Strong Coupling Corrections in Quantum Thermodynamics

Quantum Work Statistics at Strong Reservoir Coupling

Determining the statistics of work done on a quantum system while strongly coupled to a reservoir is a formidable task, requiring the calculation of the full eigenspectrum of the combined system and reservoir. Here, we show that this issue can be circumvented by using a polaron transformation that maps the system into a new frame where weak-coupling theory can be applied. Crucially, this polaron approach reproduces the Jarzynski fluctuation theorem, thus ensuring consistency with the laws of stochastic thermodynamics. We apply our formalism to a system driven across the Landau-Zener transition, where we identify clear signatures in the work distribution arising from a non-negligible coupling to the environment. Our results provide a new method for studying the stochastic thermodynamics of driven quantum systems beyond Markovian, weak-coupling regimes.

Quantum Carnot thermal machines reexamined: Definition of efficiency and the effects of strong coupling

Whether the strong coupling to thermal baths can improve the performance of quantum thermal machines remains an open issue under active debate. Here we revisit quantum thermal machines operating with the quasistatic Carnot cycle and aim to unveil the role of strong coupling in maximum efficiency. Our analysis builds upon definitions of excess work and heat derived from an exact formulation of the first law of thermodynamics for the working substance, which captures the non-Gibbsian thermal equilibrium state that emerges at strong couplings during quasistatic isothermal processes. These excess definitions differ from conventional ones by an energetic cost for maintaining the non-Gibbsian characteristics. With this distinction, we point out that one can introduce two different yet thermodynamically allowed definitions for efficiency of both the heat engine and refrigerator modes. We dub them excess and hybrid definitions, which differ in the way of defining the gain for the thermal machines at strong couplings by either just analyzing the energetics of the working substance or instead evaluating the performance from an external system upon which the thermal machine acts, respectively. We analytically demonstrate that the excess definition predicts that the Carnot limit remains the upper bound for both operation modes at strong couplings, whereas the hybrid one reveals that strong coupling can suppress the maximum efficiency rendering the Carnot limit unattainable. These seemingly incompatible predictions thus indicate that it is imperative to first gauge the definition for efficiency before elucidating the exact role of strong coupling, thereby shedding light on the ongoing investigation on strong-coupling quantum thermal machines.

Dynamics of a strongly coupled quantum heat engine-Computing bath observables from the hierarchy of pure states

We present a fully quantum dynamical treatment of a quantum heat engine and its baths based on the Hierarchy of Pure States (HOPS), an exact and general method for open quantum system dynamics. We show how the change of the bath energy and the interaction energy can be determined within HOPS for arbitrary coupling strength and smooth time dependence of the modulation protocol. The dynamics of all energetic contributions during the operation can be carefully examined both in its initial transient phase and, also later, in its periodic steady state. A quantum Otto engine with a qubit as an inherently nonlinear work medium is studied in a regime where the energy associated with the interaction Hamiltonian plays an important role for the global energy balance and, thus, must not be neglected when calculating its power and efficiency. We confirm that the work required to drive the coupling with the baths sensitively depends on the speed of the modulation protocol. Remarkably, departing from the conventional scheme of well-separated phases by allowing for temporal overlap, we discover that one can even gain energy from the modulation of bath interactions. We visualize these various work contributions using the analog of state change diagrams of thermodynamic cycles. We offer a concise, full presentation of HOPS with its extension to bath observables, as it serves as a universal tool for the numerically exact description of general quantum dynamical (thermodynamic) scenarios far from the weak-coupling limit.

Thermodynamics of the Ramsey Zone

We studied the thermodynamic properties such as the entropy, heat (JQ), and work (JW) rates involved when an atom passes through a Ramsey zone, which consists of a mode field inside a low-quality factor cavity that behaves classically, promoting rotations on the atomic state. Focusing on the atom, we show that JW predominates when the atomic rotations are successful, maintaining its maximum purity as computed by the von Neumann entropy. Conversely, JQ stands out when the atomic state ceases to be pure due to its entanglement with the cavity mode. With this, we interpret the quantum-to-classical transition in light of the heat and work rates. Besides, we show that, for the cavity mode to work as a Ramsey zone (classical field), several photons (of the order of 106) need to cross the cavity, which explains its classical behavior, even when the inside average number of photons is of the order of unity.

Quantum Otto cycle under strong coupling

Quantum heat engines are often discussed under the weak-coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak-coupling assumption is proposed. We replace the thermalization process in the weak-coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and indicates that, when the contribution of the interaction terms is neglected in the weak-interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak-coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined by using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak-coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians, which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak-coupling counterpart.

Experimental Activation of Strong Local Passive States with Quantum Information

Strong local passivity is a property of multipartite quantum systems from which it is impossible to extract energy locally. Surprisingly, if the strong local passive state displays entanglement, it could be possible to locally activate energy density by adding classical communication between different partitions of the system, through so-called "quantum energy teleportation" protocols. Here, we report both the first experimental observation of local activation of energy density on an entangled state and the first realization of a quantum energy teleportation protocol using nuclear magnetic resonance on a bipartite quantum system.

Assigning temperatures to eigenstates

In the study of thermalization in finite isolated quantum systems, an inescapable issue is the definition of temperature. We examine and compare different possible ways of assigning temperatures to energies or equivalently to eigenstates in such systems. A commonly used assignment of temperature in the context of thermalization is based on the canonical energy-temperature relationship, which depends only on energy eigenvalues and not on the structure of eigenstates. For eigenstates, we consider defining temperature by minimizing the distance between (full or reduced) eigenstate density matrices and canonical density matrices. We show that for full eigenstates, the minimizing temperature depends on the distance measure chosen and matches the canonical temperature for the trace distance; however, the two matrices are not close. With reduced density matrices, the minimizing temperature has fluctuations that scale with subsystem and system size but appears to be independent of distance measure. In particular limits, the two matrices become equivalent while the temperature tends to the canonical temperature.

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.

Optimal linear cyclic quantum heat engines cannot benefit from strong coupling

Uncovering whether strong system-bath coupling can be an advantageous operation resource for energy conversion can facilitate the development of efficient quantum heat engines (QHEs). Yet, a consensus on this ongoing debate is still lacking owing to challenges arising from treating strong couplings. Here, we conclude the debate for optimal linear cyclic QHEs operated under a small temperature difference by revealing the detrimental role of strong system-bath coupling in their optimal operations. We analytically demonstrate that both the efficiency at maximum power and maximum efficiency of strong-coupling linear cyclic QHEs are upper bounded by their weak-coupling counterparts with the same degree of time-reversal symmetry breaking. Under strong time-reversal symmetry breaking, we further reveal a quadratic suppression of the optimal efficiencies relative to the Carnot limit when away from the weak-coupling regime, along with a quadratic enhancement of the mean entropy production rate.

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.

Robust Nonequilibrium Edge Currents with and without Band Topology

We study two-dimensional bosonic and fermionic lattice systems under nonequilibrium conditions corresponding to a sharp gradient of temperature imposed by two thermal baths. In particular, we consider a lattice model with broken time-reversal symmetry that exhibits both topologically trivial and nontrivial phases. Using a nonperturbative Green function approach, we characterize the nonequilibrium current distribution in different parameter regimes. For both bosonic and fermionic systems, we find chiral edge currents that are robust against coupling to reservoirs and to the presence of defects on the boundary or in the bulk. This robustness not only originates from topological effects at zero temperature but, remarkably, also persists as a result of dissipative symmetries in regimes where band topology plays no role. Chirality of the edge currents implies that energy locally flows against the temperature gradient without any external work input. In the fermionic case, there is also a regime with topologically protected boundary currents, which nonetheless do not circulate around all system edges.

Strong system-bath coupling effects in quantum absorption refrigerators

We study the performance of three-level quantum absorption refrigerators, paradigmatic autonomous quantum thermal machines, and reveal central impacts of strong couplings between the working system and the thermal baths. Using the reaction coordinate quantum master equation method, which treats system-bath interactions beyond weak coupling, we demonstrate that in a broad range of parameters the cooling window at strong coupling can be captured by a weak-coupling theory, albeit with parameters renormalized by the system-bath coupling energy. As a result, at strong system-bath couplings the window of cooling is significantly reshaped compared to predictions of weak-coupling treatments. We further show that strong coupling admits direct transport pathways between the thermal reservoirs. Such beyond-second-order transport mechanisms are typically detrimental to the performance of quantum thermal machines. Our study reveals that it is inadequate to claim for either a suppression or an enhancement of the cooling performance as one increases system-bath coupling-when analyzed against a single parameter and in a limited domain. Rather, a comprehensive approach should be adopted so as to uncover the reshaping of the operational window.

Steady state in strong system-bath coupling regime: Reaction coordinate versus perturbative expansion

Motivated by the growing importance of strong system-bath coupling in several branches of quantum information and related technological applications, we analyze and compare two strategies currently used to obtain (approximately) steady states in strong-coupling regime. The first strategy is based on perturbative expansions while the second one uses reaction coordinate mapping. Focusing on the widely used spin-boson model, we show that the predictions of these two strategies coincide in many situations. This confirms and strengthens the relevance of both techniques. Beyond that, it is also crucial to know precisely their respective range of validity. In that perspective, thanks to their different limitations, we use one to benchmark the other. We introduce and successfully test some very simple validity criteria for both strategies, bringing some answers to the question of the validity range.

Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State

The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature T. However, non-negligible interactions between system and environment can give rise to an altered state. Here, we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reservoir. First, we derive the state in the weak coupling limit and find that, in general, it maintains coherences with respect to the bare system Hamiltonian. Second, we develop a new expansion method suited to investigate the ultrastrong coupling regime. This allows us to derive the explicit form for the mean force Gibbs state, and we find that it becomes diagonal in the basis set by the system-reservoir interaction instead of the system Hamiltonian. Several examples are discussed including a single qubit, a three-level V-system, and two coupled qubits all interacting with bosonic reservoirs. The results shed light on the presence of coherences in the strong coupling regime, and provide key tools for nanoscale thermodynamics investigations.

Periodically Driven Quantum Thermal Machines from Warming up to Limit Cycle

Theoretical treatments of periodically driven quantum thermal machines (PD-QTMs) are largely focused on the limit-cycle stage of operation characterized by a periodic state of the system. Yet, this regime is not immediately accessible for experimental verification. Here, we present a general thermodynamic framework that handles the performance of PD-QTMs both before and during the limit-cycle stage of operation. It is achieved by observing that periodicity may break down at the ensemble average level, even in the limit-cycle phase. With this observation, and using conventional thermodynamic expressions for work and heat, we find that a complete description of the first law of thermodynamics for PD-QTMs requires a new contribution, which vanishes only in the limit-cycle phase under rather weak system-bath couplings. Significantly, this contribution is substantial at strong couplings even at limit cycle, thus largely affecting the behavior of the thermodynamic efficiency. We demonstrate our framework by simulating a quantum Otto engine building upon a driven resonant level model. Our results provide new insights towards a complete description of PD-QTMs, from turn-on to the limit-cycle stage and, particularly, shed light on the development of quantum thermodynamics at strong coupling.

Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian

For a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations of motion and operator calculus. The special and limiting cases are discussed.

Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine

Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production.

von Neumann entropy and entropy production of a damped harmonic oscillator

In this paper we analyze the entropy and entropy production of a nonisolated quantum system described within the quantum Brownian motion framework. This is a very general and paradigmatic framework for describing nonisolated quantum systems and can be used in any kind of coupling regime. We start by considering the application of von Neumann entropy to an arbitrarily damped quantum system making use of its reduced density operator. We argue that this application is formally valid and develop a path-integral method to evaluate that quantity analytically. We apply this technique to a harmonic oscillator in contact with a heat bath and obtain an exact form for its entropy. Then we study the entropy production of this system and enlighten important characteristics of its thermodynamical behavior on the pure quantum realm and also address their transition to the classical limit.

Quantum thermodynamics of single particle systems

Thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a theory of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two-level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system-reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system-reservoir coupling regime where the Born-Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non-Markovian memory effect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by inflationary dynamics associated with negative dynamical temperature. The corresponding dynamical criticality provides a border separating classical and quantum worlds. The inflationary dynamics may also relate to the origin of big bang and universe inflation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved.

Steady-state quantum transport through an anharmonic oscillator strongly coupled to two heat reservoirs

We investigate the transport properties of an anharmonic oscillator, modeled by a single-site Bose-Hubbard model, coupled to two different thermal baths using the numerically exact thermofield based chain-mapping matrix product states (TCMPS) approach. We compare the effectiveness of TCMPS to probe the nonequilibrium dynamics of strongly interacting system irrespective of the system-bath coupling against the global master equation approach in Gorini-Kossakowski-Sudarshan-Lindblad form. We discuss the effect of on-site interactions, temperature bias as well as the system-bath couplings on the steady-state transport properties. Last, we also show evidence of non-Markovian dynamics by studying the nonmonotonicity of the time evolution of the trace distance between two different initial states.

Large deviations and fluctuation theorem for the quantum heat current in the spin-boson model

We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the noninteracting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well-known fluctuation dissipation relation. Finally, we present numerical results for the heat current.

Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force

The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited by the necessity to measure differences in equilibrium properties of the system-bath composite. We make use of the freedom involved in defining thermodynamic quantities, which leaves the thermodynamics unchanged, to show that the Hamiltonian of mean force can be inferred from measurements on the system alone, up to that irrelevant freedom. In doing so, we refute a key criticism expressed in the works by P. Talkner and P. Hänggi [Phys. Rev. E 94, 022143 (2016)10.1103/PhysRevE.94.022143 and arXiv:1911.11660]. We also discuss the remaining part of the criticism.

Quantum limit to nonequilibrium heat-engine performance imposed by strong system-reservoir coupling

We show that finite system-reservoir coupling imposes a distinct quantum limit on the performance of a nonequilibrium quantum heat engine. Even in the absence of quantum friction along the isentropic strokes, finite system-reservoir coupling induces correlations that result in the generation of coherence between the energy eigenstates of the working system. This coherence acts to hamper the engine's power output, as well as the efficiency with which it can convert heat into useful work, and cannot be captured by a standard Born-Markov analysis of the system-reservoir interactions.

Strong Coupling Thermodynamics of Open Quantum Systems

A general thermodynamic framework is presented for open quantum systems in fixed contact with a thermal reservoir. The first and second law are obtained for arbitrary system-reservoir coupling strengths, and including both factorized and correlated initial conditions. The thermodynamic properties are adapted to the generally strong coupling regime, approaching the ones defined for equilibrium, and their standard weak-coupling counterparts as appropriate limits. Moreover, they can be inferred from measurements involving only system observables. Finally, a thermodynamic signature of non-Markovianity is formulated in the form of a negative entropy production rate.

Analytical derivation of equilibrium state for open quantum system

Calculation of the equilibrium state of an open quantum system interacting with a bath remains a challenge to this day, mostly due to a huge number of bath degrees of freedom. Here, we present an analytical expression for the reduced density operator in terms of an effective Hamiltonian for a high temperature case. Comparing with numerically exact results, we show that our theory is accurate for slow baths and up to intermediate system-bath coupling strengths. Our results demonstrate that the equilibrium state does not depend on the shape of spectral density in the slow bath regime. The key quantity in our theory is the effective coupling between the states, which depends exponentially on the ratio of the reorganization energy to temperature and, thus, has opposite temperature dependence than could be expected from the small polaron transformation.

Work Fluctuations in Slow Processes: Quantum Signatures and Optimal Control

An important result in classical stochastic thermodynamics is the work fluctuation-dissipation relation (FDR), which states that the dissipated work done along a slow process is proportional to the resulting work fluctuations. We show that slowly driven quantum systems violate this FDR whenever quantum coherence is generated along the protocol, and we derive a quantum generalization of the work FDR. The additional quantum terms in the FDR are found to lead to a non-Gaussian work distribution. Fundamentally, our result shows that quantum fluctuations prohibit finding slow protocols that minimize both dissipation and fluctuations simultaneously, in contrast to classical slow processes. Instead, we develop a quantum geometric framework to find processes with an optimal trade-off between the two quantities.

Measurement Based Quantum Heat Engine with Coupled Working Medium

We consider measurement based single temperature quantum heat engine without feedback control, introduced recently by Yi, Talkner and Kim [Phys. Rev. E96, 022108 (2017)]. Taking the working medium of the engine to be a one-dimensional Heisenberg model of two spins, we calculate the efficiency of the engine undergoing a cyclic process. Starting with two spin-1/2 particles, we investigate the scenario of higher spins also. We show that, for this model of coupled working medium, efficiency can be higher than that of an uncoupled one. However, the relationship between the coupling constant and the efficiency of the engine is rather involved. We find that in the higher spin scenario efficiency can sometimes be negative (this means work has to be done to run the engine cycle) for certain range of coupling constants, in contrast to the aforesaid work of Yi, Talkner and Kim, where they showed that the extracted work is always positive in the absence of coupling. We provide arguments for this negative efficiency in higher spin scenarios. Interestingly, this happens only in the asymmetric scenarios, where the two spins are different. Given these facts, for judiciously chosen conditions, an engine with coupled working medium gives advantage for the efficiency over the uncoupled one.

Fundamental Limitations to Local Energy Extraction in Quantum Systems

We examine when it is possible to locally extract energy from a bipartite quantum system in the presence of strong coupling and entanglement, a task which is expected to be restricted by entanglement in the low-energy eigenstates. We fully characterize this distinct notion of "passivity" by finding necessary and sufficient conditions for such extraction to be impossible, using techniques from semidefinite programing. This is the first time in which such techniques are used in the context of energy extraction, which opens a way of exploring further kinds of passivity in quantum thermodynamics. We also significantly strengthen a previous result of Frey et al., by showing a physically relevant quantitative bound on the threshold temperature at which this passivity appears. Furthermore, we show how this no-go result also holds for thermal states in the thermodynamic limit, provided that the spatial correlations decay sufficiently fast, and we give numerical examples.

Repeated Interactions and Quantum Stochastic Thermodynamics at Strong Coupling

The thermodynamic framework of repeated interactions is generalized to an arbitrary open quantum system in contact with a heat bath. Based on these findings, the theory is then extended to arbitrary measurements performed on the system. This constitutes a direct experimentally testable framework in strong coupling quantum thermodynamics. By construction, it provides many quantum stochastic processes and quantum causal models with a consistent thermodynamic interpretation. The setting can be further used, for instance, to rigorously investigate the interplay between non-Markovianity and nonequilibrium thermodynamics.

Operational approach to quantum stochastic thermodynamics

We set up a framework for quantum stochastic thermodynamics based solely on experimentally controllable but otherwise arbitrary interventions at discrete times. Using standard assumptions about the system-bath dynamics and insights from the repeated interaction framework, we define internal energy, heat, work, and entropy at the trajectory level. The validity of the first law (at the trajectory level) and the second law (on average) is established. The theory naturally allows one to treat incomplete information and it is able to smoothly interpolate between a trajectory-based and an ensemble level description. We use our theory to compute the thermodynamic efficiency of recent experiments reporting on the stabilization of photon number states using real-time quantum feedback control. Special attention is paid to limiting cases of our general theory, where we recover or contrast it with previous results. We point out various interesting problems, which the theory is able to address rigorously, such as the detection of quantum effects in thermodynamics.

Heat capacities of thermally manipulated mechanical oscillator at strong coupling

Coherent quantum oscillators are basic physical systems both in quantum statistical physics and quantum thermodynamics. Their realizations in lab often involve solid-state devices sensitive to changes in ambient temperature. We represent states of the solid-state optomechanical oscillator with temperature-dependent frequency by equivalent states of the mechanical oscillator with temperature-dependent energy levels. We interpret the temperature dependence as a consequence of strong coupling between the oscillator and the heat bath. We explore parameter regimes corresponding to anomalous behavior of mechanical and thermodynamic characteristics as a consequence of the strong coupling: (i) The localization and the purification induced by heating, and (ii) the negativity of two generalized heat capacities. The capacities can be used to witness non-linearity in the temperature dependency of the energy levels. Our phenomenological experimentally-oriented approach can stimulate development of new optomechanical and thermomechanical experiments exploring basic concepts of strong coupling thermodynamics.

Strong coupling and non-Markovian effects in the statistical notion of temperature

We investigate the emergence of temperature T in the system-plus-reservoir paradigm starting from the fundamental microcanonical scenario at total fixed energy E where, contrary to the canonical approach, T=T(E) is not a control parameter but a derived auxiliary concept. As shown by Schwinger for the regime of weak coupling γ between subsystems, T(E) emerges from the saddle-point analysis leading to the ensemble equivalence up to corrections O(1/sqrt[N]) in the number of particles N that defines the thermodynamic limit. By extending these ideas for finite γ, while keeping N→∞, we provide a consistent generalization of temperature T(E,γ) in strongly coupled systems, and we illustrate its main features for the specific model of quantum Brownian motion where it leads to consistent microcanonical thermodynamics. Interestingly, while this T(E,γ) is a monotonically increasing function of the total energy E, its dependence with γ is a purely quantum effect notably visible near the ground-state energy and for large energies differs for Markovian and non-Markovian regimes.

Thermal power of heat flow through a qubit

In this paper we consider the thermal power of a heat flow through a qubit between two baths. The baths are modeled as a set of harmonic oscillators initially at equilibrium, at two temperatures. Heat is defined as the change of energy of the cold bath, and thermal power is defined as expected heat per unit time, in the long-time limit. The qubit and the baths interact as in the spin-boson model, i.e., through qubit operator σ_{z}. We compute thermal power in an approximation analogous to a "noninteracting blip" (NIBA) and express it in the polaron picture as products of correlation functions of the two baths, and a time derivative of a correlation function of the cold bath. In the limit of weak interaction we recover known results in terms of a sum of correlation functions of the two baths, a correlation functions of the cold bath only, and the energy split.

Non-Markovianity and negative entropy production rates

Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.