Showing papers on "Non-equilibrium thermodynamics published in 1998"

Modern Thermodynamics: From Heat Engines to Dissipative Structures

Abstract: I Historical Roots: From Heat Engines to Cosmology 1 Basic Concepts and the Law of Gases 2 The First Law of Thermodynamics 3 The Second Law of Thermodynamics and the Arrow of Time 4 Entropy in the Realm of Chemical Reactions II Equilibrium Thermodynamics 5 Extremum Principles and General Thermodynamics Relations 6 Basic Thermodynamics of Gases, Liquids and Solids 7 Thermodynamics of Phase Change 8 Thermodynamics of Solutions 9 Thermodynamics of Chemical Transformations 10 Fields and Internal Degrees of Freedom 11 Thermodynamics of Radiation III Fluctuations and Stability 12 The Gibbs Stability Theory 13 Critical Phenomena and Configurational Heat Capacity 14 Entropy Productions, Fluctuations and Small Systems IV Linear Nonequilibrium Thermodynamics 15 Nonequilibrium Thermodynamics: The Foundations 16 Nonequilibrium Thermodynamics: The Linear Regime 17 Nonequilibrium Stationary State and Their Stability: Linear Regime V Order Through Fluctuations 18 Nonlinear Thermodynamics 19 Dissipative Structures 20 Elements of Statistical Thermodynamics 21 Self-Organization and Dissipative Structures in Nature

Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems

Abstract: An equality has recently been shown relating the free energy difference between two equilibrium ensembles of a system and an ensemble average of the work required to switch between these two configurations. In the present paper it is shown that this result can be derived under the assumption that the system's dynamics is Markovian and microscopically reversible.

Steady State Thermodynamics

Abstract: A phenomenological framework corresponding to equilibrium thermodynamics is con­ structed for steady states. All the key concepts including entropy are operationally defined. If a system is strictly linear, the resultant Gibbs relation justifies the postulated form in the extended irreversible thermodynamics. The resultant Maxwell's relations and stability criteria give various le Chatelier-Braun type qualitative predictions. A phenomenological fluctuation theory around steady states is also formulated.

Solute trapping and solute drag in a phase-field model of rapid solidification

Abstract: During rapid solidification, solute may be incorporated into the solid phase at a concentration significantly different from that predicted by equilibrium thermodynamics. This process, known as solute trapping, leads to a progressive reduction in the concentration change across the interface as the solidification rate increases. Theoretical treatments of rapid solidification using traditional sharp-interface descriptions require the introduction of separately derived nonequilibrium models for the behavior of the interfacial temperature and solute concentrations. In contrast, phase-field models employ a diffuse-interface description and eliminate the need to specify interfacial conditions separately. While at low solidification rates equilibrium behavior is recovered, at high solidification rates nonequilibrium effects naturally emerge from these models. In particular, in a previous study we proposed a phase-field model of a binary alloy [A. A. Wheeler et al., Phys. Rev. E 47, 1893 (1993)] in which we demonstrated solute trapping. Here we show that solute trapping is also possible in a simpler diffuse interface model. We show that solute trapping occurs when the solute diffusion length DI/V is comparable to the diffuse interface thickness. Here V is the interface velocity and DI characterizes the solute diffusivity in the interfacial region. We characterize the dependence of the critical speed for solute trapping on the equilibrium partition coefficient kE that shows good agreement with experiments by Aziz and co-workers [see M. J. Aziz, Metall. Mater. Trans. A 27, 671 (1996)]. We also show that in the phase-field model, there is a dissipation of energy in the interface region resulting in a solute drag, which we quantify by determining the relationship between the interface temperature and velocity.

On the anomalous thermal conductivity of one-dimensional lattices

Abstract: The divergence of the thermal conductivity in the thermodynamic limit is thoroughly investigated. The divergence law is consistently determined with two different numerical approaches based on equilibrium and nonequilibrium simulations. A possible explanation in the framework of linear-response theory is also presented, which traces back the physical origin of this anomaly to the slow diffusion of the energy of long-wavelength Fourier modes. Finally, the results of dynamical simulations are compared with the predictions of mode-coupling theory.

Nonequilibrium Steady States of Driven Periodic Media

Abstract: We study a periodic medium driven over a random or periodic substrate. Our work is based on nonequilibrium continuum hydrodynamic equations of motion, which we derive microscopically. We argue that in the random case instabilities will always destroy the LRO of the lattice. In most, if not all, cases, the stable driven ordered state is a transverse smectic, with ordering wavevector perpendicular to the velocity. It consists of a periodic array of flowing liquid channels, with transverse displacements and density (``permeation mode'') as hydrodynamic variables. We present dynamic functional renormalization group calculations in two and three dimensions for an approximate model of the smectic. The finite temperature behavior is much less glassy than in equilibrium, owing to a disorder-driven effective ``heating'' (allowed by the absence of the fluctuation-dissipation theorem). This, in conjunction with the permeation mode, leads to a fundamentally analytic transverse response for $T>0$. Our results are compared to recent experiments and other theoretical work.

On the shock structure problem for hyperbolic system of balance laws and convex entropy

Abstract: In this paper we give a brief survey of the problem of shock structure solutions in fluid dynamics. For a generic system of balance laws compatible with an entropy principle and a convex entropy we prove that $C^1$ solutions cannot exist when the shock velocity exceeds the maximum characteristic velocity in the equilibrium state in front of the shock. This is in agreement with a conjecture of Extended Thermodynamics.

Nonequilibrium statistical mechanics near equilibrium: computing higher-order terms

Abstract: Using Sinai - Ruelle - Bowen measures to describe nonequilibrium steady states, one can in principle compute the coefficients of expansions around equilibrium We discuss how this can be done in practice, and how the results correspond to the zero noise limit when there is a stochastic perturbation The approach used is formal rather than rigorous

The thermodynamics and evolution of complexity in biological systems.

Abstract: Recent advances in nonequilibrium thermodynamics leads to the conclusion that similar processes, constrained by the second law of thermodynamics, give rise to the emergence of structure and process in a broad class of dissipative systems. The second law suggests that, in systems moved away from equilibrium, processes can emerge so that the system organizes in a way that reduces the effect of the applied gradient. If dynamic and or kinetic conditions permit, self organization processes can be expected. As biosystems grow and develop, they should increase their total dissipation, and develop more complex structures with more energy flow, increase their cycling activity, develop greater diversity and generate more hierarchical levels. As a corollary to this general statement, biosystems which do not increase their total dissipation, are organisms dedicated to death, like observed during the aging of any biosystem. Species which survive in ecosystems are those that funnel energy into their own production and reproduction and contribute to autocatalytic processes which increase the total dissipation of the ecosystem while at same time surviving within the constraints of their changing environment. In a broad class of biosystems, stress and aging have similar thermodynamic properties and suggests common underlying principles.

Transport coefficients for high temperature nonequilibrium air flows

Abstract: A new transport coefficient model based on the first approximation of the Chapman-Cowling theory is implemented into the URANUS nonequilibrium NavierStokes Code in order to predict re-entry flows more accurately. The new model is compared to the widely used, simplified model of Gupta and Yos. The simplifications used to obtain the latter model are described in detail. The transport coefficients computed with both methods differ by up to a factor of two in the case of partially ionized air under equilibrium conditions. Therefore, the new model allows a more accurate description of the thermo-chemical relaxation in the shock region of significantly ionized, high-temperature flows. The differences in surface heat fluxes between the new model and the model of Yos and Gupta are smaller than 4%.

Thermodynamics of viscoelastic fluids: the temperature equation

Abstract: From the thermodynamics with internal variables we will derive the temperature equation for viscoelastic fluids. We consider the type of storage of mechanical energy, the dissipation of mechanical energy, the compressibility of the fluid, the nonequilibrium heat capacity and thermal expansion, and deformation induced anisotropy of the heat conduction. The well-known stress differential models that fit into the thermodynamic theory will be treated as an example. Adapting a power-law scaling of the shear moduli on temperature and density, as is usual in rubber elasticity, we will derive an approximation of the temperature equation in measurable quantities. This equation will be compared with experimental results.

The approach to thermal equilibrium in quantized chaotic systems

Abstract: We consider many-body quantum systems that exhibit quantum chaos, in the sense that the observables of interest act on energy eigenstates like banded random matrices. We study the time-dependent expectation values of these observables, assuming that the system is in a definite (but arbitrary) pure quantum state. We induce a probability distribution for the expectation values by treating the zero of time as a uniformly distributed random variable. We show explicitly that if an observable has a nonequilibrium expectation value at some particular moment, then it is overwhelmingly likely to move towards equilibrium, both forwards and backwards in time. For deviations from equilibrium that are not much larger than a typical quantum or thermal fluctuation, we find that the time dependence of the move towards equilibrium is given by the Kubo correlation function, in agreement with Onsager's postulate. These results are independent of the details of the system's quantum state.

Nonequilibrium fluctuations in time-dependent diffusion processes

Abstract: A fluctuating hydrodynamics approach is presented for the calculation of the structure factor for imedependentnonequilibrium diffusive processes in binary liquid mixtures. The hydrodynamic equations are linearized around the time-dependent macroscopic state given by the usual phenomenological diffusion equation. The cases of free diffusion, thermal diffusion, and barodiffusion are considered in detail. The results are used to describe the low-angle scattered intensity distributions from the time-dependent concentration profiles during the approach to steady state. The theoretical predictions are found to be in agreement with experimental data from thermal diffusion and free diffusion experiments. It is shown that in general the presence of nonequilibrium concentration fluctuations yields a substantial increase in the static structure factor over the equilibrium value, at least for the cases of free diffusion and thermal diffusion. As in the case of nonequilibrium fluctuations at steady state, the static structure factor displays a fast k divergence at larger wave vectors k, and saturation to a constant value for k smaller than a critical wave vector kRO. It is also shown that the static structure factor from a sedimenting mixture is actually temporarily lowered below the equilibrium value for k smaller thankRO. As the steady state is approached, the structure factor loses any k dependence and it attains the equilibrium value.@S1063-651X~98!14910-3#

Finite-time thermodynamics: Conditions of minimal dissipation for thermodynamic process with given rate

Abstract: The class of thermodynamic processes with given rate and minimal entropy production is considered. The general conditions they obey are derived. It is shown how the application of those conditions to a number of particular systems produces a number of known bounds on entropy production (for heat and mass transfer processes and chemical conversion) as well as previously unknown bounds (for throttling, crystallization, and mechanical friction).

New method to calculate thermodynamic and transport properties of a multi-temperature plasma : application to n2 plasma

Abstract: Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently Andre et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N 2 and N 2 + partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species Th , electrons Te , and vibrational T v temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio θ=Te/Th was varied between 1 and 2 as well as the ratio θ v =T v /T h for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N 2 are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N + . The effects of θv and θe on thermodynamic and transport properties of N 2 are then discussed.

Dissipative Particle Dynamics with Energy Conservation: Heat Conduction

Abstract: We study, by means of numerical simulations, the model of dissipative particle dynamics with energy conservation for the simple case of thermal conduction. It is shown that the model displays correct equilibrium fluctuations and reproduces Fourier law. The connection between "mesoscopic coarse-graining" and "resolution" is clarified.

Physical nonequilibrium in soils : modeling and application

Abstract: Coupling Sorption Rate Heterogeneity and Physical Nonequilibrium in Soils, R.J. Wagenet and W. Chen Hydraulic and Physical Nonequilibrium Effects on Multiregion Flow, G.V. Wilson, J.P. Gwo, P.M. Jardine, and R.J. Luxmoore Multiprocess Nonequilibrium and Nonideal Transport of Solutes in Porous Media, M.L. Brusseau Coupling of Retention Approaches to Physical Nonequilibrium Models, L. Ma and H.M. Selim Analytical Solutions for Nonequilibrium Transport Models, F.J. Leij and N. Toride Use of Fractals to Describe Soil Structure, H.W.G. Booltink, J. Bouma, and P. Droogers Modeling the Impact of Preferential Flow on Nonpoint Source Pollution, N. Jarvis Modeling the Interaction between Leaching and Intraped Diffusion, T.M. Addiscott, A.C. Armstrong, and P.B. Leeds-Harrison Experimental Techniques for Confirming and Quantifying Physical Nonequilibrium Processes in Soils, P.M. Jardine, R. O'Brien, G.V. Wilson, and J.-P. Gwo Transport in Unsaturated Soil: Aggregates, Macropores, and Exchange, B.E. Clothier, I. Vogeler, S.R. Green, and D.R. Scotter Field Parameterization of the Mobile/Immobile Domain Model, D.B. Jaynes and R. Horton Transfer Function Approaches to Modeling Solute Transport in Soils, R.E. White, L.K. Heng, and R.B. Edis Field-Scale Solute Transport in the Vadose Zone: Experimental Observations and Interpretation, M. Flury, W.A. Jury, and E.J. Kladivko Density-Coupled Water Flow and Contaminant in Soils, R.S. Mansell, J.H. Dane, D. Shinde, and H.H. Liu Numerical Modeling of NAPL Dissolution Fingering in Porous Media, C.T. Miller, S.N. Gleyzer, and P.T. Imhoff Flow and Entrapment of Nonaqueous Phase Liquids in Heterogeneous Soil Formations, T.H. Illangasekare Strategies for Describing Preferential Flow: The Continuum Approach and Cellular-Automation Fluids, L. Di Pietro Using GIS and Geostatistics to Model Nonequilibrium Flow at a Farm Scale, A.S. Rogowski

Density matrix theory of coherent ultrafast dynamics

Abstract: The carrier dynamics in semiconductor nanostructures on ultrashort timescales exhibits a variety of phenomena which cannot be understood on a semiclassi-cal level based completely on the particle aspect of the elementary excitations. Instead, these phenomena are at least partially related to the wave aspect and therefore a quantum-mechanical theory has to be used. Recently there have been mainly two different approaches used for the theoretical analysis of the ultrafast carrier dynamics in systems far from the thermodynamic equilibrium. These are the nonequilibrium Green’s function theory [1, 2, 3, 4] as discussed in Chapter 5 of this book and the density matrix theory [5, 6, 7, 8] which will be reviewed in this chapter. Both theories are quantum kinetic theories in the sense that the basic variables are some generalizations of the classical concept of a distribution function which may then be used to calculate expectation values of any observable quantity such as the electric current or polarization. This is in contrast to other approaches such as for example, the Kubo formalism [9] which are used in situations close to equilibrium where an expression directly for the desired observable is derived.

The kinetic chemical equilibrium regime

Abstract: We investigate reactive gas mixtures in the kinetic chemical equilibrium regime. Our starting point is a generalized Boltzmann equation with a chemical source term valid for arbitrary reaction mechanisms and yielding a positive entropy production. We first study the Enskog expansion in the kinetic chemical equilibrium regime. We derive a new set of macroscopic equations in the zeroth- and first-order regimes, expressing conservation of element densities, momentum and energy. The transport fluxes arising in the Navier–Stokes equilibrium regime are the element diffusion velocities, the heat flux vector and the pressure tensor and are written in terms of transport coefficients. Upon introducing species diffusion velocities, the kinetic equilibrium regime appears to be formally equivalent to the one obtained for gas mixtures in chemical nonequilibrium and then letting the chemical reactions approach equilibrium. The actual values of the transport coefficients are, however, different. Finally, we derive the entropy conservation equation in the Navier–Stokes equilibrium regime and show that the source term is positive and that it is compatible with Onsager’s reciprocal relations.

A steady-state system in non-equilibrium thermodynamics including thermal and electrical effects

Abstract: The steady-state equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear elliptic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet Neumann boundary conditions are prescribed. The existence of generalized solutions is proven. The key of the proof is a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrize the equations. The uniqueness of weak solutions is shown under the assumption that the boundary data are not far from the thermal equilibrium. A general uniqueness result cannot he expected for physical reasons. © 1998 B. G. Teubner Stuttgart--John Wiley & Sons, Ltd.

Nonequilibrium Statistical Mechanics: Ensemble Method

Abstract: 1. Introduction. 2. Thermodynamics of Irreversible Processes. 3. Boltzmann Equation. 4. Equilibrium Solution and Local Variables. 5. Mathematical Preparation. 6. The Chapman-Enskog and Moment Methods. 7. Classical Nonequilibrium Ensemble Method. 8. Transport Processes in Fluids. 9. Quantum Nonequilibrium Ensemble Method. 10. Nonequilibrium Ensemble Method for Dense Fluids. A. Addition Theorem of Tensor Hermite Polynomials. B. Density Matrix and Evolution Equations. Index.

Time-dependent density functional theory and the kinetics of lattice gas systems in contact with a wall

Abstract: We develop an improved mean-field theory which allows us to describe the diffusive dynamics near phase transformations in condensed systems. Starting from a master equation for a stochastic lattice gas we obtain evolution equations on the single-particle level, whose stationary solutions in principle are consistent with the exact equilibrium statistics. Our method, which generalizes an approach proposed earlier, is based on a combination of a local equilibrium assumption and the lattice version of classical density functional theory. In the continuum limit, which is worked out for attractive interactions, generalized Cahn–Hilliard-type equations are recovered. Microscopic kinetic coefficients can be identified, which in general depend on the instantaneous local correlations in the nonequilibrium state. Moreover we study semi-infinite systems interacting with a planar wall and derive the appropriate boundary conditions to be imposed on the continuum equations. Applications to problems of the kinetics of phase changes influenced by a near wall are pointed out.

The Spin-Echo Experiments and the Second Law of Thermodynamics

Abstract: We introduce a simple model for so-called spin-echo experiments. We show that the model is a mincing system. On the basis of this model we study fine-grained entropy and coarse-grained entropy descriptions of these experiments. The coarse-grained description is shown to be unable to provide an explanation of the echo signals, as a result of the way in which it ignores dynamically generated correlations. This conclusion is extended to the general debate on the foundations of statistical mechanics. We emphasize the need for an appropriate mechanism to explain the gradual suppression over time of the correlations in a thermodynamic system. We argue that such a mechanism can only be provided by the interventionist approach, in which the interaction of the system with its environment is taken into account. Irreversible behavior is then seen to arise not as a result of limited measurement accuracy , but as a result of the fact that thermodynamic systems are limited systems which interact with their environment. A detailed discussion is given of recent objections to the interventionist approach in the literature.

Feasibility Study of Magnetohydrodynamics Acceleration of Unseeded and Seeded Airflows

Abstract: Nonequilibrium, reacting, ionized gas flow modeling is used to study the feasibility of magnetohydrodynamics (MHD) acceleration of airflows for the energy addition wind tunnel. The kinetic model incorporates equations of one-dimensional magnetogasdynamics, the master equation for vibrational level populations of diatomic species, equations of chemical and ionization kinetics, and the Boltzmann equation for electrons. The model is validated by comparison with the experiments in MHD accelerators. Calculations are made for two accelerator schemes, the first using an electron beam to sustain nonequilibrium ionization in unseeded air and the second using alkali-seeded air. Although at low pressures external ionization allows substantial increase of the flow total enthalpy, the obtained test section pressure is much lower than required, and the flow quality is poor. Calculations for alkali-seeded flows predict test section flow parameters closer to the target values, with O atom and NO concentrations lower than in the e-beam-controlled flows. Flow stability is analyzed using the linear stability theory. A thermodynamic energy addition criterion is used to demonstrate the advantage of direct kinetic energy increase in MHD acceleration over thermal energy addition methods

Thermodynamic and theoretical aspects of emulsions and their stability

Abstract: Recent advances in the thermodynamics of equilibrium oil-water-surfactant systems facilitate understanding of the dynamics of nonequilibrium systems. In particular, understanding of nucleation and flickering of small holes joining emulsion droplets has gradually grown, with implications for progress in coalescence, Ostwald ripening and solubilization kinetics. The molecular parameters of surfactants affecting these processes are becoming clearer. On the other hand, surface forces approach (e.g. classical Derjaguin-Landau-Verwey-Overbeek theory) has shown little predictive power when applied to emulsions.

Markovian kinetic equations in a nonequilibrium statistical ensemble formalism

Abstract: The nonlinear quantum kinetic theory for many-body systems either near or far from equilibrium that a nonequilibrium ensemble formalism provides is revisited In this communication we consider an important limit of such transport equations, consisting of the memoryless approximation, which leads to the so-called Markovian kinetic equations They are derived in Zubarev's approach to the method, and next applied to a particular model of a spin system in interaction with a thermal bath of lattice vibrations The limitations of the approach, as well as some criticism it has received, are discussed

Relativistic and nonrelativistic description of fluids with anisotropic heat conduction

Abstract: We formulate a set of Lorentz-covariant equations for an imperfect fluid with viscosity, dilatational viscosity, and anisotropic thermal conductivity that possess the full GENERIC structure of nonequilibrium thermodynamics. The GENERIC structure, which includes and goes beyond prior nonequilibrium generalizations of the second law of thermodynamics, is shown to provide a guideline for modifying previous phenomenological or kinetic-theory based equations of extended relativistic hydrodynamics. In the nonrelativistic limit, we discuss the form of the equations for viscous and viscoelastic fluids with anisotropic heat conduction.

Liouville's theorems, Gibbs' entropy, and multifractal distributions for nonequilibrium steady states

Abstract: Liouville’s best-known theorem, ḟ({q,p},t)=0, describes the incompressible flow of phase-space probability density, f({q,p},t). This incompressible-flow theorem follows directly from Hamilton’s equations of motion. It applies to simulations of isolated systems composed of interacting particles, whether or not the particles are confined by a box potential. Provided that the particle–particle and particle–box collisions are sufficiently mixing, the long-time-averaged value 〈f〉 approaches, in a “coarse-grained” sense, Gibbs’ equilibrium microcanonical probability density, feq, from which all equilibrium properties follow, according to Gibbs’ statistical mechanics. All these ideas can be extended to many-body simulations of deterministic open systems with nonequilibrium boundary conditions incorporating heat transfer. Then Liouville’s compressible phase-space-flow theorem—in the original ḟ≠0 form—applies. I illustrate and contrast Liouville’s two theorems for two simple nonequilibrium systems, in each case co...