Nonequilibrium Energy Research Articles

Generalized enthalpy based equation of state for multi-component mixtures

An equation of state using pressure and temperature as independent variables, including non-equilibrium thermal energies of components and explicit accounting of thermal electron effects, is formulated for multi component mixtures. As pressure equilibration is faster in mixtures, this approach is more suited than earlier schemes using Mie-Gruneisen equation of state. Due to the reliance on enthalpy, in lieu of energy, it is directly applicable also to treat porosity effects. The formulation leads to an expression for mixture volume which consists of a term depended on enthalpy differences of components, in addition to those depending on average mixture parameters. A method to estimate non-equilibrium thermal effects, using component Hugoniot to compute non-equilibrium temperatures, is also proposed in this work. Results obtained for two and three component mixtures compare well with experimental Hugoniot data.

Optically excited structural transition in atomic wires on surfaces at the quantum limit.

Transient control over the atomic potential-energy landscapes of solids could lead to new states of matter and to quantum control of nuclear motion on the timescale of lattice vibrations. Recently developed ultrafast time-resolved diffraction techniques combine ultrafast temporal manipulation with atomic-scale spatial resolution and femtosecond temporal resolution. These advances have enabled investigations of photo-induced structural changes in bulk solids that often occur on timescales as short as a few hundred femtoseconds. In contrast, experiments at surfaces and on single atomic layers such as graphene report timescales of structural changes that are orders of magnitude longer. This raises the question of whether the structural response of low-dimensional materials to femtosecond laser excitation is, in general, limited. Here we show that a photo-induced transition from the low- to high-symmetry state of a charge density wave in atomic indium (In) wires supported by a silicon (Si) surface takes place within 350 femtoseconds. The optical excitation breaks and creates In-In bonds, leading to the non-thermal excitation of soft phonon modes, and drives the structural transition in the limit of critically damped nuclear motion through coupling of these soft phonon modes to a manifold of surface and interface phonons that arise from the symmetry breaking at the silicon surface. This finding demonstrates that carefully tuned electronic excitations can create non-equilibrium potential energy surfaces that drive structural dynamics at interfaces in the quantum limit (that is, in a regime in which the nuclear motion is directed and deterministic). This technique could potentially be used to tune the dynamic response of a solid to optical excitation, and has widespread potential application, for example in ultrafast detectors.

Thermal Performance Analysis of Biporous Metal Foam Heat Sink

The present study presents a concept of biporous metal foam heat sink applicable to electronic cooling. This heat sink has two metal foam layers arranged in parallel along the primary flow direction, with different metal foam thickness, porosity, and pore density for each layer. The forced convective heat transfer in biporous metal foam heat sink is numerically investigated by employing the Forchheimer–Brinkman extended Darcy momentum equation and local thermal nonequilibrium energy equation. The effects of geometrical and morphological parameters on thermal and hydraulic performance are discussed in detail, and the heat transfer enhancement mechanism of biporous metal foam is analyzed. The thermal performance of biporous metal foam heat sink is compared with that of uniform metal foam heat sink. The results show that the thermal resistance of the biporous metal foam heat sink decreases with decrease of top layer metal foam porosity at a fixed bottom metal foam porosity of 0.9. It is seen that the biporous metal foam heat sink can outperform the uniform metal foam heat sink with a proper selection of foam geometrical and morphological parameters, which is attributed to the presence of high velocity gradient at the boundary layer that can enhance the convective heat transfer. The best observed thermal performance of biporous metal foam heat sink is achieved by employing 30 pores per inch (PPI) metal foam at the bottom layer, with a fixed 50 PPI metal foam at the top layer for the porosities of both layers equal to 0.9, and the optimal thickness of the bottom foam layer is about 1 mm.

Laser-excitation of electrons and nonequilibrium energy transfer to phonons in copper

After the irradiation of a copper sample with an ultrashort laser pulse, electrons do not follow a Fermi distribution anymore but instead are in a nonequilibrium state. In contrast, the lattice cannot be excited directly by the laser pulse, due to the frequency mismatch. The energy increase in the phononic system only happens due to electron–phonon scattering. We investigate the initial electron dynamics using full Boltzmann-type collision integrals, including material-dependent characteristics by implementing a realistic density of states. We show results on the absorbed energy, details of the electronic nonequilibrium and the resulting electron–phonon coupling parameter in dependence on the photon energy. Our results show a counteracting dependence on the photon energy, which, on the one hand, enables the d-band electrons to absorb high-energy photons and on the other hand, increases the probability of multi-photon absorption.

Free energy for non-equilibrium quasi-stationary states

We study a class of non-equilibrium quasi-stationary states for a Markov system interacting with two different thermal baths. We show that the work done under a slow, external change of parameters admits a potential, i.e., the free energy. Three conditions are needed for the existence of free energy in this non-equilibrium system: time-scale separation between variables of the system, partial controllability (external fields couple only with the slow variable), and an effective detailed balance. These conditions are facilitated in the continuous limit for the slow variable. In contrast to its equilibrium counterpart, the non-equilibrium free energy can increase with temperature. One example of this is that entropy reduction by means of external fields (cooling) can be easier (in the sense of the work cost) if it starts from a higher temperature.

Lattice Instabilities and Phase Transformations in Fe from Atomistic Simulations

The stability of the body- and face-centered cubic lattices corresponding to the α and γ phases of Fe, respectively, as well as the transformation of one phase to the other were investigated by atomistic simulations. Two interatomic potentials were used: the embedded atom method (EAM) potential of Meyer and Entel and the bond order potential (BOP) developed by Muller et al. The suitability of the potentials for investigating structural transformations in Fe was verified using nonequilibrium free energy calculations and molecular dynamics simulations. The results showed that the EAM potential is capable of describing the bcc → fcc and fcc → bcc transformations whereas no transformation was observed for the computationally more expensive BOP potential with the simulation set up used.

Non-equilibrium vibrational and electron energy distribution functions in mtorr, high-electron-density nitrogen discharges and afterglows

Non-equilibrium vibrational distributions (vdf) and non-equilibrium electron energy distribution functions (eedf) in a nitrogen plasma at low pressure (mtorr) have been calculated by using a time-dependent plasma physics model coupled to the Boltzmann equation and heavy particle kinetics. Different case studies have been selected showing the non-equilibrium character of both vdf and eedf under discharge and post-discharge conditions in the presence of large concentrations of electrons. Particular attention is devoted to the electron-molecule resonant vibrational excitation cross sections acting in the whole vibrational ladder. The results in the post-discharge conditions show the interplay of superelastic vibrational and electronic collisions in forming structures in the eedf. The link between the present results in the mtorr afterglow regime with the existing eedf in the torr and atmospheric regimes is discussed.

Ionization of CO in radio-frequency electric field

The rate coefficients for the electron impact ionization of the CO molecule have been calculated in the presence of the radio-frequency (RF) electric field. The non-equilibrium electron energy distribution functions, used for the rate coefficient calculations, were generated by using a Monte Carlo simulation. The rate coefficients were obtained, time resolved within one period, in the frequency range from 13.56 up to 500 MHz, at effective reduced electric field values up to 700 Td. A temporal behavior of the rate coefficients under the influence of magnitude and frequency of the fields has been studied. The total ionization rate coefficients and the rate coefficients for the production of different ion fragments have been period averaged and presented in the order to be of use for practical implementation in the RF discharges in CO. Also, the temporal characteristics of the electron energy distribution functions and the diffusion coefficients have been studied separately revealing some interesting features in their time dependence within the period of electric field oscillations.

Theoretical study on electron–phonon coupling factor and electron–ion nonequilibrium process in uranium

Rapid laser heating is an important experimental technique to achieve extreme conditions for uranium. Theoretical simulations of the electron–ion nonequilibrium energy relaxation after laser heating usually employ a two-temperature model using the thermal quantities of the electron heat capacity and the electron–phonon coupling factor as input parameters. Based on the first-principles calculations of the electron density of states and Eliashberg function, we theoretically determine the thermal quantities and their dependence on electron temperature and external pressure for uranium and revealed the connection between the thermal quantities and the electron density of states. The electron/ion temperature evolution was examined by employing the two-temperature model with the obtained thermal quantities. The time/temperature at the peak/equilibrium point of the temperature evolution curve was examined for different external pressures and different laser energy densities. We found that the approximation of a linear temperature-dependent electron heat capacity is acceptable at a low energy density, while at a high energy density, the electron temperature dependence of the electron heat capacity and the coupling factor from the first-principles calculations must be considered.

Electronic Excitation Dynamics in Liquid Water under Proton Irradiation

Molecular behaviour of liquid water under proton irradiation is of great importance to a number of technological and medical applications. The highly energetic proton generates a time-varying field that is highly localized and heterogeneous at the molecular scale, and massive electronic excitations are produced as a result of the field-matter interaction. Using first-principles quantum dynamics simulations, we reveal details of how electrons are dynamically excited through non-equilibrium energy transfer from highly energetic protons in liquid water on the atto/femto-second time scale. Water molecules along the path of the energetic proton undergo ionization at individual molecular level, and the excitation primarily derives from lone pair electrons on the oxygen atom of water molecules. A reduced charge state on the energetic proton in the condensed phase of water results in the strongly suppressed electronic response when compared to water molecules in the gas phase. These molecular-level findings provide important insights into understanding the water radiolysis process under proton irradiation.

Thermodynamic stability of driven open systems and control of phase separation by electro-autocatalysis.

Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn-Hilliard and Allen-Cahn equations. The Glansdorff-Prigogine stability criterion is extended for driving chemical work, based on variations of nonequilibrium Gibbs free energy. Linear stability is generally determined by the competition of chemical diffusion and driven autocatalysis. Novel features arise for electrochemical systems, related to controlled total current (galvanostatic operation), concentration-dependent exchange current (Butler-Volmer kinetics), and negative differential reaction resistance (Marcus kinetics). The theory shows how spinodal decomposition can be controlled by solo-autocatalytic charge transfer, with only a single faradaic reaction. Experimental evidence is presented for intercalation and electrodeposition in rechargeable batteries, and further applications are discussed in solid state ionics, electrovariable optics, electrochemical precipitation, and biological pattern formation.

Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics

We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations with mass action kinetics. Our most general framework considers open networks driven by time-dependent chemostats. The energy and entropy balances are established and a nonequilibrium Gibbs free energy is introduced. The difference between this latter and its equilibrium form represents the minimal work done by the chemostats to bring the network to its nonequilibrium state. It is minimized in nondriven detailed-balanced networks (i.e., networks that relax to equilibrium states) and has an interesting information-theoretic interpretation. We further show that the entropy production of complex-balanced networks (i.e., networks that relax to special kinds of nonequilibrium steady states) splits into two non-negative contributions: one characterizing the dissipation of the nonequilibrium steady state and the other the transients due to relaxation and driving. Our theory lays the path to study time-dependent energy and information transduction in biochemical networks.Received 23 February 2016DOI:https://doi.org/10.1103/PhysRevX.6.041064Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChemical kinetics, dynamics & catalysisNonequilibrium & irreversible thermodynamicsNonequilibrium statistical mechanicsStatistical PhysicsNonlinear DynamicsNetworksInterdisciplinary Physics

Nonlinear transport in an out-of-equilibrium single-site Bose-Hubbard model: Scaling, rectification, and time dynamics

Recent experiments in hybrid-quantum systems facilitate the potential realization of one of the most fundamental interacting Hamiltonian-reservoir systems, namely the single-site Bose-Hubbard model coupled to two reservoirs at different temperatures. Using Redfield equations in a Born-Markov approximation, we compute nonequilibrium average particle number, energy, and currents beyond linear response regime, both time dynamics and steady state, and investigate its dependence on various tunable parameters analytically. We find interesting scaling laws in high-temperature regimes that are independent of choice of bath spectral functions. We also demonstrate that the system shows very interesting particle and energy current rectification properties which can be controlled via the relative strength of interaction and temperatures, as well as via the degree of asymmetry in system-bath coupling. Specifically, we find inversion of direction of energy rectification as a function of the relative strength of the interaction strength and the temperatures. We also show that, in the limit of low-temperature and high interaction strength, our results are consistent with the nonequilibrium spin-Boson model. Our results are experimentally relevant not only to hybrid quantum systems but also in other areas such as molecular junctions.

Statistical dynamics of direct three-body recombination of heavy ions in the presence of argon and xenon atoms

Recombination of singly charged heavy Cs+ and Br– ions with stabilization with neutral Ar or Xe atoms was studied by the classic trajectory method in the range of ion collision energy and third body energy from 1 to 10 eV. The elementary reaction of recombination was studied on the potential energy surface (PES), which quantitatively reproduces the experimental results of collision-induced dissociation of CsBr molecules (the reverse of recombination). An analysis of the statistically reliable number of trajectories revealed a complex multifactor dynamics of recombination, which involves various mechanisms whose realization depends both on the mass and energy ratio of colliding particles and on the PES structure and spatial configurations of collision determined by impact parameters, orientation angles, etc. The molecules that formed as a result of recombination have nonequilibrium vibrational energy distributions and rotational energy distributions comparable to equilibrium.

Classical noise and the structure of minimum uncertainty states

Which quantum states minimise the unavoidable uncertainty arising from the non-commutativity of two observables? The immediate answer to such a question is: it depends. Due to the plethora of uncertainty measures there are many answers. Here, instead of restricting our study to a particular measure, we present plausible axioms for the set $\mathcal{F}$ of bona-fide information-theoretic uncertainty functions. Then, we discuss the existence of states minimising uncertainty with respect to all members of $\mathcal{F}$, i.e., universal minimum uncertainty states (MUS). We prove that such states do not exist within the full state space and study the effect of classical noise on the structure of minimum uncertainty states. We present an explicit example of a qubit universal MUS that arises when purity is constrained by introducing a threshold amount of noise. For higher dimensional systems we derive several no-go results limiting the existence of noisy universal MUS. However, we conjecture that universality may emerge in an approximate sense. We conclude by discussing connections with thermodynamics, and highlight the privileged role that non-equilibrium free energy $F_2$ plays close to equilibrium.

Energy and exergy analyses of medium temperature latent heat thermal storage with high porosity metal matrix

Thermal energy storage system in a concentrating solar plant (CSP) reduces the gap between energy demand and supply caused by the intermittent behaviour of solar radiation. In this paper, detailed exergy and energy analyses of shell and tube type latent heat thermal storage system (LHTES) for medium temperature solar thermal power plant (∼200°C) are performed to estimate the net useful energy during the charging and discharging period in a cycle. A commercial-grade organic phase change material (PCM) is stored inside the annular space of the shell and the heat transfer fluid (HTF) flows through the tubes. Thermal conductivity enhancer (TCE) in the form of metal matrix is embedded in PCM to augment heat transfer. A numerical model is developed to investigate the fluid flow and heat transfer characteristics using the momentum equation and the two-temperature non-equilibrium energy equation coupled with the enthalpy method to account for phase change in PCM. The effects of storage material, porosity and pore-diameter on the net useful energy that can be stored and released during a cycle, are studied. It is found that the first law efficiency of sensible heat storage system is less compared to LHTES. With the decrease in porosity, the first law and second law efficiencies of LHTES increase for both the charging and discharging period. There is no significant variation in energy and exergy efficiencies with the change in pore-diameter of the metal matrix.

Numerical analysis of latent heat thermal energy storage using encapsulated phase change material for solar thermal power plant

Thermal energy storage improves the load stability and efficiency of solar thermal power plants by reducing fluctuations and intermittency inherent to solar radiation. This paper presents a numerical study on the transient response of packed bed latent heat thermal energy storage system in removing fluctuations in the heat transfer fluid (HTF) temperature during the charging and discharging period. The packed bed consisting of spherical shaped encapsulated phase change materials (PCMs) is integrated in an organic Rankine cycle-based solar thermal power plant for electricity generation. A comprehensive numerical model is developed using flow equations for HTF and two-temperature non-equilibrium energy equation for heat transfer, coupled with enthalpy method to account for phase change in PCM. Systematic parametric studies are performed to understand the effect of mass flow rate, inlet charging system, storage system dimension and encapsulation of the shell diameter on the dynamic behaviour of the storage system. The overall effectiveness and transient temperature difference in HTF temperature in a cycle are computed for different geometrical and operational parameters to evaluate the system performance. It is found that the ability of the latent heat thermal energy storage system to store and release energy is significantly improved by increasing mass flow rate and inlet charging temperature. The transient variation in the HTF temperature can be effectively reduced by decreasing porosity.

Nonequilibrium thermodynamic formalism of nonlinear chemical reaction systems with Waage–Guldberg’s law of mass action

Macroscopic entropy production rate σ(tot) in the general nonlinear isothermal chemical reaction system with mass action kinetics is decomposed into a free energy dissipation rate and a house-keeping heat dissipation rate: σ(tot)=σ(fd)+σ(hk); σ(fd)=-dA/dt, where A is a generalized free energy function. This yields a novel nonequilibrium free energy balance equation dA/dt=-σ(tot)+σ(hk), which is on a par with celebrated entropy balance equation dS/dt=σ(tot)+η(ex) where η(ex) is the rate of entropy exchange with the environment. For kinetic systems with complex balance, σ(fd) and σ(hk) are the macroscopic limits of stochastic free energy dissipation rate and house-keeping heat dissipation rate, which are both nonnegative, in the Delbrück–Gillespie description of the stochastic chemical kinetics. A full kinetic and thermodynamic theory of chemical reaction systems that transcends mesoscopic and macroscopic levels emerges.

Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example

In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory%.~\cite{freidlin1984}.In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory%, ~\cite{bertini2014},which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to $1/\sqrt{N}$, where $N$ is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter $\lambda$, starting from a known quasi-potential for $\lambda=0$. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner%. ~\cite{dawson1987,dawson1987b}. Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators%. ~\cite{shinomoto1986}. This is one of few systems for which non-equilibrium free energies can be computed and analyzed in an effective way, at least perturbatively.

Broadband illumination of superconducting pair breaking photon detectors

Understanding the detailed behaviour of superconducting pair breaking photon detectors such as Kinetic Inductance Detectors (KIDs) requires knowledge of the nonequilibrium quasiparticle energy distributions. We have previously calculated the steady state distributions resulting from uniform absorption of monochromatic sub gap and above gap frequency radiation by thin films. In this work, we use the same methods to calculate the effect of illumination by broadband sources, such as thermal radiation from astrophysical phenomena or from the readout system. Absorption of photons at multiple above gap frequencies is shown to leave unchanged the structure of the quasiparticle energy distribution close to the superconducting gap. Hence for typical absorbed powers, we find the effects of absorption of broadband pair breaking radiation can simply be considered as the sum of the effects of absorption of many monochromatic sources. Distribution averaged quantities, like quasiparticle generation efficiency η, match exactly a weighted average over the bandwidth of the source of calculations assuming a monochromatic source. For sub gap frequencies, however, distributing the absorbed power across multiple frequencies does change the low energy quasiparticle distribution. For moderate and high absorbed powers, this results in a significantly larger η–a higher number of excess quasiparticles for a broadband source compared to a monochromatic source of equal total absorbed power. Typically in KIDs the microwave power absorbed has a very narrow bandwidth, but in devices with broad resonance characteristics (low quality factors), this increase in η may be measurable.