Showing papers on "Non-equilibrium thermodynamics published in 1996"

Hamiltonian approach to the transport properties of superconducting quantum point contacts

Abstract: A microscopic theory of the transport properties of quantum point contacts giving a unified description of the normal conductor-superconductor (N-S) and superconductor-superconductor (S-S) cases is presented. It is based on a model Hamiltonian describing charge transfer processes in the contact region and makes use of nonequilibrium Green function techniques for the calculation of the relevant quantities. It is explicitly shown that when calculations are performed up to infinite order in the coupling between the electrodes, the theory contains all known results predicted by the more usual scattering approach for N-S and S-S contacts. For the latter we introduce a specific formulation for dealing with the nonstationary transport properties. An efficient algorithm is developed for obtaining the dc and ac current components, which allows a detailed analysis of the different current-voltage characteristics for all range of parameters. We finally address the less understood small bias limit, for which some analytical results can be obtained within the present formalism. It is shown that four different physical regimes can be reached in this limit depending on the values of the inelastic scattering rate and the contact transmission. The behavior of the system in these regimes is discussed together with the conditions for their experimental observability. \textcopyright{} 1996 The American Physical Society.

Simulating equilibrium within aerosols and nonequilibrium between gases and aerosols

Abstract: A numerical method to solve chemical equilibrium equations and a method of coupling the equilibrium calculations to nonequilibrium growth and evaporation are discussed. The equilibrium program solves any number of equations for gas, aqueous, ionic, and solid equilibrium concentrations over large spatial grids and particle size grids. It also simultaneously computes electrolyte mean mixed activity coefficients and aerosol liquid water content. Mean mixed activity coefficient calculations require mean binary activity coefficient information. Temperature-dependent mean binary activity coefficient polynomials were constructed using mean binary activity coefficient data at 298 K, apparent molal enthalpy data, and apparent molal heat capacity data. The equilibrium solver is mole and charge conserving, requires iteration, but always converges. Solutions to the equilibrium equations are used for two purposes. The first is to estimate surface vapor pressures over particles containing a solution and/or a solid phase. Such vapor pressures are then applied in gas-aerosol transfer equations. The second is to estimate intraparticle composition and size immediately after gas-aerosol transfer.

The quantum heat engine and heat pump: An irreversible thermodynamic analysis of the three-level amplifier

Abstract: The manifestations of the three laws of thermodynamics are explored in a model of an irreversible quantum heat engine. The engine is composed of a three‐level system simultaneously coupled to hot and cold heat baths, and driven by an oscillating external field. General quantum heat baths are considered, which are weakly coupled to the three‐level system. The work reservoir is modeled by a classical electro‐magnetic field of arbitrary intensity, which is driving the three‐level system. The first law of thermodynamics is related to the rate of change of energy obtained from the quantum master equation in the Heisenberg picture. The fluxes of the thermodynamic heat and work are then directly related to the expectation values of quantum observables. An analysis of the standard quantum master equation for the amplifier, first introduced by Lamb, is shown to be thermodynamically inconsistent when strong driving fields are used. A generalized master equation is rigorously derived, starting from the underlying quantum dynamics, which includes relaxation terms that explicitly depend upon the field. For weak fields the generalized master equation reduces to the standard equation. In very intense fields the amplifier splits into two heat engines. One engine accelerates as the field intensifies, while the other slows down and eventually switches direction to become a heat pump. The relative weight of the slower engine increases with the field intensity, leading to a maximum in power as a function of the field intensity. The amplifier is shown to go through four ‘‘phases’’ as the driving field is intensified, throughout all of which the second law of thermodynamics is generally satisfied. One phase corresponds to a ‘‘refrigeration window’’ which allows for the extraction of heat out of a cold bath of temperatures down to the absolute zero. This window disappears at absolute zero, which is conjectured to be a dynamical manifestation of the third law of thermodynamics.

Non-equilibrium thermodynamics and anomalous diffusion

Abstract: The convenience of a new thermodynamic frame for the description of anomalous diffusion is explored. Our research, which makes use of a recent new definition for entropy arising from multifractal analysis, shows that both dynamical and thermodynamical effects may contribute to non-classical diffusion.

Entropy-enthalpy compensation: Perturbation and relaxation in thermodynamic systems

Abstract: The response of an equilibrium molecular system to perturbations depends on its environmental constraints. For example, the response of an equilibrium P, V, T system to a small temperature perturbation (specific heat) depends on whether the environmental constraint on the system is constant pressure or constant volume. In general, there are two classes of thermodynamic quantities of a system; one is completely determined by its equilibrium distribution, and the other also depends on how the distribution responds to macroscopic changes. The former class is independent of the environment of the thermodynamic system, while the latter class is a function of environmental constraints. In response to a small perturbation, the free energy change of an equilibrium system belongs to the first class but the entropy and enthalpy changes belong to the second. Therefore the thermodynamics of perturbation exhibit compensation between entropy and enthalpy of systems with different environments. The thermodynamic analysis presented here provides a framework for the interpretation of experimental observations of this phenomenon, and is illustrated by a real experimental example.

Hydrodynamics and fluctuations outside of local equilibrium: Driven diffusive systems

Abstract: We derive hydrodynamic equations for systems not in local thermodynamic equilibrium, that is, where the local stationary measures are “non-Gibbsian” and do not satisfy detailed balance with respect to the microscopic dynamics. As a main example we consider thedriven diffusive systems (DDS), such as electrical conductors in an applied field with diffusion of charge carriers. In such systems, the hydrodynamic description is provided by a nonlinear drift-diffusion equation, which we derive by a microscopic method ofnonequilibrium distributions. The formal derivation yields a Green-Kubo formula for the bulk diffusion matrix and microscopic prescriptions for the drift velocity and “nonequilibrium entropy” as functions of charge density. Properties of the hydrodynamic equations are established, including an “H-theorem” on increase of the thermodynamic potential, or “entropy”, describing approach to the homogeneous steady state. The results are shown to be consistent with the derivation of the linearized hydrodynamics for DDS by the Kadanoff-Martin correlation-function method and with rigorous results for particular models. We discuss also the internal noise in such systems, which we show to be governed by a generalizedfluctuation-dissipation relation (FDR), whose validity is not restricted to thermal equilibrium or to time-reversible systems. In the case of DDS, the FDR yields a version of a relation proposed some time ago by Price between the covariance matrix of electrical current noise and the bulk diffusion matrix of charge density. Our derivation of the hydrodynamic laws is in a form—the so-called “Onsager force-flux form” which allows us to exploit the FDR to construct the Langevin description of the fluctuations. In particular, we show that the probability of large fluctuations in the hydrodynamic histories is governed by a version of the Onsager “principle of least dissipation,” which estimates the probability of fluctuations in terms of the Ohmic dissipation required to produce them and provides a variational characterization of the most probable behavior as that associated to least (excess) dissipation. Finally, we consider the relation of longrange spatial correlations in the steady state of the DDS and the validity of ordinary hydrodynamic laws. We also discuss briefly the application of the general methods of this paper to other cases, such as reaction-diffusion systems or magnetohydrodynamics of plasmas.

Multiple time step nonequilibrium molecular dynamics simulation of the rheological properties of liquid n-decane

Abstract: Nonequilibrium and equilibrium molecular dynamics simulations are reported for a united‐atom model of n‐decane at a state point in the liquid phase. The viscosity calculated by our nonequilibrium molecular dynamics simulations is in good agreement with that obtained from our equilibrium molecular dynamics simulations via the Green–Kubo relation and with that obtained by Mundy et al. [J. Chem. Phys. 102, 3776 (1995)] using the same potential model at the same state conditions. Additionally, the viscosity calculated by nonequilibrium molecular dynamics is in very good agreement with experimental results for n‐decane. The algorithm used for the equilibrium molecular dynamics simulations is an application to alkanes of the multitime step Nose dynamics algorithm developed by Tuckerman and Berne. For the nonequilibrium molecular dynamics simulations, an extension of the multitime step method is derived for the nonequilibrium equations of motion describing planar Couette flow with Nose thermostat. The contributions of the intramolecular interactions to the stress tensor and its relaxation have been analyzed; the bond stretching motions play a dominant role in the short‐time behavior of the atomic stress–stress correlation.

Thermodynamic constitutive equations for materials with memory on a material time scale

Abstract: We present a complete, self‐consistent set of thermodynamic constitutive equations for viscoelastic solid and fluid materials which can be applied during arbitrary, three‐dimensional deformations and thermal processes. Deformational and thermal histories are measured using a fading memory norm in a material time which provides a quantitative indication of the constitutive models’ ability to represent the dynamic response. The free energy constitutive equation is a Frechet expansion about the deformation and temperature histories of arbitrarily large but sufficiently slow departures from equilibrium in material time. The kinetic relationship between the laboratory and material time scales does not depend on equilibrium considerations. This approach greatly extends the applicability of low‐order memory expansions to nonequilibrium polymer states. Constitutive equations for stress, internal energy, entropy, enthalpy, and heat capacity are derived. All the required material properties can be evaluated unambig...

Molecular physics and hypersonic flows

Abstract: Preface. Relevance of Aerothermochemistry for Hypersonic Technology G.S.R. Sarma. Vibrational Energy Exchanges Between Diatomic Molecules of Relevance to Atmospheric Chemistry M. Cacciatore. Reactive Vibrational Deexcitation: The N + N2 and O + O2 Reactions A. Lagana, et al. Reactive Cross Sections Involving Atomic Nitrogen and Ground and Vibrationally Excited Molecular Oxygen and Nitric Oxide M. Gilibert, et al. Vibrational Relaxation, Nonequilibrium Chemical Reactions, and Kinetics of No Formation Behind Strong Shock Waves I.V. Adamovich, et al. Non-Equilibrium Chemistry Models for Shock-Related Gases P.L. Varghese, D.A. Gonzales. Electron - Air Molecule Collisions in Hypersonic Flows W.M. Huo, H.T. Thummel. Heterogeneous Catalysis: Theory, Models and Applications M. Barbato, C. Bruno. Recombination of Atomic Species on Surfaces C.D. Scott. Recombination of Oxygen and Nitrogen on Silicabased Thermal Protection Surfaces: Mechanism and Implications E. Jumper. Phenomenological Theory for Heterogeneous Recombination of Partially Dissociated Air on High-Temperature Surfaces V.L. Kovalev, et al. Chemical Reactions and Thermal Non Equilibrium on Silica Surfaces A. Daiss, et al. Sputtered Excited Atoms: Boundary Conditions G. Falcone, F. Piperno. Semi-Classical Treatment of the Dynamics of Molecule Surface Interaction G.D. Billing. Thermodynamic Equilibrium of Multi-Temperature Gas Mixtures D. Giordano. Thermodynamic Approach of a Flow with Thermal Non Equilibrium (translation - electron - vibration) M. Dudeck. Thermodynamic Properties of High Temperature Air Components M. Capitelli, et al. Old and New Problems Related to High Temperature Transport Properties M. Capitelli, et al. Potential Energies and CollisionIntegrals for the Interactions of Air Components. I. Ab Initio Calculation of Potential Energies and Neutral Interactions H. Partridge, et al. Potential Energies and Collision Integrals for the Interactions of Air Components. II. Scattering Calculations and Interactions Involving Ions J.R. Stallcop, et al. Measurements and Nature of Intermolecular Forces: Their Role in Gaseous Properties F. Pirani, et al. Transport Properties of Non Equilibrium Gas Flows R. Brun. The Influence of Non-Boltzmann Vibrational Distribution on Thermal Conductivity and Viscosity E.V. Kustova, E. Nagnibeda. The Role of Inelastic Rotational and Vibrational Collisions on Transport Coefficients C. Nyeland. Analysis of Approximation Introduced Using Simplified Sum Rules in Calculations of High Energy Air Transport Coefficients F. De Filippis. The Analytical Approaches to the Non Equilibrium Vibrational Kinetics B.F. Gordiets. Non-Equilibrium Vibrational, Electronic and Dissociation Kinetics in Molecular Plasmas and their Coupling with the Electron Energy Distribution Function C. Gorse, M. Capitelli. Self Consistent Modeling of Free Electron Kinetics S. Longo. Electron-Impact Ionization of Air Molecules and Its Application to the Abatement of Volatile Organic Compounds B.M. Penetrante, et al. Fluid Dynamic Modeling of Plasma Reactors P. Vitello. Multicomponent Reactive Gas Dynamic Model for Low-Pressure Discharges in Flowing Oxygen M.J. Pinheiro, et al. Mathematical Models for Plasma and Gas Flows in Induction Plasmatrons S.A. Vasil'evskii, et al. N2(A3SIGMAu+, v=0) Decay in N2-O2 Pulsed Post-Discharge S. De Benedictis, G. Dilecce. Investigations of Species in Flowing Nitrogen After

Energetic and thermodynamic aspects of hysteresis.

Abstract: A thermodynamic description of hysteresis phenomena is proposed, where the system evolution is described as a sequence of Barkhausen jumps, and the Preisach model is used to characterize the jump sequence. Expressions for Gibbs energy, entropy, and entropy production are derived. The equilibrium states of the minimum Gibbs energy are defined and the equations for the thermal relaxation of a generic initial state are derived.

Nonequilibrium Structures in Condensed Systems

Abstract: When the temperature of a substance in thermal equilibrium is lowered, it often becomes more ordered. When externally excited, such systems can exhibit new structures that are not in equilibrium. Mikhailov and Ertl describe in their Perspective such structures that have recently been observed in films of ordered molecules (called Langmuir-Blodgett films) by a group at the Electrotechnical Laboratory in Tsukuba, Japan. The results show important connections with similar behavior in reacting chemical systems.

Photon emission from a parton gas at chemical nonequilibrium

Abstract: We compute the hard photon production rate of a chemically nonequilibrated quark-gluon plasma We assume that the plasma is already thermally equilibrated, ie, describable by a temperature, but with a phase-space distribution that deviates from the Fermi-Bose distribution by a time dependent factor (fugacity) The photon spectrum is obtained by integrating the photon rate over the space-time evolution of the quark-gluon plasma Some consequences for ultrarelativistic heavy ion collisions are discussed {copyright} {ital 1996 The American Physical Society}

Master equation based formulation of nonequilibrium statistical mechanics

Abstract: For a nonequilibrium system characterized by its state space, by a dynamics defined by a transfer matrix and by a reference equilibrium dynamics given by a detailed‐balance transfer matrix, we define various nonequilibrium concepts: relative entropy, dissipation during the relaxation to the stationary state, path entropy, cost for maintaining the system in a nonequilibrium state, fluctuation‐dissipation theory, and finally a tree integral formula for the stationary state.

Thermodynamic theory of transport processes in semiconductors

Abstract: Important energetic processes in semiconductors are analyzed from the point of view of equilibrium and irreversible thermodynamics. After carefully defining the necessary local variables and current densities, the continuity equations for particles, energy, and entropy are derived, leading to an expression for entropy generation. From this, the conjugate fluxes and affinities are directly obtained and the transport equations written using these quantities. The Onsager relations are applied to the kinetic coefficients defined in the transport equations and, after further manipulations, the experimental transport parameters may be found in terms of these quantities. Particular care is taken to ensure that the thermal conductivity is correctly defined. A new thermoinjection coefficient is found which describes the transport of heat by electrons and holes under conditions of zero total electric current and zero temperature gradient. The heat dissipation is derived in a number of different ways and compared with formula proposed by other authors. Expressions for the generation of useful external work using both photovoltaic and thermoelectric conversion are also found and related to the difference between free energy input and entropy generation. The equations presented form a suitable basis for the improved design of energy conversion devices. In two Appendixes, the thermodynamic methods used in the main text are compared with those based on the Boltzmann transport equations for electrons, holes, and phonons. Theoretical expressions are derived in these Appendixes for the kinetic coefficients. Issues relating to the definition of internal energy and chemical potential are analyzed in a third Appendix.

Equilibrium Thermodynamics of Lipid Monolayer Domains

Abstract: Coexisting thermodynamic phases of lipid molecules at the air−water interface exhibit domains with a variety of sizes and shapes. Both the sizes and shapes of these domains are affected by a competition between a line tension and long-range dipole−dipole repulsion. In the case of coexisting liquid phases, line tension favors large, circular domains, whereas the dipolar repulsions favor small and/or highly elongated domains. The present work discusses the thermodynamics of the equilibrium size and shape of these domains. It is shown that whereas there is only one stable equilibrium domain size, there is an infinite number of sizes that represent metastable equilibrium at different monolayer pressures. Circular domains that are far enough apart as to not interact with one another electrostatically have the same radii under this condition of metastable equilibrium. It is shown that, in principle, the metastable equilibrium radius reached in a monolayer can depend on the initial distribution of nonequilibrium...

Collisional equilibrium, particle production, and the inflationary universe.

Abstract: Particle production processes in the expanding universe are described within a simple kinetic model. The equilibrium conditions for a Maxwell-Boltzmann gas with variable particle number are investigated. We find that radiation and nonrelativistic matter may be in equilibrium at the same temperature provided the matter particles are created at a rate that is half the expansion rate. Using the fact that the creation of particles is dynamically equivalent to a nonvanishing bulk pressure we calculate the backreaction of this process on the cosmological dynamics. It turns out that the `adiabatic' creation of massive particles with an equilibrium distribution for the latter necessarily implies power-law inflation. Exponential inflation in this context is shown to become inconsistent with the second law of thermodynamics after a time interval of the order of the Hubble time.

Approach to thermal equilibrium in a system with adiabatic constraints

Abstract: The problem of prediction of the equilibrium state in an isolated composite system with an adiabatic internal wall is a delicate problem, whose solution is easily seen to be not entirely determined in the frame of elementary thermodynamics. We show how this indeterminacy can be removed by introducing a suitable kinetic model, in which the influence of the finite velocity of the wall on the change of momentum of the gas molecules impinging on it plays a relevant role. An interesting feature of the entropy behavior of the system is discussed.

Short-wave limit of hydrodynamics : a soluble example

Abstract: A derivation of hydrodynamics from the Boltzmann kinetic equation is the classical problem of physical kinetics. The Chapman-Enskog (CE) method [1] gives, in principle, a possibility to compute a solution as a formal series in powers of Knudsen number e (where e is a ratio between the mean free path of a particle and the scale of variations of hydrodynamic quantities, density, mean flux, and temperature). The CE solution leads to a formal expansion of stress tensor and of heat flux vector in balance equations for density, momentum, and energy. Retaining the first order term (e) in the latter expansions, we come to the NavierStokes equations, while further corrections are known as the Burnett (e 2 ) and the super-Burnett (e 3 ) corrections [1]. However, as demonstrated by Bobylev [2], even in the simplest regime (one-dimensional linear deviation from global equilibria), the Burnett and super-Burnett hydrodynamics violate the basic physics behind the Boltzmann equation. Namely, sufficiently short acoustic waves are increasing with time instead of decaying. This contradicts the H theorem, since all near-equilibrium perturbations must decay. It should also be noted that the instability of equilibria just mentioned is not a feature of the NavierStokes approximation where waves of arbitrary length are decaying, though this approximation is formally not valid in a short-wave domain. A possible root of this violation is poor convergency properties of CE series, and this, in particular, creates serious difficulties for an extension of hydrodynamics, as derived from a microscopic description, into a highly nonequilibrium domain. The latter problem remains one of the central open problems of the Boltzmann equation theory, in particular, and of the physical kinetics, in general. In this Letter we consider the CE procedure for a simple model of nonhydrodynamic description (one-dimensional linearized 10-moment Grad equations [3]). The CE series, which is due to a nonlinear procedure even here and which also suffers the Bobylev instability in low-order approximations, is summed up in a closed form. This result leads to a quantitative discussion of the CE solution in a shortwave domain in frames of the model, and to a preliminary discussion of what can be expected in more realistic models. Exact results on the CE method for other Grad moment systems will be reported elsewhere. Throughout the Letter, p and u are dimensionless deviations of pressure and of mean flux from their equilibrium values, respectively (see Ref. [4] for relations of these variables to dimensional quantities). The point of departure is the set of linearized Grad equations [4] for p, u, and s, where s is a dimensionless xx component of stress tensor,

Numerical method and composition in multi-temperature plasmas: Application to an Ar-H2 mixture

Abstract: To take into account the nonequilibrium between the temperatures (electronic, rotation, vibration, translation) in plasmas, the partition function are modified. Then they are used to determine the concentration in a Gibbs free energy minimization method adopted to a multi-temperature plasma. Their influence oil the results for different temperature hypotheses is quantified. The composition and thermodynamic properties of an Ar-H2 mixture are given and discussed for different temperature nonequilibria.

On extended thermodynamics of discrete systems

Abstract: Work-, heat- and material-exchange between a discrete system and its environment are derived by field-theoretical methods and can be represented by Pfaffians. The work-exchange includes the volume work as well as the deformation work. The state space of these discrete systems in nonequilibrium contains the heat exchange in addition to the time rates of the equilibrium variables, thus inducing the notation “extended” thermodynamics. The dissipation inequality is not exploited by constitutive ansatzes as usual in irreversible thermodynamics, but by Liu's procedure which considers all materials compatible with the chosen nonequilibrium state space. The nonequilibrium entropy does not depend on time rates and on the heat-exchange, although these variables are included into the state space. Entropy production as well as entropy-exchange are state functions. A classification of the different kinds of variables spanning the state space of a discrete system is achieved.

Simple model for Maxwell's-demon-type information engine

Abstract: We have investigated the recently proposed self-consistent theory of fluctuation-induced transport. In this framework the subsystem under study is coupled to two independent baths at different temperatures. In this nonequilibrium system one can extract energy at the expense of increased entropy. This is a simple model of Maxwell's-demon-type engine that extracts work out of a nonequilbrium bath by rectifying internal fluctuations. We point out an error in the earlier results. We have obtained an analytical expression for the fluctuation-induced transport current in a nonequilibrium state that is valid at any temperatures, and various cases of physical interest have been elucidated.

Response reactions in chemical thermodynamics

Abstract: The fundamental differential equations of chemical thermodynamics within the De Donder (stoichiometric) approach are reformulated in terms of a special class of chemical reactions, which we call response reactions, RERs. The RERs have the remarkable property of being independent of the actual choice of the stoichiometrically independent reactions, by means of which the chemical processes in the system considered are usually described. The concept of RERs is shown to be applicable in both equilibrium and non-equilibrium chemical thermodynamics. This approach enables one to overcome some difficulties and ambiguities of the standard thermodynamic description of complex chemical systems. In particular, the concept of thermodynamic coupling of chemical reactions may be given a new qualitative and quantitative meaning.