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Prior attempts to formulate the Laws of Thermodynamics for a small region within a larger quantum system have led to inconsistencies and unexplained infinities. The entropy and external work, in particular, require careful analysis when partitioning over the various subsystems. In this work, we analyze the thermodynamics of a quantum subsystem driven quasi-statically by external forces. We show that the thermodynamic functions of a quantum subsystem can be defined dynamically in terms of its local spectrum. The external work is found to be intrinsically nonlocal due to the nonlocal character of the underlying quantum states. This nonlocal quantum work can be harnessed in a "quantum lever" to provide up to 100% amplification of the local work done on a quantum subsystem., Comment: 8+4 pages, 6 figures. A preliminary version appeared in Sec. II-IV of arxiv:2402.18855v1

The Aharonov-Bohm (AB) effect on the thermoelectric properties of three-terminal quantum devices is investigated. Thermodynamic relations among the linear-response coefficients of these devices are derived and interpreted. General expressions are derived using nonequilibrium Green's functions, and applied to calculate the thermoelectric response of a model quantum thermocouple. It is shown that the AB effect can generate a large thermoelectric response in a device with particle-hole symmetry, which nominally has zero Seebeck and Peltier coefficients. In addition to modifying the external electric and thermal currents of the device, the AB effect also induces persistent electric and thermal currents. One might expect that a persistent electric current in a quantum thermocouple, through the Peltier effect, could lead to persistent Peltier cooling, violating the 1st and 2nd Laws of Thermodynamics. However, this apparent paradox is resolved by elucidating the distinction between persistent and dissipative currents in quantum thermoelectrics.

A key question in the thermodynamics of open quantum systems is how to partition thermodynamic quantities such as entropy, work, and internal energy between the system and its environment. We show that the only partition under which entropy is nonsingular is based on a partition of Hilbert space, which assigns half the system-environment coupling to the system and half to the environment. However, quantum work partitions nontrivially under Hilbert-space partition, and we derive a work sum rule that accounts for quantum work at a distance. All state functions of the system are shown to be path independent once this nonlocal quantum work is properly accounted for. Our results are illustrated with application to a driven resonant level strongly coupled to a reservoir., Comment: Close to published version, 7+13 pages, 3+5 figures

We present a partition of quantum observables in an open quantum system which is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, non-local observables. This formalism is employed to describe the local evolution of the von Neumann entropy of a system of independent quantum particles out of equilibrium. Crucially, we find that all local fluctuations in the entropy are governed by an entropy current operator, implying that the production of entanglement entropy is not measured by this partitioned entropy. For systems linearly perturbed from equilibrium, it is shown that this entropy current is equivalent to a heat current, provided that the system-reservoir coupling is partitioned symmetrically. Finally, we show that any other partition of the coupling leads directly to a divergence of the von Neumann entropy. Thus, we conclude that Hilbert-space partitioning is the only partition of the von Neumann entropy which is consistent with the Laws of Thermodynamics., Comment: 7 pages, 1 figure

How to rigorously define thermodynamic quantities such as heat, work, and internal energy in open quantum systems driven far from equilibrium remains a significant open question in quantum thermodynamics. Heat is a quantity whose fundamental definition applies only to processes in systems infinitesimally perturbed from equilibrium, and as such, must be accounted for carefully in strongly-driven systems. A key insight from Mesoscopics is that infinitely far from the local driving and coupling of an open quantum system, reservoirs are indeed only infinitesimally perturbed, thereby allowing the heat dissipated to be defined. The resulting partition of the entropy necessitates a Hilbert-space partition of the energetics, leading to an unambiguous operator for the internal energy of an interacting time-dependent open quantum system. Fully general expressions for the heat current and the power delivered by various agents to the system are derived using the formalism of nonequilibrium Green's functions, establishing an experimentally meaningful and quantum mechanically consistent division of the energy of the system under consideration into Heat flowing out of and Work done on the system. The spatio-temporal distribution of internal energy in a strongly-driven open quantum system is also analyzed. This formalism is applied to analyze the thermodynamic performance of a model quantum machine: a driven two-level quantum system strongly coupled to two metallic reservoirs, which can operate in several configurations--as a chemical pump/engine or a heat pump/engine., Comment: Revised and updated version. 29 pages, 9 figures

We consider open quantum systems consisting of a finite system of independent fermions with arbitrary Hamiltonian coupled to one or more equilibrium fermion reservoirs (which need not be in equilibrium with each other). A strong form of the third law of thermodynamics, $S(T) \rightarrow 0$ as $T\rightarrow 0$, is proven for fully open quantum systems in thermal equilibrium with their environment, defined as systems where all states are broadened due to environmental coupling. For generic open quantum systems, it is shown that $S(T)\rightarrow g\ln 2$ as $T\rightarrow 0$, where $g$ is the number of localized states lying exactly at the chemical potential of the reservoir. For driven open quantum systems in a nonequilibrium steady state, it is shown that the local entropy $S({\bf x}; T) \rightarrow 0$ as $T({\bf x})\rightarrow 0$, except for cases of measure zero arising due to localized states, where $T({\bf x})$ is the temperature measured by a local thermometer., Comment: 8 pages, 2 figure files

Temperature imaging of nanoscale systems is a fundamental problem which has myriad potential technological applications. For example, nanoscopic cold spots can be used for spot cooling electronic components while hot spots could be used for precise activation of chemical or biological reactions. More fundamentally, imaging the temperature fields in quantum coherent conductors can provide a wealth of information on heat flow and dissipation at the smallest scales. However, despite significant technological advances, the spatial resolution of temperature imaging remains in the few nanometers range. Here we propose a method to map electronic temperature variations in operating nanoscale conductors by relying solely upon electrical tunneling current measurements. The scanning tunneling thermometer, owing to its operation in the tunneling regime, would be capable of mapping sub-angstrom temperature variations, thereby enhancing the resolution of scanning thermometry by some two orders of magnitude., Comment: Main article has 11 pages and 3 figures. Supplementary Information has 9 pages and 4 figures

The microscopic origins of Fourier's venerable law of thermal transport in quantum electron systems has remained somewhat of a mystery, given that previous derivations were forced to invoke intrinsic scattering rates far exceeding those occurring in real systems. We propose an alternative hypothesis, namely, that Fourier's law emerges naturally if many quantum states participate in the transport of heat across the system. We test this hypothesis systematically in a graphene flake junction, and show that the temperature distribution becomes nearly classical when the broadening of the individual quantum states of the flake exceeds their energetic separation. We develop a thermal resistor network model to investigate the scaling of the sample and contact thermal resistances, and show that the latter is consistent with classical thermal transport theory in the limit of large level broadening., Comment: 7 pages, 4 figures

The local entropy of a nonequilibrium system of independent fermions is investigated, and analyzed in the context of the laws of thermodynamics. It is shown that the local temperature and chemical potential can only be expressed in terms of derivatives of the local entropy for linear deviations from local equilibrium. The first law of thermodynamics is shown to lead to an inequality, not an equality, for the change in the local entropy as the nonequilibrium state of the system is changed. The maximum entropy principle (second law of thermodynamics) is proven: a nonequilibrium distribution has a local entropy less than or equal to a local equilibrium distribution satisfying the same constraints. It is shown that the local entropy of the system tends to zero when the local temperature tends to zero, consistent with the third law of thermodynamics., Comment: 7 pages, 5 figures

We show that a local measurement of temperature and voltage for a quantum system in steady state, arbitrarily far from equilibrium, with arbitrary interactions within the system, is unique when it exists. This is interpreted as a consequence of the second law of thermodynamics. We further derive a necessary and sufficient condition for the existence of a solution. In this regard, we find that a positive temperature solution exists whenever there is no net population inversion. However, when there is a net population inversion, we may characterize the system with a unique negative temperature. Voltage and temperature measurements are treated on an equal footing: They are simultaneously measured in a noninvasive manner, via a weakly-coupled thermoelectric probe, defined by requiring vanishing charge and heat dissipation into the probe. Our results strongly suggest that a local temperature measurement without a simultaneous local voltage measurement, or vice-versa, is a misleading characterization of the state of a nonequilibrium quantum electron system. These results provide a firm mathematical foundation for voltage and temperature measurements far from equilibrium., Comment: 16 pages, 6 figures

We consider a question motivated by the third law of thermodynamics: can there be a local temperature arbitrarily close to absolute zero in a nonequilibrium quantum system? We consider nanoscale quantum conductors with the source reservoir held at finite temperature and the drain held at or near absolute zero, a problem outside the scope of linear response theory. We obtain local temperatures close to absolute zero when electrons originating from the finite temperature reservoir undergo destructive quantum interference. The local temperature is computed by numerically solving a nonlinear system of equations describing equilibration of a scanning thermoelectric probe with the system, and we obtain excellent agreement with analytic results derived using the Sommerfeld expansion. A local entropy for a nonequilibrium quantum system is introduced, and used as a metric quantifying the departure from local equilibrium. It is shown that the local entropy of the system tends to zero when the probe temperature tends to zero, consistent with the third law of thermodynamics., Comment: 12 pages, 4 figures, 1 table

It is shown that quantum interference can be employed to create an exciton transistor. An applied potential gates the quasi-particle motion and also discriminates between quasi-particles of differing binding energy. When implemented within nanoscale assemblies, such control elements could mediate the flow of energy and information. Quantum interference can also be used to dissociate excitons as an alternative to using heterojunctions. A finite molecular setting is employed to exhibit the underlying discrete, two-particle, mesoscopic analog to Fano anti-resonance. Selected entanglement measures are shown to distinguish regimes of behavior which cannot be resolved from population dynamics alone., Comment: 5 pages, 5 figures

We present a theoretical approach for understanding the stability of simple metal nanowires, in particular monovalent metals such as the alkalis and noble metals. Their cross sections are of order one nanometer so that small perturbations from external (usually thermal) noise can cause large geometrical deformations. The nanowire lifetime is defined as the time required for making a transition into a state with a different cross-sectional geometry. This can be a simple overall change in radius, or a change in the cross section shape, or both. We develop a stochastic field theoretical model to describe this noise-induced transition process, in which the initial and final states correspond to locally stable states on a potential surface derived by solving the Schrodinger equation for the electronic structure of the nanowire numerically. The numerical string method is implemented to determine the optimal transition path governing the lifetime. Using these results, we tabulate the lifetimes of sodium and gold nanowires for several different initial geometries., Comment: 16 pages, 10 figures

A theory of local temperature measurement of an interacting quantum electron system far from equilibrium via a floating thermoelectric probe is developed. It is shown that the local temperature so defined is consistent with the zeroth, first, second, and third laws of thermodynamics, provided the probe-system coupling is weak and broad band. For non-broad-band probes, the local temperature obeys the Clausius form of the second law and the third law exactly, but there are corrections to the zeroth and first laws that are higher-order in the Sommerfeld expansion. The corrections to the zeroth and first laws are related, and can be interpreted in terms of the error of a nonideal temperature measurement. These results also hold for systems at negative absolute temperature., Comment: 19 pages, 1 figure

A generalization of Buttiker's voltage probe concept for nonzero temperatures is an open third terminal of a quantum thermoelectric circuit. An explicit analytic expression for the thermoelectric correction to an ideal quantum voltage measurement is derived, and interpreted in terms of local Peltier cooling/heating within the nonequilibrium system. The thermoelectric correction is found to be large (up to +-24% of the peak voltage) in a prototypical ballistic quantum conductor (graphene nanoribbon). The effects of measurement non-ideality are also investigated. Our findings have important implications for precision local electrical measurements., Comment: 5 pages, 3 figures

We investigate the local electron temperature distribution in carbon nano-ribbon (CNR) and graphene junctions subject to an applied thermal gradient. Using a realistic model of a scanning thermal microscope, we predict quantum temperature oscillations whose wavelength is related to that of Friedel oscillations. Experimentally, this wavelength can be tuned over several orders of magnitude by gating/doping, bringing quantum temperature oscillations within reach of the spatial resolution of existing measurement techniques., Comment: 5 pages, 4 figures

We provide a series of generic results regarding the structure of nodes in the retarded Green's function G of an interacting system, as exemplified by the extended Hubbard model. In particular: (1) due to an incompatibility between interactions of nearly any form and a precise definition of series propagation, degenerate geometric nodes are split or lifted by interactions; (2) degenerate nodes generically exist at the boundary between regimes of node splitting and node lifting and, in the presence of interactions, they require fine-tuning; (3) degenerate nodes are highly sensitive to perturbation and their sensitivity increases with their degeneracy. Moreover, for high degeneracies there is a tendency toward lifting rather than splitting. We also propose a characterization of the node structure in extended Hubbard models at arbitrary filling in terms of either the eigenvalues of G, or equivalently, the roots of a polynomial. This shows that "Mott nodes" previously predicted to occur in the transmission spectra of molecular radicals are fundamentally associated with nodes in the eigenvalues of the retarded Green's function that occur in open-shelled systems. This is accompanied by a low-energy two-pole approximation wherein each of the eigenvalues of G are mapped onto a Fermi-liquid-like renormalization of the Anderson model, for which the exact self-energy is provided., Comment: 18 pages, 14 figures

A precise definition for a quantum electron thermometer is given, as an electron reservoir coupled locally (e.g., by tunneling) to a sample, and brought into electrical and thermal equilibrium with it. A realistic model of a scanning thermal microscope with atomic resolution is then developed, where the resolution is limited in ultrahigh vacuum by thermal coupling to the electromagnetic environment. We show that the temperatures of individual atomic orbitals or bonds in a conjugated molecule with a temperature gradient across it exhibit quantum oscillations, whose origin can be traced to a realization of Maxwell's demon at the single-molecule level. These oscillations may be understood in terms of the rules of covalence describing bonding in \pi-electron systems. Fourier's law of heat conduction is recovered as the resolution of the temperature probe is reduced, indicating that the macroscopic law emerges as a consequence of coarse graining., Comment: 10 pages, 12 figures

The exact ground-state exchange-correlation functional of Kohn-Sham density functional theory yields the exact transmission through an Anderson junction at zero bias and temperature. The exact impurity charge susceptibility is used to construct the exact exchange-correlation potential. We analyze the successes and limitations of various types of approximations, including smooth and discontinuous functionals of the occupation, as well as symmetry-broken approaches., Comment: 6 pages, 5 figures, submitted to Phys. Rev. B

We develop a \pi-electron effective field theory (\pi-EFT) wherein the two-body Hamiltonian for a \pi-electron system is expressed in terms of three effective parameters: the \pi-orbital quadrupole moment, the on-site repulsion, and a dielectric constant. As a first application of this \pi-EFT, we develop a model of screening in molecular junctions based on image multipole moments, and use this to investigate the reduction of the HOMO-LUMO gap of benzene. Beyond this, we also use \pi-EFT to calculate the differential conductance spectrum of the prototypical benzenedithiol-Au single-molecule junction and the \pi-electron contribution to the van der Waals interaction between benzene and a metallic electrode., Comment: 13 pages, 9 figures

The transport through a quantum-scale device may be characterized by the transmission eigenvalues. These values constitute a junction PIN code where, for example, in single-atom metallic contacts the number of transmission channels is also the chemical valence of the atom. Recently, highly conductive single-molecule junctions (SMJ) with multiple transport channels have been formed from benzene molecules between Pt electrodes. Transport through these multi-channel SMJs is a probe of both the bonding properties at the lead-molecule interface and of the molecular symmetry. Here we utilize a many-body theory that properly describes the complementary nature of the charge carrier to calculate transport distributions through Pt-benzene-Pt junctions. We develop an effective field theory of interacting pi-electrons to accurately model the electrostatic influence of the leads and an ab initio tunneling model to describe the lead-molecule bonding. With this state-of-the-art many-body technique we calculate the transport using the full molecular spectrum and using an `isolated resonance approximation' for the molecular Green's function. We confirm that the number of transmission channels in a SMJ is equal to the degeneracy of the relevant molecular orbital. In addition, we demonstrate that the isolated resonance approximation is extremely accurate and determine that transport occurs predominantly via the HOMO orbital in Pt-benzene-Pt junctions. Finally, we show that the transport occurs in a lead-molecule coupling regime where the charge carriers are both particle-like and wave-like simultaneously, requiring a many-body description., Comment: 21 pages, 8 figures

Transport through an Anderson junction (two macroscopic electrodes coupled to an Anderson impurity) is dominated by a Kondo peak in the spectral function at zero temperature. The exact single-particle Kohn-Sham potential of density functional theory reproduces the linear transport exactly, despite the lack of a Kondo peak in its spectral function. Using Bethe ansatz techniques, we calculate this potential exactly for all coupling strengths, including the cross-over from mean-field behavior to charge quantization caused by the derivative discontinuity. A simple and accurate interpolation formula is also given., Comment: 5 pages, 4 figures

We give a detailed discussion of the Quantum Interference Effect Transistor (QuIET), a proposed device which exploits interference between electron paths through aromatic molecules to modulate current flow. In the off state, perfect destructive interference stemming from the molecular symmetry blocks current, while in the on state, current is allowed to flow by locally introducing either decoherence or elastic scattering. Details of a model calculation demonstrating the efficacy of the QuIET are presented, and various fabrication scenarios are proposed, including the possibility of using conducting polymers to connect the QuIET with multiple leads., Comment: 12 pages, 7 figures

Persistent currents in a Moebius ladder are shown to be very sensitive to the effects of intrachain interactions on the hopping of electrons between chains. Their periodicity as a function of flux is doubled for strong enough repulsive interactions because electrons cannot hop coherently between the chains and have to travel along the full edge of the Moebius ladder, thus encircling the flux twice. Mesoscopic devices that should enable one to observe these effects are proposed., Comment: 4 Latex pages with 5 encapsulated figures. Requires psfig.sty

We propose a quantum-dot version of the quantum-well cascade laser of Faist et al. [Science {\bf 264}, 553 (1994)]. The elimination of single phonon decays by the three-dimensional confinement implies a several order-of-magnitude reduction in the threshold current. The requirements on dot size (10-20nm) and on dot density and uniformity [one coupled pair of dots per (180nm)^3 with 5% nonuniformity] are close to current technology., Comment: 8 pages, REVTEX 3.0, 3 compressed postscript figures

The time average of the fully nonlinear current through a double quantum dot, subject to an arbitrary combination of ac and dc voltages, is calculated exactly using the Keldysh nonequilibrium Green function technique. When driven on resonance, the system functions as an efficient electron pump due to Rabi oscillation between the dots. The pumping current is maximum when the coupling to the leads equals the Rabi frequency., Comment: 6 pages, REVTEX 3.0, 3 postscript figures