Showing papers on "Non-equilibrium thermodynamics published in 1994"

Thermodynamics of flowing systems : with internal microstructure

Abstract: PART 1: THEORY Introduction 1. Symplectic geometry in optics 2. Hamiltonian mechanics of discrete particle systems 3. Equilibrium thermodynamics 4. Poisson brackets in continuous media 5. Non-equilibrium thermodynamics 6. The dissipation bracket PART 2: APPLICATIONS 7. Incompressible viscoelastic flows 8. Transport phenomena in viscoelastic fluids 9. Non-standard transport phenomena 10. The dynamical theory of liquid crystals 11. Multi-fluid transport/reactions models with application in the modelling of weakly ionized plasma dynamics Epilogue Bibliography Appendices

On the out-of-equilibrium relaxation of the Sherrington-Kirkpatrick model

Abstract: Starting from a set of assumptions on the long-time limit behaviour of the nonequilibrium relaxation of mean-field models in the thermodynamic limit, we derive analytical results for the long-time relaxation of the Sherrington-Kirkpatrick model, starting from a random configuration. The system never achieves local equilibrium in any fixed sector of phase space, but remains in an asymptotic out-of-equilibrium regime. We clearly state and motivate the assumptions made. For the study of the out-of-equilibrium dynamics of spin-glass models, we propose as a tool, both numerical and analytical, the use of 'triangle relations' which describe the geometry of the configurations at three (long) different times.

Advanced thermodynamics for engineers

Abstract: Basic relations and the First Law the Second Law of thermodynamics availability analysis availability analysis of cycles equations of state thermodynamic property relations the Third Law of thermodynamics thermodynamic properties of homogeneous mixtures multiphase-multicomponent systems chemical reactions chemical availability chemical availability of fuels a statistical viewpoint of entropy. Appendices: supplementary tables and figures symbols.

Thermodynamics with Internal Variables. Part I. General Concepts

Abstract: The first part of this review replaces the concept of internal variables of state in the general context of non-equilibrium thermodynamics. This offers the slightest deviation from the classical Theory of irreversible processes (TIP) while exhibiting a flexibility and versatility that other attempts at generalizing TIP cannot sustain. Here the basic working hypotheses on which the application of internal-variable theory relies, are specified. The use of TIP, after introduction of the appropriate axiom of local equilibrium state, or of a pseudopotentia l of dissipation is emphasized. The role of internal state variables in describing miscrostructures and the current misunderstanding with internal degrees of freedom are clarified. However, the resemblance or identity with order parameters of phase-transition theory as well as essential differences with extended thermodynamics are acknowledged. In all, internal variables epitomize the use of systems of evolution in mathematical continuum physics.

Thermodynamics of materials

Abstract: Thermodynamics: Review. Statistical Thermodynamics. Defects in Solids. Surfaces and Interfaces. Diffusion. Transformations. Reaction Kinetics. Nonequilibrium Thermodynamics. Index.

Convergence properties of free energy calculations : alpha -cyclodextrin complexes as a case study

Abstract: By considering all possible mutations among four para-substituted phenols, p-chlorophenol, p-methylphenol, p-cyanophenol, and p-methoxyphenol, which bind as inclusion compounds in alpha-cyclodextrin, the convergence properties of thermodynamic integration free energy calculations using slow growth as compared to numerical quadrature are investigated and interpreted in terms of structural and dynamical properties of the molecular system. It is shown that a systematic increase in the calculated hysteresis can be expected with increasing simulation time in slow-growth calculations if the system is perturbed faster than the rate at which the various states that make up the equilibrium ensemble are sampled. Using numerical quadrature the effects of nonequilibrium can be largely separated from the effects of insufficient sampling. It is shown, however, that the apparent degree of convergence when using numerical quadrature does not necessarily reflect the accuracy of the calculation. The utility of formulating closed cycles in both the bound and unbound states as a means of determining the minimum error in a given calculation is demonstrated. The effects of the choice of pathway and of the choice of integration scheme on convergence within closed cycles are also discussed. Finally, the quality of the force field used and the relative importance of the force field as opposed to sampling considerations are assessed by comparing the estimated free energy differences to experimental data. It is shown that a meaningful appraisal of a specific force field cannot be made independent of sampling considerations. A modification to the GROMOS force field that improved the agreement between the calculated and experimental free energies for the mutation of p-chlorophenol to p-methylphenol is also proposed.

Thermodynamics with Internal Variables. Part II. Applications

Abstract: The second part of this synthetic work presents and discusses the most spectacular and successful applications of the irreversible thermodynamics with internal variables. These include viscosity in both fluids and solids (in the former case, in complex fluids and structurally complex flows), viscoplasticity and rate-independent plasticity in small and finite strains, damage and cyclic plasticity, electric and magnetic relaxation, magnetic and electric hysteresis, normal and semi-conduction, superconductivity of deformable solids, and ferrofluids. In all cases the internal variables of interest are given some physical significance in terms of quantities defined at a sublevel of description. The relevant internal variables may be as varied as second-order tensors, real or complex valued scalars, and polar or axial vectors. Furthermore, the role played by internal variables in wave-propagation problems is emphasized through appropriate examples. The presentation ends with reaction-diffusion problems. This is illustrated by damage, plastic-strain localization and models for nerve-pulse dynamics. Globally, we have all ingredients of a truly post-Duhemian irreversible thermodynamics of complex behaviors.

Linear disturbances in hypersonic, chemically reacting shock layers

Abstract: The effects of equilibrium- and nonequilihrium-air chemical reactions on the linear stability of a Mach 25, 10-deg half-angle sharp-cone shock layer are investigated. First, the basic state is computed using the parabolized Navier-Stokes equations with a shock-fitting scheme. This eliminates spurious numerical oscillations that could adversely affect the stability analysis. Spatial stability analyses are then described for three different approximations of the physics: perfect gas, air in local chemical equilibrium, and air in chemical nonequilibrium. It is shown in both the equilibrium- and nonequilibrium-air calculations that the second mode of Mack is shifted to lower frequencies

Nonequilibrium Statistical Mechanics of Preasymptotic Dispersion.

Abstract: Turbulent transport in bulk-phase fluids and transport in porous media with fractal character involve fluctuations on all space and time scales. Consequently one anticipates constitutive theories should be nonlocal in character and involve constitutive parameters with arbitrary wavevector and frequency dependence. We provide here a nonequilibrium statistical mechanical theory of transport which involves both diffusive and convective mixing (dispersion) at all scales. The theory is based on a generalization of classical approaches used in molecular hydrodynamics and on time-correlation functions defined in terms of nonequilibrium expectations. The resulting constitutive laws are nonlocal and constitutive parameters are wavevector and frequency dependent. All results reduce to their convolution-Fickian quasi-Fickian, or Fickian counterparts in the appropriate limits.

Nonequilibrium evolution of scalar fields in FRW cosmologies.

Abstract: We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies. The calculation is performed both to one loop and in a nonperturbative, self-consistent Hartree approximation. The method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. The renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. We investigate the high temperature expansion and show that it breaks down at long times. We also obtain the time evolution of the initial Boltzmann distribution functions, and argue that to one-loop order or in the Hartree approximation the time evolved state is a squeezed'' state. We illustrate the departure from thermal equilibrium by numerically studying the case of a free massive scalar field in de Sitter and radiation-dominated cosmologies. It is found that a suitably defined nonequilibrium entropy per mode increases linearly with comoving time in a de Sitter cosmology, whereas it is [ital not] a monotonically increasing function in the radiation-dominated case.

Thermodynamics of Irreversible Processes: Applications to Diffusion and Rheology

Abstract: The Continuum View of Matter Classical Thermodynamics Basic Axioms of the TIP Multicomponent Simple Fluids Statistical Foundation of the Onsager Casimir Reciprocal Relations for Homogeneous Systems Multicomponent Diffusion Rheology Appendices Indexes

A survey of thermodynamics

Abstract: Partial Contents: 1. Temperature and equilibrium. 2. Heat and work. 3. The emergence of thermodynamics. 4. Entropy and the Second Law. 5. Special topics. 6. Equilibrium thermodynamics. 7. Applications. 8. Secondary Effects the Third Law of Thermodynamics. 9. Phase Transitions. 10. Microscopic Theories. 11. Statistical Mechanics. 12. Thermodynamics in Special Relativity.

Nonequilibrium temperature versus local-equilibrium temperature.

Abstract: We discuss the conceptual differences between a nonequilibrium absolute temperature (defined as the partial derivative of the steady-state nonequilibrium entropy) and the local-equilibrium absolute temperature. We explore two situations in which this difference could be observed in molecular-dynamical situations. By using a simple model for the nonequilibrium entropy, we compute the difference between both temperatures for gases, metals, and electromagnetic radiation. We analyze the compatibility of both temperatures in two simple examples in the kinetic theory of gases and in an information-theoretic analysis of harmonic chains. Finally, we compare with some other works which have proposed non- equilibrium temperatures on several different grounds.

Onsager-Casimir reciprocity relations for open gaseous systems at arbitrary rarefaction: I. General theory for single gas

Abstract: A new statistical approach to the nonequilibrium thermodynamics is worked out. The approach is based on general properties of the Boltzmann equation and boundary condition for the distribution function. It allows to obtain the Onsager-Casimir reciprocity relations for open gaseous systems at any rarefaction including situations when the local equilibrium is broken. Thus, in contrast to the conventional opinion, it is shown that an application of the main results of non-equilibrium thermodynamics can be extended to systems not being in the local equilibrium

Conservation laws in variational thermo-hydrodynamics

Abstract: Preface. Introduction: aims and scope. 1. Physical significance of Noether's symmetries and extremum principles. 2. Lagrangian and Eulerian descriptions of perfect fluids. 3. Conservation laws for given system of equations. 4. Thermodynamics and kinetics of nonequilibrium fluids. 5. Lagrangian and Hamiltonian formalism for reversible nonequilibrium fluids with heat flow. 6. Extended reversible problem involving mass diffusion, heat flow and thermal inertia. 7. A generalized action with dissipative potentials. 8. Thermohydrodynamic potentials and geometries: the union of thermodynamics and hydromechanics. 9. Intrinsic symmetries and conservation of mass in chemically reacting systems. 10. Conservation laws as given constraints for processes at mechanical equilibrium. 11. Generalized minimum dissipation in presence of convection and chemical reactions. 12. Some associated relativistic results. References. Glossary of principal symbols. Index.

On mean field glassy dynamics out of equilibrium

Abstract: We study the off equilibrium dynamics of a mean field disordered systems which can be interpreted both as long range interaction spin glass and as a particle in a random potential. The statics of this problem is well known and exhibits a low temperature spin glass phase with continous replica symmetry breaking. We study the equations of off equilibrium dynamics with analytical and numerical methods. In the spin glass phase, we find that the usual equilibrium dynamics (observed when the observation time is much smaller than the waiting time) coexists with an aging regime. In this aging regime, we propose a solution implying a hierarchy of crossovers between the observation time and the waiting time.

Onsager-Casimir reciprocity relations for open gaseous systems at arbitrary rarefraction: II. Application of the theory for single gas

Abstract: On the basis of the general theory presented in part I a number of the following typical and practically important problems of rarefied gas dynamics are considered: evaporation and condensation of a gas between two parallel plates, evaporation and condensation in a closed cylinder, two-dimensional gas flow through a capillary and gas flow past a particle. The explicit expressions of the thermodynamic fluxes and kinetic coefficients satisfying the Onsager-Casimir reciprocity relations are derived. The couplings between cross effects arising in the gas flows are obtained from these relations.

Many-body theory for charge transfer in atom-surface collisions.

Abstract: A theory for the effect of a strong intra-atomic Coulomb repulsion U on the nonadiabatic transfer of charge between a metallic surface and a moving atomic species is presented. Using slave bosons and a nonequilibrium Green's-function technique, we solve the equations appropriate for the U=\ensuremath{\infty} problem in the case when either the atom-surface hopping matrix element is small, or the number of degenerate atomic states is large. We generalize the earlier treatment of Langreth and Nordlander (LN) to include off-diagonal self-energies and present a general numerical scheme for the exact solution of the Dyson equations. We verify that our scheme gives the correct answer in several limiting cases where an exact solution is known, and give quantitative predictions of when deviations from these limits become important. These limits include (1) the simple master equation limit for low velocities and weak coupling, (2) the generalized master equation of LN for larger velocities and atom-surface coupling, (3) the approach to thermal equilibrium when the time dependence is removed, and (4) the maintenance of local thermal equilibrium when the energy parameters vary sufficiently slowly. From a calculation of the instantaneous (nonequilibrium) spectral function of the level on the scattering atom, we are able to study the rate of formation of the Kondo and mixed valent resonances near the Fermi level. We find a slow formation rate for such resonances relative to that of the broader parts of the spectral density centered near the bare atom level positions.

About the “normal growth” approximation in the dynamical theory of phase transitions

Abstract: Nonequilibrium phase transitions can often be modeled by a surface of discontinuity propagating into a metastable region. The physical hypothesis of “normal growth” presumes a linear relation between the velocity of the phase boundary and the degree of metastability. The phenomenological coefficient, which measures the “mobility” of the phase boundary, can either be taken from experiment or obtained from an appropriate physical model. This linear approximation is equivalent to assuming the surface entropy production (caused by the kinetic dissipation in a transition layer) to be quadratic in a mass flux. In this paper we investigate the possibility of deducing the “normal growth” approximation from the viscosity-capillarity model which incorporates both strain rates and strain gradients into constitutive functions. Since this model is capable of describing fine structure of a “thick” advancing phase boundary, one can derive, rather than postulate, a kinetic relation governing the mobility of the phase boundary and check the validity of the “normal growth” approximation. We show that this approximation is always justified for sufficiently slow phase boundaries and calculate explicitly the mobility coefficient. By using two exact solutions of the structure problem we obtained unrestricted kinetic equations for the cases of piecewise linear and cubic stress-strain relations. As we show, the domain of applicability of the “normal growth” approximation can be infinitely small when the effective viscosity is close to zero or the internal capillary length scale tends to infinity. This singular behavior is related to the existence of two regimes for the propagation of the phase boundary — dissipation dominated and inertia dominated.

Exact solutions for stochastic adsorption-desorption models and catalytic surface processes.

Abstract: We investigate the stochastic kinetics of adsorption-desorption cooperative processes with single particle biased diffusion. For certain choices of the transition probability rates a quantum spin analogy allows for an exact solution of dynamic correlation functions in the steady state. For nonequilibrium translationally invariant initial conditions, equal time correlation functions and nonsteady currents are calculated exactly, working from the master equation. Depending on the relative values of the transition rates, these quantities exhibit either power-law decay or exponential decay (with a variety of subdominant power-law prefactors). Our results are compared with Monte Carlo simulations.

Numerical Simulation of Nonequilibrium Effects in an Argon Plasma Jet

Abstract: Departures from thermal (translational), ionization, and excitation equilibrium in an axisymmetric argon plasma jet have been studied by two‐dimensional numerical simulations. Electrons, ions, and excited and ground states of neutral atoms are represented as separate chemical species in the mixture. Transitions between excited states, as well as ionization/recombination reactions due to both collisional and radiative processes, are treated as separate chemical reactions. Resonance radiation transport is represented using Holstein escape factors to simulate both the optically thin and optically thick limits. The optically thin calculation showed significant underpopulation of excited species in the upstream part of the jet core, whereas in the optically thick calculation this region remains close to local thermodynamic equilibrium, consistent with previous experimental observations. Resonance radiation absorption is therefore an important effect. The optically thick calculation results also show overpopulations (relative to equilibrium) of excited species and electron densities in the fringes and downstream part of the jet core. In these regions, however, the electrons and ions are essentially in partial local thermodynamic equilibrium with the excited state at the electron temperature, even though the ionized and excited states are no longer in equilibrium with the ground state. Departures from partial local thermodynamic equilibrium are observed in the outer fringes and far downstream part of the jet. These results are interpreted in terms of the local relative time scales for the various physical and chemical processes occurring in the plasma.

Entropy and the second law: A pedagogical alternative

Abstract: Thermodynamics in introductory physics typically begins with the ideas of temperature and heating and with the first law of thermodynamics. Then the more difficult parts come: entropy and the second law of thermodynamics. This second portion of the course can begin with a microscopic conception of entropy and a qualitative idea of how thermal systems evolve. The key concept is the ‘‘multiplicity of a macrostate:’’ the number of microstates associated with a macrostate. Starting from these notions—a point of departure and a concept—this paper develops the second law of thermodynamics, the relationship ΔS≥(energy input by heating)/T, and the Carnot efficiency. Offer the entire development both as a specific alternative to what appears in typical introductory texts and as a contribution to a continuing discussion of how to teach thermodynamics to various college audiences.