We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit. DOI: 10.1103/PhysRevLett.114.080602 PACS numbers: 05.70.Ln, 05.60.Gg Nonequilibrium thermodynamics of open quantum systems is a powerful tool for the study of mesoscopic and nanoscale systems. It allows one to reliably assess the performance of energy-converting devices such as thermoelectrics or photoelectrics, by identifying the system entropy production. It enables one to meaningfully compare these different devices by discriminating the systemspecific features from the universal ones and to appraise the role of quantum effects. It can also be used to verify the thermodynamic consistency of approximation schemes. Such a theory is nowadays available for systems weakly interacting with their surrounding [1][2][3][4][5][6], where it has proven very useful [7][8][9][10][11][12][13][14][15]. However, in case of strong system-reservoir interactions, finding definitions for heat, work, entropy, and entropy production, which satisfy the basic laws of thermodynamics is an open problem. Each proposal has its own limitations [16][17][18][19][20][21][22][23], even at equilibrium [24][25][26][27][28][29][30]. Reversible transformations, for instance, are never explicitly characterized. Establishing a consistent nonequilibrium thermodynamics for open quantum systems strongly coupled to their surrounding is therefore an important step towards a more realistic thermodynamic description of mesoscopic and nanoscale devices. It is also essential to improve our understanding of the microscopic foundations of thermodynamics.In this Letter, we use the nonequilibrium Green's functions (NEGF) to establish a fully consistent nonequilibrium thermodynamic description of a fermionic single quantum level strongly coupled to multiple fermionic reservoirs. A slow time-dependent driving force controls the level energy as well as the system-reservoir interaction. We propose definitions for the particle number, the energy, and the entropy of the system, as well as for entropy production, heat, and work, which give rise to a consistent zeroth, first, second, and third law. These definitions can be seen as energy resolved versions of the weak coupling definitions used in stochastic thermodynamics. An interesting outcome of our approach is that the general form of the energy and particle currents is different from the standard form used in the NEGF and cannot be expressed as an expectation value of operators. We recover the known expressions when considering nonequilibrium steady states (i.e., in absenc...

We show that any heat definition expressed as an energy change in the reservoir energy plus any fraction of the system-reservoir interaction is not an exact differential when evaluated along reversible isothermal transformations, except when that fraction is zero. Even in that latter case the reversible heat divided by temperature, namely entropy, does not satisfy the third law of thermodynamics and diverges in the low temperature limit. These results are found within the framework of nonequilibrium Greens functions (NEGF) using a single level quantum dot strongly coupled to fermionic reservoirs and subjected to a time-dependent protocol modulating the dot energy as well as the dot-reservoir coupling strength.

We present a method, based on charaterizing efficiency fluctuations, to asses the performance of nanoscale thermoelectric junctions. This method accounts for effects typically arising in small junctions, namely, stochasticity in the junction's performance, quantum effects, and nonequilibrium features preventing a linear response analysis. It is based on a nonequilibrium Green's function (NEGF) approach, which we use to derive the full counting statistics (FCS) for heat and work, and which in turn allows us to calculate the statistical properties of efficiency fluctuations. We simulate the latter for a variety of simple models where our method is exact. By analyzing the discrepancies with the semi-classical prediction of a quantum master equation (QME) approach, we emphasize the quantum nature of efficiency fluctuations for realistic junction parameters. We finally propose an approximate Gaussian method to express efficiency fluctuations in terms of nonequilibrium currents and noises which are experimentally measurable in molecular junctions.

We study the energy distribution in the extended resonant level model at equilibrium. Previous investigations [Phys. Rev. B 89, 161306 (2014), Phys. Rev. B 93, 115318 (2016] have found, for a resonant electronic level interacting with a thermal free electron wide-band bath, that the expectation value for the energy of the interacting subsystem can be correctly calculated by considering a symmetric splitting of the interaction Hamiltonian between the subsystem and the bath. However, the general implications of this approach were questioned [Phys. Rev. B 92, 235440 (2015)]. Here we show that already at equilibrium, such splitting fails to describe the energy fluctuations, as measured here by the second and third central moments (namely width and skewness) of the energy distribution. Furthermore, we find that when the wide-band approximation does not hold, no splitting of the system-bath interaction can describe the system thermodynamics. We conclude that in general no proper division subsystem of the Hamiltonian of the composite system can account for the energy distribution of the subsystem. This also implies that the thermodynamic effects due to local changes in the subsystem cannot in general be described by such splitting.

We present a protocol for the study of the dynamics and thermodynamics of quantum systems strongly coupled to a bath and subject to an external modulation. Our protocol quantifies the evolution of the system-bath composite by expanding the full density matrix as a series in the powers of the modulation rate, from which the functional form of work, heat and entropy rates can be obtained. Under slow driving, thermodynamic laws are established. The entropy production rate is positive and is found to be related to the excess work dissipated by friction, at least up to second order in the driving speed. As an example of the present methodology, we reproduce the results for the quantum thermodynamics of the driven resonance level model. We also emphasize that our formalism is quite general and allows for electron-electron interactions, which can give rise to exotic Kondo resonances appearing in thermodynamic quantities. arXiv:1808.08176v1 [cond-mat.stat-mech]

We introduce diagrammatic technique for Hubbard nonequilibrium Green functions (NEGF). The formulation is an extension of equilibrium considerations for strongly correlated lattice models to description of current carrying molecular junctions. Within the technique intra-system interactions are taken into account exactly, while molecular coupling to contacts is used as a small parameter in perturbative expansion. We demonstrate the viability of the approach with numerical simulations for a generic junction model of quantum dot coupled to two electron reservoirs.Comment: 13 pages, 12 figure

The slow response of electronic components in junctions limits the direct applicability of pump-probe type spectroscopy in assessing the intramolecular dynamics. Recently the possibility of getting information on a sub-picosecond time scale from dc current measurements was proposed. We revisit the idea of picosecond resolution by pump-probe spectroscopy from dc measurements and show that any intramolecular dynamics not directly related to charge transfer in the current direction is missed by current measurements. We propose a pump-probe dc shot noise spectroscopy as a suitable alternative. Numerical examples of time-dependent and average responses of junctions are presented for generic models.

Observation of a chemical transformation at the single-molecule level yields a detailed view of kinetic pathways contributing to the averaged results obtained in a bulk measurement. Studies of a fluorogenic reaction catalyzed by gold nanoparticles have revealed heterogeneous reaction dynamics for these catalysts. Measurements on single nanoparticles yield binary trajectories with stochastic transitions between a dark state in which no product molecules are adsorbed and a fluorescent state in which one product molecule is present. The mean dwell time in either state gives information corresponding to a bulk measurement. Quantifying fluctuations from mean kinetics requires identifying properties of the fluorescence trajectory that are selective in emphasizing certain dynamic processes according to their time scales. We propose the use of constrained mean dwell times, defined as the mean dwell time in a state with the constraint that the immediately preceding dwell time in the other state is, for example, less than a variable time. Calculations of constrained mean dwell times for a kinetic model with dynamic disorder demonstrate that these quantities reveal correlations among dynamic fluctuations at different active sites on a multisite catalyst. Constrained mean dwell times are determined from measurements of single nanoparticle catalysis. The results indicate that dynamical fluctuations at different active sites are correlated, and that especially rapid reaction events produce particularly slowly desorbing product molecules.