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Showing papers on "Non-equilibrium thermodynamics published in 2018"


Journal ArticleDOI
TL;DR: A quantum-mechanical generalization of majorization is used to derive a complete set of necessary and sufficient conditions for thermal transformations of quantum states, based on natural physical principles, namely, energy conservation, the existence of equilibrium states, and the requirement that quantum coherence be accounted for thermodynamics.
Abstract: What does it mean for one quantum process to be more disordered than another? Interestingly, this apparently abstract question arises naturally in a wide range of areas such as information theory, thermodynamics, quantum reference frames, and the resource theory of asymmetry. Here we use a quantum-mechanical generalization of majorization to develop a framework for answering this question, in terms of single-shot entropies, or equivalently, in terms of semi-definite programs. We also investigate some of the applications of this framework, and remarkably find that, in the context of quantum thermodynamics it provides the first complete set of necessary and sufficient conditions for arbitrary quantum state transformations under thermodynamic processes, which rigorously accounts for quantum-mechanical properties, such as coherence. Our framework of generalized thermal processes extends thermal operations, and is based on natural physical principles, namely, energy conservation, the existence of equilibrium states, and the requirement that quantum coherence be accounted for thermodynamically. Similarly to entropy, majorization allows to quantify deviation from uniformity in a wide range of fields. In this paper, the authors use its generalization to the quantum realm to derive a complete set of necessary and sufficient conditions for thermal transformations of quantum states.

432 citations


Journal ArticleDOI
TL;DR: In this article, the critical properties of the super-radiant phase transition and the distinction between equilibrium and none-quilibrium conditions are reviewed, as well as some aspects of real-time dynamics, including superconducting qubits, trapped ions, and using spin-orbit coupling for cold atoms.
Abstract: The Dicke model describes the coupling between a quantized cavity field and a large ensemble of two-level atoms. When the number of atoms tends to infinity, this model can undergo a transition to a superradiant phase, belonging to the mean-field Ising universality class. The superradiant transition was first predicted for atoms in thermal equilibrium and was recently realized with a quantum simulator made of atoms in an optical cavity, subject to both dissipation and driving. In this Progress Report, we offer an introduction to some theoretical concepts relevant to the Dicke model, reviewing the critical properties of the superradiant phase transition, and the distinction between equilibrium and nonequilibrium conditions. In addition, we explain the fundamental difference between the superradiant phase transition and the more common lasing transition. Our report mostly focuses on the steady states of atoms in single-mode optical cavities, but we also mention some aspects of real-time dynamics, as well as other quantum simulators, including superconducting qubits, trapped ions, and using spin-orbit coupling for cold atoms. These realizations differ in regard to whether they describe equilibrium or non-equilibrium systems.

133 citations


Journal ArticleDOI
TL;DR: In this paper, the authors analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments and show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms.
Abstract: We analyze the production of entropy along nonequilibrium processes in quantum systems coupled to generic environments. First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms. Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and nonadiabatic, based on the existence of invariant states of the local dynamics. Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin. We illustrate our results with three relevant examples of quantum thermodynamic processes far from equilibrium.

130 citations


Journal ArticleDOI
TL;DR: In this paper, the authors obtained a universal bound on current fluctuations for periodically driven systems, such as heat engines driven by periodic variation of the temperature and artificial molecular pumps driven by an external protocol.
Abstract: Small nonequilibrium systems in contact with a heat bath can be analyzed with the framework of stochastic thermodynamics. In such systems, fluctuations, which are not negligible, follow universal relations such as the fluctuation theorem. More recently, it has been found that, for nonequilibrium stationary states, the full spectrum of fluctuations of any thermodynamic current is bounded by the average rate of entropy production and the average current. However, this bound does not apply to periodically driven systems, such as heat engines driven by periodic variation of the temperature and artificial molecular pumps driven by an external protocol. We obtain a universal bound on current fluctuations for periodically driven systems. This bound is a generalization of the known bound for stationary states. In general, the average rate that bounds fluctuations in periodically driven systems is different from the rate of entropy production. We also obtain a local bound on fluctuations that leads to a trade-off relation between speed and precision in periodically driven systems, which constitutes a generalization to periodically driven systems of the so called thermodynamic uncertainty relation. From a technical perspective, our results are obtained with the use of a recently developed theory for 2.5 large deviations for Markov jump processes with time-periodic transition rates.

113 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the thermodynamic uncertainty relation (TUR), a cost-precision trade-off relationship in transport systems, and derived a condition for invalidating the TUR for general nonequilibrium (classical and quantum) systems.
Abstract: We examine the so-called thermodynamic uncertainty relation (TUR), a cost-precision trade-off relationship in transport systems. Based on the fluctuation symmetry, we derive a condition for invalidating the TUR for general nonequilibrium (classical and quantum) systems. We find that the first nonzero contribution to the TUR beyond equilibrium, given in terms of nonlinear transport coefficients, can be positive or negative, thus affirming or violating the TUR depending on the details of the system. We exemplify our results for noninteracting quantum systems by expressing the thermodynamic uncertainty relation in the language of the transmission function. We demonstrate that quantum coherent systems that do not follow a population Markovian master equation, e.g., by supporting high-order tunneling processes or relying on coherences, violate the TUR.

112 citations


Journal ArticleDOI
TL;DR: This work uses linear response theory to deriveThermodynamic uncertainty relations (TURs) in a straightforward and unified way and finds that, for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix.
Abstract: Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium, linear response (LR) theory provides the natural framework to study generic nonequilibrium processes. Here, we use LR to derive TURs in a straightforward and unified way. Our approach allows us to generalize TURs to systems without local time-reversal symmetry, including, e.g., ballistic transport and periodically driven classical and quantum systems. We find that, for broken time reversal, the bounds on the relative uncertainty are controlled both by dissipation and by a parameter encoding the asymmetry of the Onsager matrix. We illustrate our results with an example from mesoscopic physics. We also extend our approach beyond linear response: for Markovian dynamics, it reveals a connection between the TUR and current fluctuation theorems.

109 citations


Journal ArticleDOI
TL;DR: In this article, the first-order, symmetric hyperbolic partial differential equations (SHTC) with dislocations are put into the Hamiltonian form and into the form of the Godunov-type system of the first order, first order SHTC equations, and the compatibility with thermodynamics of the time reversible part of the governing equations is expressed in the former formulation as degeneracy of Hamiltonian structure and in the latter formulation as the existence of a companion conservation law.
Abstract: Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

78 citations


Journal ArticleDOI
TL;DR: It is shown that the canonical (resp. semigrand canonical) nonequilibrium free energy works as a Lyapunov function in the relaxation to equilibrium of a closed system, and its variation provides the minimum amount of work needed to manipulate the species concentrations.
Abstract: We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials are constructed exploiting the symmetries of the chemical network topology. It is shown that the canonical (resp. semigrand canonical) nonequilibrium free energy works as a Lyapunov function in the relaxation to equilibrium of a closed (resp. open) system, and its variation provides the minimum amount of work needed to manipulate the species concentrations. The theory is used to study analytically the Turing pattern formation in a prototypical reaction-diffusion system, the one-dimensional Brusselator model, and to classify it as a genuine thermodynamic nonequilibrium phase transition.

76 citations


Journal ArticleDOI
TL;DR: In this article, a macroscopic phonon hydrodynamic equation beyond Fourier's law with a relaxation term and nonlocal terms is derived through a perturbation expansion to the phonon Boltzmann equation around a four-moment nonequilibrium solution.
Abstract: The classical Fourier's law fails in extremely small and ultrafast heat conduction even at ordinary temperatures due to strong thermodynamic nonequilibrium effects. In this work, a macroscopic phonon hydrodynamic equation beyond Fourier's law with a relaxation term and nonlocal terms is derived through a perturbation expansion to the phonon Boltzmann equation around a four-moment nonequilibrium solution. The temperature jump and heat flux tangential retardant boundary conditions are developed based on the Maxwell model of the phonon-boundary interaction. Extensive steady-state and transient nanoscale heat transport cases are modeled by the phonon hydrodynamic model, which produces quantitative predictions in good agreement with available phonon Boltzmann equation solutions and experimental results. The phonon hydrodynamic model provides a simple and elegant mathematical description of non-Fourier heat conduction with a clear and intuitive physical picture. The present work will promote deeper understanding and macroscopic modeling of heat transport in extreme states.

71 citations


Journal Article
TL;DR: In this paper, an Ito stochastic differential equation for entropy production in nonequilibrium Langevin processes is derived, and entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model.
Abstract: We derive an Ito stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time, which we also generalize to non-steady-state conditions.

70 citations


Journal ArticleDOI
TL;DR: This work defines a procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production and can be viewed as the extension of the theory of generalized Gibbs ensembles to nonequilibrium situations.
Abstract: Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production. The former is expressed as the difference between changes caused by time-dependent drivings and a generalized potential difference. The latter is a sum over the minimal set of flux--force contributions controlling the dissipative flows across the system. When the system is initially prepared at equilibrium (e.g. by turning off drivings and forces), a finite-time detailed fluctuation theorem holds for the different contributions. Our approach relies on identifying the complete set of conserved quantities and can be viewed as the extension of the theory of generalized Gibbs ensembles to nonequilibrium situations.

Journal ArticleDOI
TL;DR: In this article, the thermal leads are described using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group.
Abstract: The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but it faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome by describing the thermal leads using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group. This yields quantitatively reliable results for the current (with errors ≲3%) down to the exponentially small energy scales characteristic of impurity models. We present results of benchmark quality for the temperature and magnetic field dependence of the zero-bias conductance peak for the single-impurity Anderson model.

Journal ArticleDOI
TL;DR: In this article, an ensemble of efficient nanomachines can trigger cooperative phenomena that enhance the individual power-efficiency trade-off for each machine, and the cooperative phenomena can be found to enhance the performance of each machine.
Abstract: Interactions among an ensemble of efficient nanomachines can trigger cooperative phenomena that enhance the individual power-efficiency trade-off for each machine.

Journal ArticleDOI
TL;DR: In this article, a generalized hydrodynamic description of the nonequilibrium steady states was developed using numerical simulations based on matrix product states, and the model features a low-energy conformal limit with central charge $c=\frac{4}{5}$, which affects the low-temperature energy current.
Abstract: We study energy transport in the integrable ${\mathbb{Z}}_{3}$ parafermionic chain using the partitioning protocol. By exploiting the Bethe-ansatz solution for the thermodynamics of the system, we develop a generalized hydrodynamic description of the nonequilibrium steady states, which we benchmark using numerical simulations based on matrix product states. The model features a low-energy conformal limit with central charge $c=\frac{4}{5}$, which affects the low-temperature energy current, as we explicitly show. Moreover, we exploit that, for energies close to the maximally excited state, the system is also critical and described by a conformal field theory with $c=1$. By considering the two halves prepared at two temperatures both low in value but opposite in sign, we are able to investigate in an exact and controlled way the junction between two conformal field theories with different central charges. Notwithstanding the absence of global conformal invariance, we find results that approximate to a high degree those of out-of-equilibrium conformal field theories. Our study extends the generalized hydrodynamics to a framework where it can be profitably used for exploring new physical phenomena.

Journal ArticleDOI
TL;DR: In this article, the authors utilized the chiral kinetic theory in a relaxation-time approximation to investigate the nonlinear anomalous responses of chiral fluids with viscous effects, and they found that the effects of both magnetic and vortical effects are modified by the shear and bulk strengths.
Abstract: We utilize the chiral kinetic theory in a relaxation-time approximation to investigate the nonlinear anomalous responses of chiral fluids with viscous effects. Unlike the cases in equilibrium, it is found that the chiral magnetic effect and chiral vortical effect are modified by the shear and bulk strengths. Particularly, the shear strength could result in charged Hall currents for chiral magnetic and chiral vortical effects, which propagate perpendicular to applied magnetic fields and vorticity. These quantum corrections stemming from side jumps and anomalies are dissipative and pertinent to interactions. Although the nonequilibrium effects upon charge currents are dissipative, the second law of thermodynamics is still satisfied.

Journal ArticleDOI
TL;DR: In this article, the authors compared the performance of the Green-Kubo formula and Fourier's law in nonequilibrium MD simulations in three allotropes of Si: three-dimensional bulk silicon, two-dimensional silicene, and quasi-one-dimensional silicon nanowire.
Abstract: © 2018 American Physical Society. Molecular dynamics (MD) simulations play an important role in studying heat transport in complex materials. The lattice thermal conductivity can be computed either using the Green-Kubo formula in equilibrium MD (EMD) simulations or using Fourier's law in nonequilibrium MD (NEMD) simulations. These two methods have not been systematically compared for materials with different dimensions and inconsistencies between them have been occasionally reported in the literature. Here we give an in-depth comparison of them in terms of heat transport in three allotropes of Si: three-dimensional bulk silicon, two-dimensional silicene, and quasi-one-dimensional silicon nanowire. By multiplying the correlation time in the Green-Kubo formula with an appropriate effective group velocity, we can express the running thermal conductivity in the EMD method as a function of an effective length and directly compare it to the length-dependent thermal conductivity in the NEMD method. We find that the two methods quantitatively agree with each other for all the systems studied, firmly establishing their equivalence in computing thermal conductivity.

Journal ArticleDOI
TL;DR: In this article, a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath is presented, and the authors apply the formalism to clarify issues of principle regarding the sources and signatures of nonequilibrium behaviour in a variety of polar and apolar single-particle systems and polar flocks.
Abstract: We present in detail a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath We apply the formalism to clarify issues of principle regarding the sources and signatures of nonequilibrium behaviour in a variety of polar and apolar single-particle systems and polar flocks We show that distance from thermal equilibrium depends on how time-reversal is implemented and hence on the reference equilibrium state We predict characteristic forms for the frequency-resolved entropy production for an active polar particle in a harmonic potential, which should be testable in experiments

Journal ArticleDOI
TL;DR: In this paper, a non-equilibrium regime for single-qubit thermometry is proposed, taking into account purely quantum effects such as coherence, and experimental results show that the temperature uncertainty is linked to the heat capacity of the qubit.
Abstract: Single-qubit thermometry presents the simplest tool to measure the temperature of thermal baths with reduced invasivity. At thermal equilibrium, the temperature uncertainty is linked to the heat capacity of the qubit, however the best precision is achieved outside equilibrium condition. Here, we discuss a way to generalize this relation in a non-equilibrium regime, taking into account purely quantum effects such as coherence. We support our findings with an experimental photonic simulation.

Journal ArticleDOI
TL;DR: In this paper, a generalized thermodynamic formalism is proposed to account for the binodal curve of the Cahn-Hilliard equation and a generalized surface tension that can be used to construct new thermodynamic ensembles.
Abstract: Motility-induced phase separation (MIPS) leads to cohesive active matter in the absence of cohesive forces. We present, extend and illustrate a recent generalized thermodynamic formalism which accounts for its binodal curve. Using this formalism, we identify both a generalized surface tension, that controls finite-size corrections to coexisting densities, and generalized forces, that can be used to construct new thermodynamic ensembles. Our framework is based on a nonequilibrium generalization of the Cahn-Hilliard equation and we discuss its application to active particles interacting either via quorum-sensing interactions or directly through pairwise forces.

Journal ArticleDOI
TL;DR: The single-spin test and confirmation of the Jarzynski relation in the quantum regime is reported using a single ultracold ^{40}Ca^{+} ion trapped in a harmonic potential, based on a general information-theoretic equality for a temporal evolution of the system sandwiched between two projective measurements.
Abstract: Most nonequilibrium processes in thermodynamics are quantified only by inequalities; however, the Jarzynski relation presents a remarkably simple and general equality relating nonequilibrium quantities with the equilibrium free energy, and this equality holds in both the classical and quantum regimes. We report a single-spin test and confirmation of the Jarzynski relation in the quantum regime using a single ultracold ^{40}Ca^{+} ion trapped in a harmonic potential, based on a general information-theoretic equality for a temporal evolution of the system sandwiched between two projective measurements. By considering both initially pure and mixed states, respectively, we verify, in an exact and fundamental fashion, the nonequilibrium quantum thermodynamics relevant to the mutual information and Jarzynski equality.

Journal ArticleDOI
TL;DR: In this paper, it has been shown that fluctuation theorems obeyed by liquid particles are also valid for strongly coupled dusty plasmas, which is known as strongly coupled powder.
Abstract: Particles in strongly coupled plasmas behave collectively as in liquids, with additional long-range collisions. Experimental evidence is provided that fluctuation theorems obeyed by liquid are also valid for strongly coupled dusty plasmas. Fluctuation theorems1,2,3,4 describe nonequilibrium stochastic behaviour in small systems. Whilst experiments have shown that fluctuation theorems are obeyed by single particles in liquids5 and several other physical systems6,7,8,9,10, it has not been shown if that is the case in strongly coupled plasmas. Plasmas are said to be strongly coupled when interparticle potential energies are large compared to kinetic energies. Charged particles in such plasmas can behave collectively like liquids11,12, but with essential differences, such as long-range collisions13. It remains unexplored whether, despite these differences, the stochastic behaviour of strongly coupled plasmas will obey fluctuation theorems. Here we demonstrate experimentally that a strongly coupled dusty plasma obeys the fluctuation theorem of Evans, Cohen, and Morriss (ECM)14, which was developed for a simple liquid in a nonequilibrium steady state. This fluctuation theorem describes the entropy production arising from collisions in a steady laminar shear flow.

Journal ArticleDOI
TL;DR: An efficient, accurate and robust multiple-relaxation-time (MRT) discrete Boltzmann method (DBM) is proposed for compressible exothermic reactive flows, with both specific heat ratio and Prandtl number being flexible as mentioned in this paper.

Journal ArticleDOI
TL;DR: In this article, it was shown that an anomalous power-law scaling in time of large deviations can also arise without long-range correlations in Markovian processes as simple as the Langevin equation.
Abstract: The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium systems. The definition of these functions involves a scaling limit, similar to the thermodynamic limit, in which the integration time τ appears linearly, unless the process considered has long-range correlations, in which case τ is generally replaced by τ^{ξ} with ξ≠1. Here, we show that such an anomalous power-law scaling in time of large deviations can also arise without long-range correlations in Markovian processes as simple as the Langevin equation. We describe the mechanism underlying this scaling using path integrals and discuss its physical consequences for more general processes.

Journal ArticleDOI
TL;DR: This work shows that biochemical oscillations emerge through a generic nonequilibrium phase transition, with a characteristic qualitative behavior at criticality, and argues that the number of coherent oscillations is more appropriate to quantify the precision of biochemical oscillation.
Abstract: Biochemical oscillations are ubiquitous in living organisms. In an autonomous system, not influenced by an external signal, they can only occur out of equilibrium. We show that they emerge through a generic nonequilibrium phase transition, with a characteristic qualitative behavior at criticality. The control parameter is the thermodynamic force which must be above a certain threshold for the onset of biochemical oscillations. This critical behavior is characterized by the thermodynamic flux associated with the thermodynamic force, its diffusion coefficient, and the stationary distribution of the oscillating chemical species. We discuss metrics for the precision of biochemical oscillations by comparing two observables, the Fano factor associated with the thermodynamic flux and the number of coherent oscillations. Since the Fano factor can be small even when there are no biochemical oscillations, we argue that the number of coherent oscillations is more appropriate to quantify the precision of biochemical oscillations. Our results are obtained with three thermodynamically consistent versions of known models: the Brusselator, the activator-inhibitor model, and a model for KaiC oscillations.

Journal ArticleDOI
TL;DR: In this paper, a nonequilibrium mixture of fermions and bosons is considered, and the authors show that massless bosons contribute in a nontrivial way to the bulk viscosity of a mixture.
Abstract: Kinetic equations for fermions and bosons are solved numerically in the relaxation-time approximation for the case of one-dimensional boost-invariant geometry. Fermions are massive and carry baryon number, while bosons are massless. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions, which specify the coupling between the fermionic and bosonic sectors and determine the proper-time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a nonequilibrium mixture of fermions and bosons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients. The shear viscosity of a mixture is the sum of the shear viscosities of fermion and boson components, while the bulk viscosity is given by the formula known for a gas of fermions, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless bosons contribute in a nontrivial way to the bulk viscosity of a mixture, provided fermions are massive. We further observe the hydrodynamization effect, which takes place earlier in the shear sector than in the bulk one. The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behavior is connected with the existence of an attractor solution for conformal systems.

Journal ArticleDOI
TL;DR: In this paper, the authors formulate a nonequilibrium thermodynamic description for open chemical reaction networks (CRNs) described by a chemical master equation, which is used to decompose the entropy production into a potential change and two work contributions, the first due to time dependent changes in the externally controlled chemostats concentrations and the second due to flows maintained across the system by nonconservative forces.
Abstract: We formulate a nonequilibrium thermodynamic description for open chemical reaction networks (CRNs) described by a chemical master equation. The topological properties of the CRN and its conservation laws are shown to play a crucial role. They are used to decompose the entropy production into a potential change and two work contributions, the first due to time dependent changes in the externally controlled chemostats concentrations and the second due to flows maintained across the system by nonconservative forces. These two works jointly satisfy a Jarzynski and Crooks fluctuation theorem. In the absence of work, the potential is minimized by the dynamics as the system relaxes to equilibrium and its equilibrium value coincides with the maximum entropy principle. A generalized Landauer's principle also holds: the minimal work needed to create a nonequilibrium state is the relative entropy of that state to its equilibrium value reached in the absence of any work.

Journal ArticleDOI
23 Dec 2018-Entropy
TL;DR: The fundamental variational principle of classical mechanics, namely, Hamilton’s principle, is shown, with the help of thermodynamic systems with gradually increasing complexity, how to systematically extend it to include irreversible processes.
Abstract: In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite-dimensional case of discrete systems, as well as for the infinite-dimensional case of continuum systems. Starting with the fundamental variational principle of classical mechanics, namely, Hamilton's principle, we show, with the help of thermodynamic systems with gradually increasing complexity, how to systematically extend it to include irreversible processes. In the finite dimensional cases, we treat systems experiencing the irreversible processes of mechanical friction, heat, and mass transfer in both the adiabatically closed cases and open cases. On the continuum side, we illustrate our theory using the example of multicomponent Navier-Stokes-Fourier systems.

Journal ArticleDOI
TL;DR: Results obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in quantum many-body systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement.
Abstract: In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of $N$ strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. Entropy and entanglement will be the main theme of our second paper on this subject matter.

Journal ArticleDOI
06 Sep 2018-Langmuir
TL;DR: A predictive model of evaporation based on nonequilibrium thermodynamics with no fitting parameters is cast, which provides a foundation for all liquid-vapor phase change studies including energy, water, and biological systems.
Abstract: Evaporation is a fundamental and core phenomenon in a broad range of disciplines including power generation and refrigeration systems, desalination, electronic/photonic cooling, aviation systems, and even biosciences. Despite its importance, the current theories on evaporation suffer from fitting coefficients with reported values varying in a few orders of magnitude. Lack of a sound model impedes simulation and prediction of characteristics of many systems in these disciplines. Here, we studied evaporation at a planar liquid–vapor interface through a custom-designed, controlled, and automated experimental setup. This experimental setup provides the ability to accurately probe thermodynamic properties in vapor, liquid, and close to the liquid–vapor interface. Through analysis of these thermodynamic properties in a wide range of evaporation mass fluxes, we cast a predictive model of evaporation based on nonequilibrium thermodynamics with no fitting parameters. In this model, only the interfacial temperature...

Journal ArticleDOI
TL;DR: In this paper, it was shown that a large enough amount of quantum coherence is necessary and sufficient to revert the thermodynamic arrow of time in the case of two spin systems.
Abstract: Recent research on the thermodynamic arrow of time, at the microscopic scale, has questioned the universality of its direction. Theoretical studies showed that quantum correlations can be used to revert the natural heat flow (from the hot body to the cold one), posing an apparent challenge to the second law of thermodynamics. Such an "anomalous" heat current was observed in a recent experiment (K. Micadei et al., arXiv:1711.03323), by employing two spin systems initially quantum correlated. Nevertheless, the precise relationship between this intriguing phenomenon and the initial conditions that allow it is not fully evident. Here, we address energy transfer in a wider perspective, identifying a nonclassical contribution that applies to the reversion of the heat flow as well as to more general forms of energy exchange. We derive three theorems that describe the energy transfer between two microscopic systems, for arbitrary initial bipartite states. Using these theorems, we obtain an analytical bound showing that certain type of quantum coherence can optimize such a process, outperforming incoherent states. This genuine quantum advantage is corroborated through a characterization of the energy transfer between two qubits. For this system, it is shown that a large enough amount of coherence is necessary and sufficient to revert the thermodynamic arrow of time. As a second crucial consequence of the presented theorems, we introduce a class of nonequilibrium states that only allow unidirectional energy flow. In this way, we broaden the set where the standard Clausius statement of the second law applies.