Showing papers on "Non-equilibrium thermodynamics published in 1990"

The Nonequilibrium Statistical Mechanics of Open and Closed Systems

Abstract: Part 1 Introduction: evolution of complex systems langevin equations some problems. Part 2 Evolution of probability: stochastic rate equations single degree of freedom delta-correlated gaussian fluctuation many degrees of freedom fluctuations with a finite correlation time (colored noise) statistical measures. Part 3 Open systems: thermodynamic properties (nonequilibrium) dye laser with a fluctuating pump parameter chemical reaction with a fluctuating rate coefficient bistable stochastic systems mechanical oscillators with fluctuating frequences kubo oscillator (semiclassical) Lorenz model (connection with chaos) odds and ends. Part 4 Closed systems (Hamiltonian systems) thermodynamic properties (nonequilibrium) projection operator techniques explicit integration method harmonic oscillator in a real fluid. Part 5 Reduced descriptions of non-Hamiltonian systems: statistical fluctuations in fluid flow decimation procedure projection method explicit integration method. Part 6 Evolution of quantum systems: reduced density matrix (dynamical bath) reduced density matrix (c-number fluctuations). Part 7 Open systems (c-number fluctuations): linear oscillator Haken-Strobi-Reineker (HSR) model spin relaxations in an external fluctuating magnetic field. Part 8 Closed quantum systems (operator fluctuations): linear quantum oscillators two-evel system in a linear bath stochastic liouville equations nonlinear coupling in bath variables conclusions.

Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition

Abstract: We solve exactly the one-dimensional diffusion-limited single-species coagulation process (A+A→A) with back reactions (A→A+A) and/or a steady input of particles (B→A). The exact solution yields not only the steady-state concentration of particles, but also the exact time-dependent concentration as well as the time-dependent probability distribution for the distance between neighboring particles, i. e., the interparticle distribution function (IPDF). The concentration for this diffusion-limited reaction process does not obey the classical “mean-field” rate equation. Rather, the kinetics is described by a finite set of ordinary differential equations only in particular cases, with no such description holding in general. The reaction kinetics is linked to the spatial distribution of particles as reflected in the IPDFs. The spatial distribution of particles is totally random, i. e., the maximum entropy distribution, only in the steady state of the strictly reversible process A+A↔A, a true equilibrium state with detailed balance. Away from this equilibrium state the particles display a static or dynamic self-organization imposed by the nonequilibrium reactions. The strictly reversible process also exhibits a sharp transition in its relaxation dynamics when switching between equilibria of different values of the system parameters. When the system parameters are suddenly changed so that the new equilibrium concentration is greater than exactly twice the old equilibrium concentration, the exponential relaxation time depends on the initial concentration.

Finite-time thermodynamics and thermoeconomics

Abstract: Thermodynamics and optimization optima and bounds for irreversible thermodynamic processes finite-time thermodynamics nonequilibrium thermodynamics for solar energy applications application of finite-time thermodynamics to solar power conversion non-Lorentz cycles in nonequilibrium thermodynamics thermodynamics and economics equipartition of entropy production - a design and optimization criterion in chemical engineering exergy optimization in a class of drying systems with granular solids compared energetic and economic optimization of industrial systems analysis of cumulative exergy consumption and cumulative exergy losses.

A nonlinear quantum transport theory

Abstract: A nonlinear quantum transport theory for many-body systems arbitrarily far away from equilibrium, based on the nonequilibrium statistical operator method, is discussed. An iterative process is described that allows for the calculation of the collision operator in a series of instantaneous in time partial contributions of ever increasing power in the interaction strengths. These partial collision operators are shown to be composed of three contributions to the dissipative processes: one is a direct result of the collisions, another is accounted for in the internal state variables, and the third arises from memory effects. In the lowest order, the so-called linear theory of relaxation, the equations become Markovian.

Rotational–translational energy transfer in rarefied nonequilibrium flows

Abstract: A new model for simulating the transfer of energy between the translational and rotational modes is derived for a homogeneous gas of diatomic molecules. The model has been developed specifically for use in discrete particle simulation methods where molecular motion and intermolecular collisions are treated at the molecular level. In such methods it is normal to assume a constant rotational collision number for the entire flow field. The new model differs in that a temperature dependence is introduced, which has been predicted by theory and observed in experiment. The new model is applied to the relaxation of rotational temperature, and is found to produce significant differences in comparison with the model normally employed at both high and low temperatures. Calculations have also been performed for a Mach 7 normal shock wave. Large differences in the solutions are again observed, with the new model offering an improved correspondence to the available experimental data.

Statistical Thermodynamics and Kinetic Theory

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Slow evaporation and condensation

Abstract: An analysis is given of the paradox of an inverted temperature profile in the vapor phase between an evaporating and a condensing liquid surface. This analysis is based on a description in the context of nonequilibrium thermodynamics for a two-phase system. Conditions for the occurrence of both the inverted temperature profile and for supersaturation near the evaporating surface are then given in terms of the temperature and pressure jump coefficients appearing in this description. Comparing with the description using kinetic theory in the vapor phase we obtain explicit expressions for these jump coefficients. Using these expressions the conditions found using nonequilibrium thermodynamics reduce to those given in the context of kinetic theory.

On the Nonequilibrium Statistical Operator Method

Abstract: We describe the large applicability of the Nonequilibrium Statistical Operator Method (NSOM) for the study of dissipative dynamic systems far from equilibrium. It is shown that the NSOM can be encompassed by a unifying variational principle, which produces a large family of NSO that contains existing examples as particular cases. Further, we review the application of the NSOM for the construction of a nonlinear quantum theory of large scope, and for the generation of a response function theory, for far-from-equilibrium Hamiltonian systems. An accompanying non-equilibrium thermodynamic Green's function theory is briefly described. Also it is shown that the NSOM provides mechano-statistical foundations for phenomenological irreversible thermodynamics, and for the important question of stability of far-from-equilibrium steady states and the emergence of self-organized dissipative structures in condensed matter.

Analytical traveling wave solutions for transport with nonlinear and nonequilibrium adsorption

Abstract: Transport was modeled for a soil with dual porosity, or with chemical nonequilibrium, assuming first-order kinetics. The equilibrium sorption equation in the immobile region is nonlinear. Two equilibrium equations for sorption were considered, that is, the Langmuir and the Van Bemmelen-Freundlich equations. The sorption equation in the mobile region is assumed to be linear. Analytical solutions were obtained that describe the traveling wave displacement found for initial resident concentrations that are smaller than the feed concentration and for infinite displacement times, neglecting the coupled effects of dispersion and nonequilibrium conditions. These waves travel with a fixed shape and a fixed velocity through the homogeneous flow domain. Besides expressions for the front shape, expressions for the front thickness and the front position were also presented. Differences with respect to the linear sorption case are the smaller front thickness and the non-Fickian type of displacement. The non-Fickian behavior is intrinsic to the traveling wave assumption as the front does not spread with the square root of time. The analytical solutions obtained for the equilibrium and for the nonequilibrium situations are mathematically equivalent. Only the effective diffusion/dispersion coefficient needs to be adapted to account for nonequilibrium effects, as for linear dual-porosity models. Apart from early time behavior, the traveling wave solutions agree well with numerical approximations. The front steepness depends sensitively on the degree of nonlinearity. The sensitivity on the dispersion coefficient and first-order rate coefficient may be large but depends on which mechanism controls front spreading.

Model for ion transport in bipolar membranes.

Abstract: A simple theory for multi-ionic transport, nonequilibrium water dissociation, and space-charge effects in bipolar membranes is developed on the basis of some of the concepts used in the solid-state n-p junction. Ion transport is described in terms of the Nernst-Planck flux equation and nonequilibrium water dissociation is accounted for by the Onsager theory of the second Wien effect. The model is expected to be of interest for biological and synthetic membranes, and can explain a number of observed effects.

Light-scattering measurements of entropy and viscous fluctuations in a liquid far from thermal equilibrium

Abstract: We have performed small-angle Rayleigh-scattering measurements in toluene subject to a large stationary temperature gradient \ensuremath{ abla}T. The experiments demonstrate the presence of long-range entropy and viscous fluctuations enhancing and modifying the Rayleigh spectrum. The experiments confirm that the viscous-heat-mode contributions vary with (\ensuremath{ abla}T${)}^{2}$/${q}^{4}$, where q is the wave number of the fluctuations. The observed amplitudes of both the entropy and viscous fluctuations are in excellent agreement with the theoretical predictions for the fluctuations in nonequilibrium fluids.

Internal Variables in Non-Equilibrium Thermodynamics

Abstract: The concept of internal variables is axiomatically introduced into nonequilibrium thermodynamics for avoiding small state spaces showing after effects. The connection between internal variables, projectors onto equilibrium subspace, and accompanying processes is demonstrated for discrete systems. Relaxation variables, chemical reactions, and Kestin-Ponter’s model of plasticity are discussed.

Nonequilibrium modeling of low-pressure argon plasma jets; Part I: Laminar flow

Abstract: This paper presents a modeling attempt related to low-pressure plasma spraying processes which find increasing applications for materials processing. After a review of the various models for ionization and recombination processes, a two-temperature model for argon plasmas in chemical (ionization) nonequilibrium is established using finite rate chemistry. Results of sample calculations manifest departures from kinetic as well as chemical equilibrium, demonstrating that the conventional models based on the LTE (local thermodynamic equilibrium) assumption cannot provide proper prediction for low-pressure plasma jets.

Nonequilibrium absolute temperature, thermal waves and phonon hydrodynamics

Abstract: It is shown that the nonequilibrium absolute temperature of extended irreversible thermodynamics may lead to possibly observable consequences in the propagation of thermal waves in nonequilibrium solids and in Poiseuille phonon flow.

Time-reversible equilibrium and nonequilibrium isothermal-isobaric simulations with centered-difference Stoermer algorithms.

Abstract: We describe simple, stable, and economical numerical methods for implementing temperature and pressure controls in equilibrium and nonequilibrium Nose-Hoover dynamics. These methods substantially increase the efficiency of large-scale simulations.

The generalised second law and extended thermodynamics

Abstract: The generalised second law is examined in the light of the extended thermodynamics theory of irreversible processes. Its validity during the transient regime of viscous transport can be guaranteed only if the dominant energy condition holds.

Nonequilibrium entropy and entropy distributions

Abstract: Glasses have nonzero zero-temperature entropies. Because they are out of equilibrium, the ``thermodynamic'' entropy, determined by heat flow, is not equal to the ``statistical'' entropy, which measures volumes in phase space. We discuss the relationship between the two kinds of entropy in nonequilibrium systems and show that the thermodynamic entropies measured by cooling and heating form lower and upper bounds to the statistical entropy. In a computer simulation of a glass, the distribution of thermodynamic entropies measured by repeated fast coolings provides information about the dynamics of the glass. Entropy distributions are presented for a spin glass and a simple two-level system, and the distributions are used as a tool to compare the dynamics of the two models.

On the relaxation time hierarchy in dissipative systems: An example from semiconductor physics

Abstract: We consider the question of the contraction of the macroscopic nonequilibrium thermodynamic description of dissipative dynamic systems. As argumented by Bogoliubov, this process is associated to the determination of a spectrum (hierarchy) of relaxation times. We have used studies of the irreversible evolution of highly photoexcited plasmas in polar semiconductors to provide a way to exemplify and test the existence of such a spectrum of characteristic times. It is shown that, in fact, several kinetic stages can be characterized, each accompanied by a successive contraction in the description of the macroscopic state of the system. A proper choice, depending on the experimental conditions, leads to good agreement with observational data.

Equilibrium and nonequilibrium solvation and solute electronic structure

Abstract: When a molecular solute is immersed in a polar and polarizable solvent, the electronic wave function of the solute system is altered compared to its vacuum value; the solute electronic structure is thus solvent-dependent. Further, the wave function will be altered depending upon whether the polarization of the solvent is or is not in equilibrium with the solute charge distribution. More precisely, while the solvent electronic polarization should be in equilibrium with the solute electronic wave function, the much more sluggish solvent orientational polarization need not be. We call this last situation “non-equilibrium solvation.” We outline a nonlinear Schrodinger equation approach to these issues. The nonlinearity arises from the self-consistent aspect that the solute electronic Hamiltonian depends on the solvent electronic polarization which is induced by the solute charge distribution. We illustrate the predictions of the theory for electron transfer reactions, ionic dissociations, and solvation dynamics in polar solvents. Special features of interest include activation barriers that differ markedly from standard predictions, and novel solvent dynamical features.

Kinetics of chemical reactions in condensed media in the framework of the two-dimensional stochastic model

Abstract: A chemical reaction proceeding in a continuum medium is modeled as a pair of stochastic equations with a δ-correlated random force. A numerical method for calculating the rate constant is elaborated in a quasi-one-dimensional approximation. Exact rate constants are found over a wide range of characteristic system parameters. The existence of a significant region with a nonequilibrium kinetic behavior, as predicted previously by Berezhkovskii and Zitserman, is confirmed. Moreover, the nonequilibrium rate constant is shown to describe not only the extreme of quasi-one-dimensional dynamics but also the case when the complete two-dimensional equation of motion operates

On the relationship between radiative entropy and temperature distributions

Abstract: The Earth can be viewed as a complex nonequilibrium system that exchanges primarily radiative energy and entropy with its surroundings. The energy balance equation provides an important constraint on the distribution of outgoing radiation since the net global energy exchange will be close to zero over some appropriately long time interval. The entropy of the radiation does not obey such a conservation law, instead the outgoing entropy irradiance is much greater than the incoming amount. Most of this increase in the entropy flux is due to the conversion of short wavelength photons from a small solid angle into longer wavelength photons that are emitted nearly isotropically. If the entropy irradiance is calculated with sufficient precision, it is possible to relate it to the distribution of radiative temperature over position, direction, wavenumber and polarization spaces. The radiative entropy decreases as the variance of the radiative temperature distribution increases over any of the four spaces...

Thermodynamic and stochastic theory for nonequilibrium systems with more than one reactive intermediate: Nonautocatalytic or equilibrating systems

Abstract: We consider chemical reactions occurring in a compartment separated by semipermeable membranes from reservoirs of reactant and product, both held at constant pressure. In earlier work, we have developed a nonequilibrium thermodynamic theory applicable to systems with a single reactive intermediate, and we have established a link between the thermodynamic and stochastic analyses of such systems. Here we show that our results generalize directly to cases with two or more reactive intermediates, if the reaction mechanism is nonautocatalytic, or if the system is evolving toward an equilibrium steady state in the reaction compartment without first exhausting the reactant or product reservoir. Starting with nonautocatalytic mechanisms, we identify effective driving forces for each intermediate; we then obtain the driving force for an arbitrary system by mapping to an instantaneously equivalent nonautocatalytic system. The driving force can be cast thermodynamically in terms of the difference between the actual ...