider a model for stationary electronic transport through a one-dimensional chain of two leads attached to a perturbed central region (quantum dot) in the regime where the theory proposed …
We consider a model for stationary electronic transport through a one-dimensional chain of two leads attached to a perturbed central region (quantum dot) in the regime where the theory proposed recently by Čápek for a similar model of phonon transport predicts the striking phenomenon of a permanent current between the leads. We show that Čápek's results based on a rigorous but asymptotic Davies theory differ from direct transport calculations that yield, in full agreement with the second law of thermodynamics, zero current. We find the permanent current to be within the error of the asymptotic expansion for finite couplings, and identify cancelling terms of the same order.
We consider stochastic and open quantum systems with a finite number of states, where a stochastic transition between two specific states is monitored by a detector. The long-time counting statistics …
We consider stochastic and open quantum systems with a finite number of states, where a stochastic transition between two specific states is monitored by a detector. The long-time counting statistics of the observed realizations of the transition, parametrized by cumulants, is the only available information about the system. We present an analytical method for reconstructing generators of the time evolution of the system compatible with the observations. The practicality of the reconstruction method is demonstrated by the examples of a laser-driven atom and the kinetics of enzyme-catalyzed reactions. Moreover, we propose cumulant-based criteria for testing the non-classicality and non-Markovianity of the time evolution, and lower bounds for the system dimension. Our analytical results rely on the close connection between the cumulants of the counting statistics and the characteristic polynomial of the generator, which takes the role of the cumulant generating function.
We compare different quantum master equations for the time evolution of the reduced density matrix. The widely applied secular approximation (rotating wave approximation) applied in combination with the Born-Markov approximation …
We compare different quantum master equations for the time evolution of the reduced density matrix. The widely applied secular approximation (rotating wave approximation) applied in combination with the Born-Markov approximation generates a Lindblad-type master equation ensuring for completely positive and stable evolution and is typically well applicable for optical baths. For phonon baths however, the secular approximation is expected to be invalid. The usual Markovian master equation does not generally preserve positivity of the density matrix. As a solution we propose a coarse-graining approach with a dynamically adapted coarse-graining time scale. For some simple examples we demonstrate that this preserves the accuracy of the integro-differential Born equation. For large times we analytically show that the secular approximation master equation is recovered. The method can in principle be extended to systems with a dynamically changing system Hamiltonian, which is of special interest for adiabatic quantum computation. We give some numerical examples for the spin-boson model of cases where a spin system thermalizes rapidly, and other examples where thermalization is not reached.
Thermodynamics of a three-level maser was studied in the pioneering work of Scovil and Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)]. In this work we consider the same three-level model, …
Thermodynamics of a three-level maser was studied in the pioneering work of Scovil and Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)]. In this work we consider the same three-level model, but treat both the matter and the light quantum mechanically. Specifically, we analyze an extended (three-level) dissipative (ED) Jaynes-Cummings model (JCM) within the framework of a quantum heat engine, using formulas for heat flux and power in bipartite systems introduced in our previous work [E. Boukobza and D. J. Tannor Phys. Rev. A 74, 063823 (2006)] Amplification of the selected cavity mode occurs even in this simple model, as seen by a positive steady state power. However, initial field coherence is lost, as seen by the decaying off-diagonal field density matrix elements, and by the Husimi-Kano $Q$ function. We show that after an initial transient time the field's entropy rises linearly during the operation of the engine, which we attribute to the dissipative nature of the evolution and not to matter-field entanglement. We show that the second law of thermodynamics is satisfied in two formulations (Clausius, Carnot) and that the efficiency of the ED JCM heat engine agrees with that defined intuitively by Scovil and Schulz-DuBois. Finally, we compare the steady state heat flux and power of the fully quantum model with the semiclassical counterpart of the ED JCM, and derive the engine efficiency formula of Scovil and Schulz-DuBois analytically from fundamental thermodynamic fluxes.
In this work we investigate the late-time steady states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily …
In this work we investigate the late-time steady states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is nonvanishing or equivalently if the relaxation time scales are finite. Using a variety of nonequilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system $=$ system+environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multitime correlations of the open system evolve towards those of the closed system thermal state. Multitime correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations.
Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linear-response variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in …
Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linear-response variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations arbitrarily far from equilibrium. In particular, we prove a linear-response-like bound on the large deviation function for currents in Markov jump processes. We find that nonequilibrium current fluctuations are always more likely than what is expected from a linear-response analysis. As a small-fluctuations corollary, we derive a recently conjectured uncertainty bound on the variance of current fluctuations.
A system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. A new quantum master equation which improves shortcomings of the …
A system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. A new quantum master equation which improves shortcomings of the master equation known in the so-called local approach is derived. The usual quantum master equation describing the weak coupling of the system with reservoir requires the knowledge of eigenvalues and eigenvectors of the Hamiltonian of the system, so it often becomes impractical. By this reason, when the inter-site couplings are weak, the local approach, which neglects the influence of the inter-site couplings on the system-reservoir couplings, is often used. However, recently, it was reported that the local approach master equation leads to the violation of the second law of thermodynamics. We develop a systematic perturbation expansion to derive corrections to the local approach master equation. Using this improvement of the local approach, we derive an expression for the heat flux for a particular model and show that it does not violate the second law of thermodynamics.
Hot-carrier solar cells are envisioned to utilize energy filtering to extract power from photogenerated electron–hole pairs before they thermalize with the lattice, and thus potentially offer higher power conversion efficiency …
Hot-carrier solar cells are envisioned to utilize energy filtering to extract power from photogenerated electron–hole pairs before they thermalize with the lattice, and thus potentially offer higher power conversion efficiency compared to conventional, single absorber solar cells. The efficiency of hot-carrier solar cells can be expected to strongly depend on the details of the energy filtering process, a relationship which to date has not been satisfactorily explored. Here, we establish the conditions under which electron–hole separation in hot-carrier solar cells can occur reversibly, that is, at maximum energy conversion efficiency. We thus focus our analysis on the internal operation of the hot-carrier solar cell itself, and in this work do not consider the photon-mediated coupling to the Sun. After deriving an expression for the voltage of a hot-carrier solar cell valid under conditions of both reversible and irreversible electrical operation, we identify separate contributions to the voltage from the thermoelectric effect and the photovoltaic effect. We find that, under specific conditions, the energy conversion efficiency of a hot-carrier solar cell can exceed the Carnot limit set by the intra-device temperature gradient alone, due to the additional contribution of the quasi-Fermi level splitting in the absorber. We also establish that the open-circuit voltage of a hot-carrier solar cell is not limited by the band gap of the absorber, due to the additional thermoelectric contribution to the voltage. Additionally, we find that a hot-carrier solar cell can be operated in reverse as a thermally driven solid-state light emitter. Our results help explore the fundamental limitations of hot-carrier solar cells, and provide a first step towards providing experimentalists with a guide to the optimal configuration of devices.
Clausius' statement of the second law of thermodynamics reads: Heat will flow spontaneously from a hot to cold reservoir. This statement should hold for transport of energy through a quantum …
Clausius' statement of the second law of thermodynamics reads: Heat will flow spontaneously from a hot to cold reservoir. This statement should hold for transport of energy through a quantum network composed of small subsystems each coupled to a heat reservoir. When the coupling between nodes is small, it seems reasonable to construct a local master equation for each node in contact with the local reservoir. The energy transport through the network is evaluated by calculating the energy flux after the individual nodes are coupled. We show by analysing the most simple network composed of two quantum nodes coupled to a hot and cold reservoir, that the local description can result in heat flowing from cold to hot reservoirs, even in the limit of vanishing coupling between the nodes. A global derivation of the master equation which prediagonalizes the total network Hamiltonian, and within this framework derives the master equation, is always consistent with the second-law of thermodynamics.
Biomolecular systems like molecular motors or pumps, transcription and translation machinery, and other enzymatic reactions, can be described as Markov processes on a suitable network. We show quite generally that, …
Biomolecular systems like molecular motors or pumps, transcription and translation machinery, and other enzymatic reactions, can be described as Markov processes on a suitable network. We show quite generally that, in a steady state, the dispersion of observables, like the number of consumed or produced molecules or the number of steps of a motor, is constrained by the thermodynamic cost of generating it. An uncertainty ε requires at least a cost of 2k(B)T/ε2 independent of the time required to generate the output.
Biomolecular networks capable of counting time can be thought of as ``Brownian clocks.'' The energy budgets necessary to run two classes of such clocks, assuming some minimal required precision, are …
Biomolecular networks capable of counting time can be thought of as ``Brownian clocks.'' The energy budgets necessary to run two classes of such clocks, assuming some minimal required precision, are theoretically determined.
We theoretically consider charge transport through two quantum dots coupled in series. The corresponding full counting statistics for noninteracting electrons is investigated in the limits of sequential and coherent tunneling …
We theoretically consider charge transport through two quantum dots coupled in series. The corresponding full counting statistics for noninteracting electrons is investigated in the limits of sequential and coherent tunneling by means of a master equation approach and a density matrix formalism, respectively. We clearly demonstrate the effect of quantum coherence on the zero-frequency cumulants of the transport process, focusing on noise and skewness. Moreover, we establish the continuous transition from the coherent to the incoherent tunneling limit in all cumulants of the transport process and compare this with decoherence described by a dephasing voltage probe model.
The dictum that ``information is physical'' indicates that we should understand how features of quantum physics, in particular, the phenomenon of quantum coherence, can be understood to be, and quantified …
The dictum that ``information is physical'' indicates that we should understand how features of quantum physics, in particular, the phenomenon of quantum coherence, can be understood to be, and quantified as, a resource for the processing of information. This Colloquium discusses how to characterize, quantify, and manipulate quantum coherence, in application areas ranging from many-body and solid state physics to biological and nanoscale systems.
An open question of fundamental importance in thermodynamics is how to describe the fluctuations of work for quantum coherent processes. In the standard approach, based on a projective energy measurement …
An open question of fundamental importance in thermodynamics is how to describe the fluctuations of work for quantum coherent processes. In the standard approach, based on a projective energy measurement both at the beginning and at the end of the process, the first measurement destroys any initial coherence in the energy basis. Here we seek extensions of this approach which can possibly account for initially coherent states. We consider all measurement schemes to estimate work and require that (i) the difference of average energy corresponds to average work for closed quantum systems and that (ii) the work statistics agree with the standard two-measurement scheme for states with no coherence in the energy basis. We first show that such a scheme cannot exist. Next, we consider the possibility of performing collective measurements on several copies of the state and prove that it is still impossible to simultaneously satisfy requirements (i) and (ii). Nevertheless, improvements do appear, and in particular, we develop a measurement scheme that acts simultaneously on two copies of the state and allows us to describe a whole class of coherent transformations.
For fluctuating currents in nonequilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We …
For fluctuating currents in nonequilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales. This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite time scales are not accessible. Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit. We illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle.
We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the observables …
We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the observables of interest and their time-evolution. Nevertheless, positive probability distributions for measurement outcomes can be obtained from the KQPD by taking into account the effect of measurement back-action and imprecision. Negativity in the KQPD can be linked to an interference effect and acts as an indicator for non-classical behavior. Notable examples of the KQPD are the Wigner function and the full counting statistics, both of which have been used extensively to describe systems in the absence as well as in the presence of a measurement apparatus. Here we discuss the KQPD and its moments in detail and connect it to various time-dependent problems including weak values, fluctuating work, and Leggett-Garg inequalities. Our results are illustrated using the simple example of two subsequent, non-commuting spin measurements.
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. …
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to an additional constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency cannot be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.
When deriving a master equation for a multipartite weakly-interacting open quantum systems, dissipation is often addressed locally on each component, i.e. ignoring the coherent couplings, which are later added ‘by …
When deriving a master equation for a multipartite weakly-interacting open quantum systems, dissipation is often addressed locally on each component, i.e. ignoring the coherent couplings, which are later added ‘by hand’. Although simple, the resulting local master equation (LME) is known to be thermodynamically inconsistent. Otherwise, one may always obtain a consistent global master equation (GME) by working on the energy basis of the full interacting Hamiltonian. Here, we consider a two-node ‘quantum wire’ connected to two heat baths. The stationary solution of the LME and GME are obtained and benchmarked against the exact result. Importantly, in our model, the validity of the GME is constrained by the underlying secular approximation. Whenever this breaks down (for resonant weakly-coupled nodes), we observe that the LME, in spite of being thermodynamically flawed: (a) predicts the correct steady state, (b) yields with the exact asymptotic heat currents, and (c) reliably reflects the correlations between the nodes. In contrast, the GME fails at all three tasks. Nonetheless, as the inter-node coupling grows, the LME breaks down whilst the GME becomes correct. Hence, the global and local approach may be viewed as complementary tools, best suited to different parameter regimes.
This Letter investigates a hybrid quantum system combining cavity quantum electrodynamics and optomechanics. The Hamiltonian problem of a photon mode coupled to a two-level atom via a Jaynes-Cummings coupling and …
This Letter investigates a hybrid quantum system combining cavity quantum electrodynamics and optomechanics. The Hamiltonian problem of a photon mode coupled to a two-level atom via a Jaynes-Cummings coupling and to a mechanical mode via radiation pressure coupling is solved analytically. The atom-cavity polariton number operator commutes with the total Hamiltonian leading to an exact description in terms of tripartite atom-cavity-mechanics polarons. We demonstrate the possibility to obtain cooling of mechanical motion at the single-polariton level and describe the peculiar quantum statistics of phonons in such an unconventional regime.
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 …
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.
In this paper three-dimensional dynamical systems are considered that are close to systems with a structurally unstable homoclinic curve, i.e. with a path biasymptotic to a structurally stable periodic motion …
In this paper three-dimensional dynamical systems are considered that are close to systems with a structurally unstable homoclinic curve, i.e. with a path biasymptotic to a structurally stable periodic motion of saddle type to which the stable and unstable manifolds are tangent. Under the assumption that the tangency is the simplest structurally unstable one, it is established that in the set of paths lying entirely in an extended neighborhood of a periodic motion there is a subset whose paths are in one-to-one correspondence with the paths of a subsystem of a Bernoulli scheme of three symbols. Bibliography: 6 items.
The coarse-graining approach to deriving the quantum Markovian master equation is revisited, with close attention given to the underlying approximations. It is further argued that the time interval over which …
The coarse-graining approach to deriving the quantum Markovian master equation is revisited, with close attention given to the underlying approximations. It is further argued that the time interval over which the coarse-graining is performed is a free parameter that can be given a physical measurement-based interpretation. In the case of the damping of composite systems to reservoirs of different temperatures, currently of much interest in the study of quantum thermal machines with regard to the validity of `local' and `global' forms of these equations, the coupling of the subsystems leads to a further timescale with respect to which the coarse-graining time interval can be chosen. Different choices lead to different master equations that correspond to the local and global forms. These can be then understood as having different physical interpretations based on the role of the coarse-graining, as well as different limitations in application.
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 …
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.
Transitions between nonequilibrium steady states obey a generalized Clausius inequality, which becomes an equality in the quasistatic limit.For slow but finite transitions, we show that the behavior of the system …
Transitions between nonequilibrium steady states obey a generalized Clausius inequality, which becomes an equality in the quasistatic limit.For slow but finite transitions, we show that the behavior of the system is described by a response matrix whose elements are given by a far-fromequilibrium Green-Kubo formula, involving the decay of correlations evaluated in the nonequilibrium steady state.This result leads to a fluctuation-dissipation relation between the mean and variance of the nonadiabatic entropy production, ∆sna.Furthermore, our results extend -to nonequilibrium steady states -the thermodynamic metric structure introduced by Sivak and Crooks for analyzing minimal-dissipation protocols for transitions between equilibrium states.
Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one-dimensional periodic potential. Two different approaches to the …
Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one-dimensional periodic potential. Two different approaches to the large deviation function of the particle current are presented. First, we derive an explicit expression for the large deviation functional of the empirical phase space density, which replaces the level 2.5 functional used for overdamped dynamics. Using this approach, we obtain several bounds on the large deviation function of the particle current. We compare these to bounds for overdamped dynamics that have recently been derived, motivated by the thermodynamic uncertainty relation. Second, we provide a method to calculate the large deviation function via the cumulant generating function. We use this method to assess the tightness of the bounds in a numerical case study for a cosine potential.
Heat engines, which cyclically transform heat into work, are ubiquitous in technology. Lasers and masers, which generate a coherent electromagnetic field, may be viewed as heat engines that rely on …
Heat engines, which cyclically transform heat into work, are ubiquitous in technology. Lasers and masers, which generate a coherent electromagnetic field, may be viewed as heat engines that rely on population inversion or coherence in the active medium. Here we put forward an unconventional paradigm of a remarkably simple electromagnetic heat-powered engine that bears basic differences to any known maser or laser: it does not rely on population inversion or coherence in its two-level working medium. Nor does it require any coherent driving or pump aside from two (hot and cold) baths. Strikingly, the proposed maser, in which the heat exchange between these baths mediated by the working medium amplifies the signal field, can attain the highest possible efficiency even if the signal is incoherent.
We propose and analyze a simple mesoscopic quantum heat engine that exhibits both high-power and high-efficiency. The system consists of a biased Josephson junction coupled to two microwave cavities, with …
We propose and analyze a simple mesoscopic quantum heat engine that exhibits both high-power and high-efficiency. The system consists of a biased Josephson junction coupled to two microwave cavities, with each cavity coupled to a thermal bath. Resonant Cooper pair tunneling occurs with the exchange of photons between cavities, and a temperature difference between the baths can naturally lead to a current against the voltage, and hence work. As a consequence of the unique properties of Cooper-pair tunneling, the heat current is completely separated from the charge current. This combined with the strong energy-selectivity of the process leads to an extremely high efficiency.