Quantum Thermodynamics: A Dynamical Viewpoint

Thermodynamics of Intrinsic Reaction Coordinate (IRC) Chemical Reaction Pathways

We address the scientific "time" concept in the context of more general relaxation processes toward the Wärmetod of thermodynamic equilibrium. More specifically, we sketch a construction of a conceptual ladder of chemical reaction steps that can rigorously bridge a description from the microscopic domain of molecular quantum chemistry to the macroscopic materials domain of Gibbsian thermodynamics. This conceptual reformulation follows the pioneering work of Kenichi Fukui (Nobel 1981) in rigorously formulating the intrinsic reaction coordinate (IRC) pathway for controlled description of non-equilibrium passages between reactant and product equilibrium states of an overall material transformation. Elementary chemical reaction steps are thereby identified as the logical building-blocks of an integrated mathematical framework that seamlessly spans the gulf between classical (pre-1925) and quantal (post-1925) scientific conceptions and encompasses both static and dynamic aspects of material change. All modern chemical reaction rate studies build on the apparent infallibility of quantum-chemical solutions of Schrödinger's wave equation and its Dirac-type relativistic corrections. This infallibility may now be properly accepted as an added"inductive law" of Gibbsian chemical thermodynamics, the only component of 19th-century physics that passed intact through the revolutionary quantum upheavals of 1925.

Impact of the sequence of system-environment interactions on the functionality and efficiency of quantum thermal machines

In this work, we investigate effects of the sequence of system-environment interactions on the functionality and performance of quantum thermal machines (QTMs). The working substance of our setup consists of two subsystems, each independently coupled to its local thermal reservoir and further interconnected with a common reservoir in a cascaded manner. We demonstrate the impact of the sequential interactions between the subsystems and the common reservoir by exchanging the temperatures of the two local reservoirs. Our findings reveal that, when the two subsystems are in resonance, such an exchange alters the efficiency of QTMs without changing their functional types. Conversely, when the two subsystems are detuned, this exchange not only changes the efficiency but also the types of QTMs. Our results indicate that the manners of system-reservoir interactions offer significant potential for designing QTMs with tailored functionalities and enhanced performance.

Strong coupling non-Markovian quantum thermodynamics of a finite-bath system

The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. To this end, a non-trivial, non-Markovian model of a central spin surrounded by a spin bath is taken up, and its exact evolution is derived for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and the original system (bath) Hamiltonian. An explicit expression for the work, a mismatch between the system and bath internal energies, is derived. The thermodynamic entropy of the system at thermal equilibrium is studied using the Hamiltonian of mean force in the strong coupling regime. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated. Furthermore, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery.

Observing time-dependent energy level renormalisation in an ultrastrongly coupled open system

Understanding how strong coupling and memory effects influence energy levels in open quantum systems is a fundamental challenge. Here, we experimentally probe these effects in a two-level open system coupled to a single-mode quantum environment, using Ramsey interferometry in a trapped ion. Operating in the strong coupling regime, we observe both dissipative effects and time-dependent energy shifts of up to 15% of the bare system frequency, with the total system effectively isolated from external environments. These dynamic shifts, likely ubiquitous across quantum platforms, arise solely from ultra-strong system-mode interactions and correlation build-up and are accurately predicted by the minimal-dissipation Ansatz. Our approach identifies these as generalised Lamb shifts, matching conventional predictions on time-average. We provide experimental fingerprints supporting the Ansatz of minimal-dissipation, thereby suggesting it as a testable quantum thermodynamics framework and establishing a foundation for future benchmarks in strong-coupling quantum thermodynamics and related technologies.

Entanglement and quantum discord in the cavity QED models

We investigate the quantum correlation between light and matter in bipartite quantum systems, drawing on the Jaynes-Cummings model and the Tavis-Cummings model, which are well-established in cavity quantum electrodynamics. Through the resolution of the quantum master equation, we can derive the dissipative dynamics in open systems. To assess the extent of quantum correlation, several measures are introduced: von Neumann entropy, concurrence and quantum discord. The effects of initial entanglement and dissipation intensity on quantum discord are carefully examined. Furthermore, we examined the dynamics of quantum discord within the O H + model.

Stochastic Scovil-Schulz-DuBois machine and its three types of cycles

Three types of cycles are identified in the quantum jump trajectories of the Scovil-Schulz-DuBois (SSDB) machine: An R cycle as refrigeration, an H cycle as a heat engine, and an N cycle in which the machine is neutral. The statistics of these cycles are investigated via a semi-Markov process method. We find that in the large time limit, whether the machine operates as a heat engine or refrigerator depends on the ratio between the numbers of R cycles and H cycles per unit time. Further increasing the hot bath temperature above a certain threshold does not increase the machine's power output. The cause is that, in this situation, the N cycle has a greater probability than the H cycle and R cycle. Although the SSDB machine operates by randomly switching between these three cycles, at the level of a single quantum jump trajectory, its heat engine efficiency and the refrigerator's coefficient of performance remain constant.

Quantum Thermodynamic Derivation of the Energy Resolution Limit in Magnetometry

It was recently demonstrated that a multitude of realizations of several magnetic sensing technologies satisfy the energy resolution limit, which connects a quantity composed by the variance of the magnetic field estimate, the sensor volume and the measurement time, and having units of action, with ℏ. A first-principles derivation of this limit is still elusive. We here present such a derivation based on quantum thermodynamic arguments. We show that the energy resolution limit is a result of quantum thermodynamic work necessarily associated with quantum measurement and Landauer erasure, the work being exchanged with the magnetic field. We apply these considerations to atomic magnetometers, diamond magnetometers, and SQUIDs, spanning an energy resolution from 10^{0}ℏ to 10^{7}ℏ. This connection between quantum thermodynamics and magnetometry can help advance quantum sensing technologies towards even more sensitive devices.

Complete positivity and thermal relaxation in quadratic quantum master equations

The ultimate goal of this paper is to develop a systematic method for deriving quantum master equations that satisfy the requirements of a completely positive and trace-preserving (CPTP) map, further describing thermal relaxation processes. In this paper, we assume that the quantum master equation is obtained through the canonical quantization of the generalized Brownian motion proposed in our recent paper [T. Koide and F. Nicacio, Phys. Lett. A 494, 129277 (2024)0375-960110.1016/j.physleta.2023.129277]. At least classically, this dynamics describes the thermal relaxation process regardless of the choice of the system Hamiltonian. The remaining task is to identify the parameters ensuring that the quantum master equation meets complete positivity. We limit our discussion to many-body quadratic Hamiltonians and establish a CPTP criterion for our quantum master equation. This criterion is useful for applying our quantum master equation to models with interaction such as a network model, which has been used to investigate how quantum effects modify heat conduction.

Exact Hidden Markovian Dynamics in Quantum Circuits

Characterizing nonequilibrium dynamics in quantum many-body systems is a challenging frontier of physics. In this Letter, we systematically construct solvable nonintegrable quantum circuits that exhibit exact hidden Markovian subsystem dynamics. This feature thus enables accurately calculating local observables for arbitrary evolution time. Utilizing the influence matrix method, we show that the influence of the time-evolved global system on a finite subsystem can be analytically described by sequential, time-local quantum channels acting on the subsystem with an ancilla of finite Hilbert space dimension. The realization of exact hidden Markovian property is facilitated by a solvable condition on the underlying two-site gates in the quantum circuit. We further present several concrete examples with varying local Hilbert space dimensions to demonstrate our approach.

Probing coherent quantum thermodynamics using a trapped ion

Quantum thermodynamics is aimed at grasping thermodynamic laws as they apply to thermal machines operating in the deep quantum regime, where coherence and entanglement are expected to matter. Despite substantial progress, however, it has remained difficult to develop thermal machines in which such quantum effects are observed to be of pivotal importance. In this work, we demonstrate the possibility to experimentally measure and benchmark a genuine quantum correction, induced by quantum friction, to the classical work fluctuation-dissipation relation. This is achieved by combining laser-induced coherent Hamiltonian rotations and energy measurements on a trapped ion. Our results demonstrate that recent developments in stochastic quantum thermodynamics can be used to benchmark and unambiguously distinguish genuine quantum coherent signatures generated along driving protocols, even in presence of experimental SPAM errors and, most importantly, beyond the regimes for which theoretical predictions are available (e.g., in slow driving).

Quantitative predictive theories through integrating quantum, statistical, equilibrium, and nonequilibrium thermodynamics

Today's thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially on the Onsager Theorem as a separate branch of thermodynamics developed in 1930s. Between them, quantum mechanics was invented and quantitatively solved in terms of density functional theory (DFT) in 1960s. These three scientific domains operate based on different principles and are very much separated from each other. In analogy to the parable of the blind men and the elephant articulated by Perdew, they individually represent different portions of a complex system and thus are incomplete by themselves alone, resulting in the lack of quantitative agreement between their predictions and experimental observations. Over the last two decades, the author's group has developed a multiscale entropy approach (recently termed as zentropy theory) that integrates DFT-based quantum mechanics and Gibbs statistical mechanics and is capable of accurately predicting entropy and free energy of complex systems. Furthermore, in combination with the combined law for nonequilibrium systems presented by Hillert, the author developed the theory of cross phenomena beyond the phenomenological Onsager Theorem. The zentropy theory and theory of cross phenomena jointly provide quantitative predictive theories for systems from electronic to any observable scales as reviewed in the present work.

Quantum Molecular Devices

Miniaturization has been the driving force in contemporary technologies. However, two main obstacles limit further progress: additional reduction in size has reached its quantum limit, and lithography has reached its threshold. Future progress requires tackling three challenges: chemical synthesis of a complete device, active cooling for exploiting quantum characteristics, and quantum coherent control for operation. Chemical synthesis replaces the current top-bottom approach to manufacturing with bottom-up synthesis from elementary building blocks. New ultracold synthetic methods should be developed. An additional challenge is the active cooling of molecules, where the bottleneck is entropy removal. Notably, the current solution, namely, diffusion, is too slow. A coherent approach offers a possible solution; specifically, quantum coherent control is the method of choice for manipulating ultracold matter. Finally, the many degrees of freedom of molecules should be an asset that allows the design and implementation of complex tasks such as sensing communication and computing.

Performance enhancement of quantum Brayton engine via Bose-Einstein condensation

Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.

Non-Equilibrium Wigner Function and Application to Model of Catalyzed Polymerization

The quantum Wigner function and non-equilibrium equation for a microscopic particle in one spatial dimension (1D) subject to a potential and a heat bath at thermal equilibrium are considered by non-trivially extending a previous analysis. The non-equilibrium equation yields a general hierarchy for suitable non-equilibrium moments. A new non-trivial solution of the hierarchy combining the continued fractions and infinite series thereof is obtained and analyzed. In a short thermal wavelength regime (keeping quantum features adequate for chemical reactions), the hierarchy is approximated by a three-term one. For long times, in turn, the three-term hierarchy is replaced by a Smoluchovski equation. By extending that 1D analysis, a new model of the growth (polymerization) of a molecular chain (template or te) by binding an individual unit (an atom) and activation by a catalyst is developed in three spatial dimensions (3D). The atom, te, and catalyst move randomly as solutions in a fluid at rest in thermal equilibrium. Classical statistical mechanics describe the te and catalyst approximately. Atoms and bindings are treated quantum-mechanically. A mixed non-equilibrium quantum-classical Wigner-Liouville function and dynamical equations for the atom and for the te and catalyst, respectively, are employed. By integrating over the degrees of freedom of te and with the catalyst assumed to be near equilibrium, an approximate Smoluchowski equation is obtained for the unit. The mean first passage time (MFPT) for the atom to become bound to the te, facilitated by the catalyst, is considered. The resulting MFPT is consistent with the Arrhenius formula for rate constants in chemical reactions.

The Thermomajorization Polytope and Its Degeneracies

Drawing inspiration from transportation theory, in this work, we introduce the notions of "well-structured" and "stable" Gibbs states and we investigate their implications for quantum thermodynamics and its resource theory approach via thermal operations. It is found that, in the quasi-classical realm, global cyclic state transfers are impossible if and only if the Gibbs state is stable. Moreover, using a geometric approach by studying the so-called thermomajorization polytope, we prove that any subspace in equilibrium can be brought out of equilibrium via thermal operations. Interestingly, the case of some subsystem being in equilibrium can be witnessed via the degenerate extreme points of the thermomajorization polytope, assuming that the Gibbs state of the system is well structured. These physical considerations are complemented by simple new constructions for the polytope's extreme points, as well as for an important class of extremal Gibbs-stochastic matrices.

Universal quantum Otto heat machine based on the Dicke model

In this paper we study a quantum Otto thermal machine where the working substance is composed of N identical qubits coupled to a single mode of a bosonic field, where the atoms and the field interact with a reservoir, as described by the so-called open Dicke model. By controlling the relevant and experimentally accessible parameters of the model we show that it is possible to build a universal quantum heat machine (UQHM) that can function as an engine, refrigerator, heater, or accelerator. The heat and work exchanges are computed taking into account the growth of the number N of atoms as well as the coupling regimes characteristic of the Dicke model for several ratios of temperatures of the two thermal reservoirs. The analysis of quantum features such as entanglement and second-order correlation shows that these quantum resources do not affect either the efficiency or the performance of the UQHM based on the open Dicke model. In addition, we show that the improvement in both efficiency and coefficient of performance of our UQHM occurs for regions around the critical value of the phase transition parameter of the model.

Controlling work output and coherence in finite-time quantum Otto engines through monitoring

We examine the role of diagnostic quantum measurements on the work statistics of a finite-time quantum Otto heat engine operated in the steady state. We consider three pointer-based measurement schemes that differ in the number of system-pointer interactions and pointer measurements. We show that the coherence of the working substance and the work output of the engine can be controlled by tuning the monitoring measurements. Moreover, for a working substance consisting of a two-level system we show that while all three schemes reproduce the predictions of the cycle without any monitoring for the average work in the limit of infinitely weak measurement, only two of the schemes can reproduce the two-point projective measurement results in the limit of strong measurement.

Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives

This article is devoted to developing an approach for manipulating the von Neumann entropy S(ρ(t)) of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy S(ρ(T)); (b) steering S(ρ(T)) to a given target value; (c) steering S(ρ(T)) to a target value and satisfying the pointwise state constraint S(ρ(t))≤S¯ for a given S¯; (d) keeping S(ρ(t)) constant at a given time interval. Under the Markovian dynamics determined by a Gorini-Kossakowski-Sudarshan-Lindblad type master equation, which contains coherent and incoherent controls, one- and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals. The corresponding numerical results are provided and discussed.

Partial Recovery of Coherence Loss in Coherence-Assisted Transformation

Coherence-assisted transformation under incoherent operations is discussed. For transformation from the pure state to the mixed state, we show that the coherence loss can be partially recovered by adding auxiliary coherent states. First, we discuss the coherence-assisted transformation for qubit states and give the sufficient and necessary condition for the partial recovery of coherence loss, and the maximum of the recovery of coherence loss is also studied in this case. Second, the maximally coherent state can be obtained in the above recovery scheme, so we give the full characterization of obtaining the maximally coherent state in a qubit system. Finally, we show that the coherence-assisted transformation for arbitrary finite-dimensional main coherent states and low-dimensional auxiliary coherent states is always possible, and the coherence loss also can be partially recovered in these cases.

Trends in the Second Law of Thermodynamics

The Second Law of Thermodynamics represents a milestone in the history of not only physics but also chemistry, engineering, and, more generally, life and natural sciences [...].

Top-ranked cycle flux network analysis of molecular photocells

We introduce a top-ranked cycle flux ranking scheme of network analysis to assess the performance of molecular junction solar cells. By mapping the Lindblad master equation to the quantum-transition network, we propose a microscopic Hamiltonian description underpinning the rate equations commonly used to characterize molecular photocells. Our approach elucidates the paramount significance of edge flux and unveils two pertinent electron transfer pathways that play equally important roles in robust photocurrent generation. Furthermore, we demonstrate that nonradiative loss processes impede the maximum power efficiency of photocells, which may otherwise be above the Curzon-Ahlborn limit. These findings shed light on the intricate functionalities that govern molecular photovoltaics and offer a comprehensive approach to address them in a systematic way.

Comparative study of quantum Otto and Carnot engines powered by a spin working substance

Quantum Otto and Carnot engines have recently been receiving attention due to their ability to achieve high efficiencies and powers based on the laws of quantum mechanics. This paper discusses the theory, progress, and possible applications of quantum Otto and Carnot engines, such as energy production, cooling, and nanoscale technologies. In particular, we investigate a two-spin Heisenberg system that works as a substance in quantum Otto and Carnot cycles while exposed to an external magnetic field with both Dzyaloshinsky-Moriya and dipole-dipole interactions. The four stages of engine cycles are subject to analysis with respect to the heat exchanges that occur between the hot and cold reservoirs, alongside the work done during each stage. The operating conditions of the heat engine, refrigerator, thermal accelerator, and heater are all achieved. Moreover, our results demonstrate that the laws of thermodynamics are strictly upheld and the Carnot cycle produces more useful work than that of the Otto cycle.

Thermodynamics 2.0: Bridging the natural and social sciences

Thermodynamics is a universal science. The language of thermodynamics is energy and its derivatives such as entropy and power. The physical theory of thermodynamics reigns across a full spectrum of non-living objects as well as living beings. In the traditions of the past, the dichotomy between matter and life resulted in the natural sciences studying matter while the social sciences focused on living beings. As the state of human knowledge continues to evolve, anticipating the sciences of matter (natural science) and of life (social science) becoming unified under a single overarching theory is not unnatural. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

Precision bound and optimal control in periodically modulated continuous quantum thermal machines

We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations, respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the chopped random basis optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.

Quantum thermal diode dominated by pure classical correlation via three triangular-coupled qubits

A quantum thermal diode is designed based on three pairwise coupled qubits, two connected to a common reservoir and the other to an independent reservoir. It is found that the internal couplings between qubits can enhance heat currents. If the two identical qubits uniformly couple with the common reservoir, the crossing dissipation will occur, leading to the initial-state-dependent steady state, which can be decomposed into the mixture of two particular steady states: the heat-conducting state generating maximum heat current and the heat-resisting state not transporting heat. However, the rectification factor doesn't depend on the initial state. In particular, we find that neither quantum entanglement nor quantum discord is present in the steady state, but the pure classical correlation shows a remarkably consistent behavior as the heat rectification factor, which reveals the vital role of classical correlation in the system.

Work Extraction from Unknown Quantum Sources

Energy extraction is a central task in thermodynamics. In quantum physics, ergotropy measures the amount of work extractable under cyclic Hamiltonian control. As its full extraction requires perfect knowledge of the initial state, however, it does not characterize the work value of unknown or untrusted quantum sources. Fully characterizing such sources would require quantum tomography, which is prohibitively costly in experiments due to the exponential growth of required measurements and operational limitations. Here, we therefore derive a new notion of ergotropy applicable when nothing is known about the quantum states produced by the source, apart from what can be learned by performing only a single type of coarse-grained measurement. We find that in this case the extracted work is defined by the Boltzmann and observational entropy in cases where the measurement outcomes are, or are not, used in the work extraction, respectively. This notion of ergotropy represents a realistic measure of extractable work, which can be used as the relevant figure of merit to characterize a quantum battery.

Multilayer Graphene as an Endoreversible Otto Engine

We examine the performance of a finite-time, endoreversible Otto heat engine with a working medium of monolayer or multilayered graphene subjected to an external magnetic field. As the energy spectrum of multilayer graphene under an external magnetic field depends strongly on the number of layers, so too does its thermodynamic behavior. We show that this leads to a simple relationship between the engine efficiency and the number of layers of graphene in the working medium. Furthermore, we find that the efficiency at maximum power for bilayer and trilayer working mediums can exceed that of a classical endoreversible Otto cycle. Conversely, a working medium of monolayer graphene displays identical efficiency at maximum power to a classical working medium. These results demonstrate that layered graphene can be a useful material for the construction of efficient thermal machines for diverse quantum device applications.

Enantiomer detection via quantum Otto cycle

Enantiomers are chiral molecules that exist in right-handed and left-handed conformations. Optical techniques of enantiomers' detection are widely employed to discriminate between left- and right-handed molecules. However, identical spectra of enantiomers make enantiomer detection a very challenging task. Here, we investigate the possibility of exploiting thermodynamic processes for enantiomer detection. In particular, we employ a quantum Otto cycle in which a chiral molecule described by a three-level system with cyclic optical transitions is considered a working medium. Each energy transition of the three-level system is coupled with an external laser drive. We find that the left- and right-handed enantiomers operate as a quantum heat engine and a thermal accelerator, respectively, when the overall phase is the control parameter. In addition, both enantiomers act as heat engines by keeping the overall phase constant and using the laser drives' detuning as the control parameter during the cycle. However, the molecules can still be distinguished because both cases' extracted work and efficiency are quantitatively very different. Accordingly, the left- and right-handed molecules can be distinguished by evaluating the work distribution in the Otto cycle.

Hybrid quantum thermal machines with dynamical couplings

Quantum thermal machines can perform useful tasks, such as delivering power, cooling, or heating. In this work, we consider hybrid thermal machines, that can execute more than one task simultaneously. We characterize and find optimal working conditions for a three-terminal quantum thermal machine, where the working medium is a quantum harmonic oscillator, coupled to three heat baths, with two of the couplings driven periodically in time. We show that it is possible to operate the thermal machine efficiently, in both pure and hybrid modes, and to switch between different operational modes simply by changing the driving frequency. Moreover, the proposed setup can also be used as a high-performance transistor, in terms of output-to-input signal and differential gain. Owing to its versatility and tunability, our model may be of interest for engineering thermodynamic tasks and for thermal management in quantum technologies.

Performance of Quantum Heat Engines Enhanced by Adiabatic Deformation of Trapping Potential

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

Heat current magnification in classical and quantum spin networks

We investigate heat current magnification (CM) due to asymmetry in the number of spins in two-branched classical as well as quantum spin systems that are kept between two heat baths at different temperatures. We study the classical Ising-like spin models using Q2R and Creutz cellular automaton dynamics. We show that just the difference in the number of spins is not enough and some other source of asymmetry like unequal spin-spin interaction strengths in the upper and lower branches is required for heat CM. We also provide a suitable physical motivation for CM along with ways to control and manipulate it. We then extend this study to a quantum system with modified Heisenberg XXZ interaction and preserved magnetization. Interestingly, in this case, just the asymmetry in the number of spins in the branches is enough to achieve heat CM. We observe that the onset of CM is accompanied by a dip in the total heat current flowing through the system. We then discuss how the observed CM characteristics can be attributed to the intersection of nondegenerate energy levels, population inversion, and atypical magnetization trends as a function of the asymmetry parameter in the Heisenberg XXZ Hamiltonian. Finally we use the concept of ergotropy to support our findings.

Quantum Advantage of Thermal Machines with Bose and Fermi Gases

In this article, we show that a quantum gas, a collection of massive, non-interacting, indistinguishable quantum particles, can be realized as a thermodynamic machine as an artifact of energy quantization and, hence, bears no classical analog. Such a thermodynamic machine depends on the statistics of the particles, the chemical potential, and the spatial dimension of the system. Our detailed analysis demonstrates the fundamental features of quantum Stirling cycles, from the viewpoint of particle statistics and system dimensions, that helps us to realize desired quantum heat engines and refrigerators by exploiting the role of quantum statistical mechanics. In particular, a clear distinction between the behavior of a Fermi gas and a Bose gas is observed in one dimension, rather than in higher dimensions, solely due to the innate differences in their particle statistics indicating the conspicuous role of a quantum thermodynamic signature in lower dimensions.

Nonlinear coherent heat machines

We propose heat machines that are nonlinear, coherent, and closed systems composed of few field (oscillator) modes. Their thermal-state input is transformed by nonlinear Kerr interactions into nonthermal (non-Gaussian) output with controlled quantum fluctuations and the capacity to deliver work in a chosen mode. These machines can provide an output with strongly reduced phase and amplitude uncertainty that may be useful for sensing or communications in the quantum domain. They are experimentally realizable in optomechanical cavities where photonic and phononic modes are coupled by a Josephson qubit or in cold gases where interactions between photons are transformed into dipole-dipole interacting Rydberg atom polaritons. This proposed approach is a step toward the bridging of quantum and classical coherent and thermodynamic descriptions.

Nonequilibrium thermodynamics in cavity optomechanics

Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium. As an emerging field, nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes, particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations. Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability, excellent mechanical performance, and ability to operate deep in the quantum regime. Here, we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems. The experimental results in entropy production assessment, fluctuation theorems, heat transfer, and heat engines are highlighted.

Universal Behavior of the Coulomb-Coupled Fermionic Thermal Diode

We propose a minimal model of a Coulomb-coupled fermionic quantum dot thermal diode that can act as an efficient thermal switch and exhibit complete rectification behavior, even in the presence of a small temperature gradient. Using two well-defined dimensionless system parameters, universal characteristics of the optimal heat current conditions are identified. It is shown to be independent of any system parameter and is obtained only at the mean transitions point "-0.5", associated with the equilibrium distribution of the two fermionic reservoirs, tacitly referred to as "universal magic mean".

Many-Body Radiative Decay in Strongly Interacting Rydberg Ensembles

When atoms are excited to high-lying Rydberg states they interact strongly with dipolar forces. The resulting state-dependent level shifts allow us to study many-body systems displaying intriguing nonequilibrium phenomena, such as constrained spin systems, and are at the heart of numerous technological applications, e.g., in quantum simulation and computation platforms. Here, we show that these interactions also have a significant impact on dissipative effects caused by the inevitable coupling of Rydberg atoms to the surrounding electromagnetic field. We demonstrate that their presence modifies the frequency of the photons emitted from the Rydberg atoms, making it dependent on the local neighborhood of the emitting atom. Interactions among Rydberg atoms thus turn spontaneous emission into a many-body process which manifests, in a thermodynamically consistent Markovian setting, in the emergence of collective jump operators in the quantum master equation governing the dynamics. We discuss how this collective dissipation-stemming from a mechanism different from the much studied superradiance and subradiance-accelerates decoherence and affects dissipative phase transitions in Rydberg ensembles.

Strongly coupled quantum Otto cycle with single qubit bath

We discuss a model of a closed quantum evolution of two qubits where the joint Hamiltonian is so chosen such that one of the qubits acts as a bath and thermalizes the other qubit which is acting as the system. The corresponding exact master equation for the system is derived. Interestingly, for a specific choice of parameters the master equation takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form, with constant coefficients representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic properties. Our analysis goes beyond the conventional weak coupling scenario and illustrates the effects of finite baths, including non-Markovianity. We find closed form expressions for efficiency (coefficient of performance), power (cooling power) for the heat engine regime (refrigerator regime), and for different modifications of the joint Hamiltonian.

A Schmidt Decomposition Approach to Quantum Thermodynamics

The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for characterizing the thermodynamics within general autonomous quantum systems, and many fundamental open questions remain unanswered. Along these lines, most current efforts and approaches restrict the analysis to particular scenarios of approximative descriptions and semi-classical regimes. Here, we propose a novel approach to describe the thermodynamics of arbitrary bipartite autonomous quantum systems based on the well-known Schmidt decomposition. This formalism provides a simple, exact, and symmetrical framework for expressing the energetics between interacting systems, including scenarios beyond the standard description regimes, such as strong coupling. We show that this procedure allows straightforward identification of local effective operators suitable for characterizing the physical local internal energies. We also demonstrate that these quantities naturally satisfy the usual thermodynamic notion of energy additivity.

Heat transport and rectification via quantum statistical and coherence asymmetries

Recent experiments at the nanoscales confirm that thermal rectifiers, the thermal equivalent of electrical diodes, can operate in the quantum regime. We present a thorough investigation of the effect of different particle exchange statistics, coherence, and collective interactions on the quantum heat transport of rectifiers with two-terminal junctions. Using a collision model approach to describe the open system dynamics, we obtain a general expression of the nonlinear heat flow that fundamentally deviates from the Landauer formula whenever quantum statistical or coherence asymmetries are present in the bath particles. Building on this, we show that heat rectification is possible even with symmetric medium-bath couplings if the two baths differ in quantum statistics or coherence. Furthermore, the associated thermal conductance vanishes exponentially at low temperatures as in the Coulomb-blockade effect. However, at high temperatures it acquires a power-law behavior depending on the quantum statistics. Our results can be significant for heat management in hybrid open quantum systems or solid-state thermal circuits.

Work extraction from single-mode thermal noise by measurements: How important is information?

Our goal in this article is to elucidate the rapport of work and information in the context of a minimal quantum-mechanical setup: a converter of heat input to work output, the input consisting of a single oscillator mode prepared in a hot thermal state along with a few much colder oscillator modes. The core issues we consider, taking account of the quantum nature of the setup, are as follows: (i) How and to what extent can information act as a work resource or, conversely, be redundant for work extraction? (ii) What is the optimal way of extracting work via information acquired by measurements? (iii) What is the bearing of information on the efficiency-power tradeoff achievable in such setups? We compare the efficiency of work extraction and the limitations of power in our minimal setup by different, generic, measurement strategies of the hot and cold modes. For each strategy, the rapport of work and information extraction is found and the cost of information erasure is allowed for. The possibilities of work extraction without information acquisition, via nonselective measurements, are also analyzed. Overall, we present, by generalizing a method based on optimized homodyning that we have recently proposed, the following insight: extraction of work by observation and feedforward that only measures a small fraction of the input is clearly advantageous to the conceivable alternatives. Our results may become the basis of a practical strategy of converting thermal noise to useful work in optical setups, such as coherent amplifiers of thermal light, as well as in their optomechanical and photovoltaic counterparts.

Numerical study of non-adiabatic quantum thermodynamics of the driven resonant level model: non-equilibrium entropy production and higher order corrections

We present our numerical study on quantum thermodynamics of the resonant level model subjected to non-equilibrium condition as well as external driving. Following our previous work on non-equilibrium quantum thermodynamics (Douet al2020Phys. Rev.B101184304), we expand the density operator into a series of power in the driving speed, where we can determine the non-adiabatic thermodynamic quantities. Particularly, we calculate the non-equilibrium entropy production rate as well as higher order non-adiabatic corrections to the energy and/or population, which is not determined previously in Douet al(2020Phys. Rev.B101184304). In the limit of weak system-bath coupling, our results reduce to the one from the quantum master equation.

Bath Engineering Enhanced Quantum Critical Engines

Driving a quantum system across quantum critical points leads to non-adiabatic excitations in the system. This in turn may adversely affect the functioning of a quantum machine which uses a quantum critical substance as its working medium. Here we propose a bath-engineered quantum engine (BEQE), in which we use the Kibble-Zurek mechanism and critical scaling laws to formulate a protocol for enhancing the performance of finite-time quantum engines operating close to quantum phase transitions. In the case of free fermionic systems, BEQE enables finite-time engines to outperform engines operating in the presence of shortcuts to adiabaticity, and even infinite-time engines under suitable conditions, thus showing the remarkable advantages offered by this technique. Open questions remain regarding the use of BEQE based on non-integrable models.

Quantum analog of the maximum power transfer theorem

We discover the quantum analog of the well-known classical maximum power transfer theorem. Our theoretical framework considers the continuous steady-state problem of coherent energy transfer through an N-node bosonic network coupled to an external dissipative load. We present an exact solution for optimal power transfer in the form of the maximum power transfer theorem known in the design of electrical circuits. Furthermore, we introduce the concept of quantum impedance matching with Thevenin equivalent networks, which are shown to be exact analogs to their classical counterparts. Our results are applicable to both ordered and disordered quantum networks with graph-like structures ranging from nearest-neighbor to all-to-all connectivities. This work points towards universal design principles adapting ideas from the classical regime to the quantum domain for various quantum optical applications in energy-harvesting, wireless power transfer, and energy transduction.

Quantum Collision Models: A Beginner Guide

In recent years, quantum collision models, sometimes dubbed repeated interaction models, have gained much attention due to their simplicity and their capacity to convey ideas without resorting to technical complications typical of many approaches and techniques used in the field of open quantum systems. In this tutorial, we show how to use these models, highlighting their strengths and some technical subtleties often overlooked in the literature. We do this by deriving the Markovian master equation and comparing the standard collisional derivation with the standard microscopic one. We then use the collision model to derive the master equation of a two-level system interacting with either a bosonic or fermionic bath to give the reader a flavour of the real use of the model.

Experimental Realization of a Quantum Refrigerator Driven by Indefinite Causal Orders

Indefinite causal order (ICO) is playing a key role in recent quantum technologies. Here, we experimentally study quantum thermodynamics driven by ICO on nuclear spins using the nuclear magnetic resonance system. We realize the ICO of two thermalizing channels to exhibit how the mechanism works, and show that the working substance can be cooled or heated albeit it undergoes thermal contacts with reservoirs of the same temperature. Moreover, we construct a single cycle of the ICO refrigerator based on the Maxwell's demon mechanism, and evaluate its performance by measuring the work consumption and the heat energy extracted from the low-temperature reservoir. Unlike classical refrigerators in which the coefficient of performance (COP) is perversely higher the closer the temperature of the high-temperature and low-temperature reservoirs are to each other, the ICO refrigerator's COP is always bounded to small values due to the nonunit success probability in projecting the ancillary qubit to the preferable subspace. To enhance the COP, we propose and experimentally demonstrate a general framework based on the density matrix exponentiation (DME) approach, as an extension to the ICO refrigeration. The COP is observed to be enhanced by more than 3 times with the DME approach. Our Letter demonstrates a new way for nonclassical heat exchange, and paves the way towards construction of quantum refrigerators on a quantum system.

Floquet quantum thermal transistor

We apply periodic control to realize a quantum thermal transistor, which we term as the Floquet quantum thermal transistor. Periodic modulation allows us to control the heat flows and achieve large amplification factors even for fixed bath temperatures. Importantly, this transistor effect persists in the cutoff region, where traditional quantum thermal transistors operating in the absence of periodic modulation, fail to act as viable heat modulation devices.

Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams

We investigate the efficiency of a quantum Carnot engine based on open quantum dynamics theory. The model includes time-dependent external fields for the subsystems controlling the isothermal and isentropic processes and for the system--bath (SB) interactions controlling the transition between these processes. Numerical simulations are conducted in a nonperturbative and non-Markovian SB coupling regime using the hierarchical equations of motion under these fields at different cycle frequencies. The work applied to the total system and the heat exchanged with the baths are rigorously evaluated. In addition, by regarding quasi-static work as free energy, we compute the quantum thermodynamic variables and analyze the simulation results using thermodynamic work diagrams for the first time. Analysis of these diagrams indicates that, in the strong SB coupling region, the fields for the SB interactions are major sources of work, while in other regions, the field for the subsystem is a source of work. We find that the maximum efficiency is achieved in the quasi-static case and is determined solely by the bath temperatures, regardless of the SB coupling strength, which is a numerical manifestation of Carnot's theorem.

Quantum Thermal Amplifiers with Engineered Dissipation

A three-terminal device, able to control the heat currents flowing through it, is known as a quantum thermal transistor whenever it amplifies two output currents as a response to the external source acting on its third terminal. Several efforts have been proposed in the direction of addressing different engineering options of the configuration of the system. Here, we adhere to the scheme in which such a device is implemented as a three-qubit system that interacts with three separate thermal baths. However, another interesting direction is how to engineer the thermal reservoirs to magnify the current amplification. Here, we derive a quantum dynamical equation for the evolution of the system to study the role of distinct dissipative thermal noises. We compare the amplification gain in different configurations and analyze the role of the correlations in a system exhibiting the thermal transistor effect, via measures borrowed from the quantum information theory.

Optimizing Thermalization

We present a rigorous approach, based on the concept of continuous thermomajorization, to algorithmically characterize the full set of energy occupations of a quantum system accessible from a given initial state through weak interactions with a heat bath. The algorithm can be deployed to solve complex optimization problems in out-of-equilibrium setups and it returns explicit elementary control sequences realizing optimal transformations. We illustrate this by finding optimal protocols in the context of cooling, work extraction, and catalysis. The same tools also allow one to quantitatively assess the role played by memory effects in the performance of thermodynamic protocols. We obtained exhaustive solutions on a laptop machine for systems with dimension d≤7, but with heuristic methods one could access much higher d.

Efficiency Fluctuations in a Quantum Battery Charged by a Repeated Interaction Process

A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction process, and the ergotropy characterizes its charge. The working cycle consists in extracting the ergotropy and charging the battery again. We discuss the fluctuating efficiency of the process, among other fluctuating properties. These fluctuations are dominated by the equilibrium distribution and depend weakly on other process properties.