Showing papers on "Non-equilibrium thermodynamics published in 1979"

Isobaric volume and enthalpy recovery of glasses. II. A transparent multiparameter theory

Abstract: A multiordering parameter model for glass-transition phenomena has been developed on the basis of nonequilibrium thermodynamics. In this treatment the state of the glass is determined by the values of N ordering parameters in addition to T and P; the departure from equilibrium is partitioned among the various ordering parameters, each of which is associated with a unique retardation time. These times are assumed to depend on T, P, and on the instantaneous state of the system characterized by its overall departure from equilibrium, giving rise to the well-known nonlinear effects observed in volume and enthalpy recovery. The contribution of each ordering parameter to the departure and the associated retardation times define the fundamental distribution function (the structural retardation spectrum) of the system or, equivalently, its fundamental material response function. These, together with a few experimentally measurable material constants, completely define the recovery behavior of the system when subjected to any thermal treatment. The behavior of the model is explored for various classes of thermal histories of increasing complexity, in order to simulate real experimental situations. The relevant calculations are based on a discrete retardation spectrum, extending over four time decades, and on reasonable values of the relevant material constants in order to imitate the behavior of polymer glasses. The model clearly separates the contribution of the retardation spectrum from the temperature-structure dependence of the retardation times which controls its shifts along the experimental time scale. This is achieved by using the natural time scale of the system which eliminates all the nonlinear effects, thus reducing the response function to the Boltzmann superposition equation, similar to that encountered in the linear viscoelasticity. As a consequence, the system obeys a rate (time) -temperature reduction rule which provides for generalization within each class of thermal treatment. Thus the model establishes a rational basis for comparing theory with experiment, and also various kinds of experiments between themselves. The analysis further predicts interesting features, some of which have often been overlooked. Among these are the impossibility of extraction of the spectrum (or response function) from experiments involving cooling from high temperatures at finite rate; and the appearance of two peaks in the expansion coefficient, or heat capacity, during the heating stage of three-step thermal cycles starting at high temperatures. Finally, the theory also provides a rationale for interpreting the time dependence of mechanical or other structure-sensitive properties of glasses as well as for predicting their long-range behavior.

Theoretical Modeling of Rapid Surface Vaporization with Back Pressure

Abstract: In this paper, a theoretical model is developed for rapid surface vaporization into a surrounding ambient atmosphere. The primary emphasis is on metallic surfaces. Power input levels are taken to be low enough so that thermodynamic equilibrium can be assumed before phase change to gas. At high evaporation rates there will be a narrow Knudsen layer region in the gaseous flow just outside the phase interface in which translational nonequilibrium prevails. The modeling treats this layer as a gasdynamic discontinuity and approximate jump conditions are derived. The flow Mach number just outside the Knudsen layer is dictated by the state well away from the surface. Its determination is discussed both for a simple model of transient flow induced by a laser pulse and for the general case of time-varying power input. Examples assume the metallic surface is aluminum and the surrounding air pressure ranges from 1 atm to hard vacuum.

On transient relativistic thermodynamics and kinetic theory. II

Abstract: This paper, the sequel to Stewart (1977), discusses the relation between transient relativistic thermodynamics and kinetic theory in the formulation of Israel (1972, 1976) which differs (mathematically) from that of the previous paper. The difference is that the moment expansions are truncated in different ways. However, identical results for the characteristic velocities of thermal transients are obtained, and this lends credence to both approaches. In this approximation at least, the Grad method of moments is insensitive to the truncation procedure.

Irreversible Processes and Physical Interpretation of Rational Thermodynamics

Abstract: The paper contains a synthesis of recent developments that have extended the domain of validity of the classical version of thermodynamics of irreversible processes and generalized its methods. The presentation is largely based on the recognition of the fact that the real, nonequilibrium state of a material particle undergoing an irreversible process always remains close to a properly selected constrained equilibrium state — known as the accompanying state — which is described by the usual variables (deformation gradient and internal energy) and an adequate set of internal variables to which a physical meaning can be attached. The selection of these internal variables depends on the intended level of description and on the pair material-process being analyzed. The preceding circumstances allow us to write down a Gibbs equation for the accompanying state of the system which, together with the conservation laws, makes it possible to calculate the volumetric rate of production of accompanying entropy. It is recognized that the latter must be nonnegative in all processes (fundamental inequality of dissipation). The generalized forces and fluxes which appear in this expression are functionally related, the state variables occurring in them in the role of parameters. It is shown that the forces or fluxes must appear in a form consisting of two parts. One part is derivable from a potential of dissipation the other part being nondissipative. The paper recalls the linear form of Onsager's relations and discusses the possibility of their generalization to nonlinear constitutive relations. Even though such a firm generalization does not yet exist, it is possible to discuss two plausible proposals and to examine the relations that link them to each other. The totality of postulates discussed in the paper constitutes a complete thermodynamic formalism. It is shown that Meixner's fundamental inequality is implied in this formalism and this provides a physical interpretation for his second temperature. Furthermore, the elimination of the internal variables leads to the formalism known as \"rational\" thermodynamics in which the constitutive relations are given in the 0340-0204/79/0229-0258S02.00 © Copyright by Walter de Gruyter & Co. · Berlin · New York 230 Bataille, J. Kestin form of functionals. This permits us to give a physical interpretation to the concepts of nonequilibrium temperature and entropy considered as \"primitive\" in \"rational\" thermodynamics. Introduction Since 1963 there has developed a movement which purports to \"rationalize\" and to generalize the thermodynamics of irreversible processes [1—9] in its classical form [10—12]. As stressed by Germain [13], such a movement is justified by the obscurities and limitations of the classical thermodynamics of irreversible processes. It is certainly true that the classical presentations of the subject which are guided by physical considerations are characterized by a certain lack of axiomatic rigor and an exposition which is not quite convincing as far as its principles and methods are concerned. In spite of these defects, this theory has rendered great service to science, and this is proved by the fact that today it is capable of describing the majority of situations of current interest and that it is even sufficiently \"general\" to provide us with new results, such as the equation of the hydrodynamics of rotating liquid helium [14], or to account for the phenomena of plastic deformation [15—21 ]. This is achieved by the introduction of supplementary internal thermodynamic variables whose physical significance can be determined in each individual case. By contrast, the protagonists of \"rational\" thermodynamics have constructed an axiomatic theory which deals with materials endowed with a \"memory\", formulates the constitutive laws in the form of functionals of such variables as temperature, deformation, and temperature gradient [ l—9J and is characterized by an elegant formalism and mathematical attractiveness. Unfortunately, all too often one gains the impression that this represents a new theory which is both more general and unrelated to the old one. It is also regrettable that rigor has been obtained by purposely disregarding certain questions of physics. For example, if it is true that the thermodynamics of \"materials with fading memory\" [3] is endowed with great generality and a formal beauty rooted in its obvious simplicity, it is also true to say that it assumes a priori the existence of a temperature and of an entropy generalized to apply to arbitrary situations when it is not at all clear how it is possible to measure them. It also assumes the validity of the traditional Clausius-Duhem inequality as an a priori postulate, both assumptions being accepted without much discussion. These are two problems of great physical importance. As far as the practical application of the results of a rational thermodynamics of such generality is concerned, it is necessary to express some doubts: indeed, how can we envisage that all those functionals can be obtained experimentally? Rational thermodynamics has made its contribution in that it induced physicists to re-examine their own point of view and to spend a considerable effort on the task of generalizing the methods of the classical discipline of thermodynamics of irreversible processes and of extending its domain of applicability by the systematic use of internal variables. 1 A somewhat different analysis can be found in refs. [7] and [22]. J. Non-Equilib. Thermodyn., VoL 4, 1979, No. 4 Physical interpretation of rational thermodynamics 231 In the present paper the authors intend to present a synthesis of the older and more , recent papers on this subject and to achieve a unified formalism which makes use of a limited, and clearly stated, number of postulates inspired by the concepts of the classical thermodynamics of irreversible processes. Moreover, we shall examine the physical background of rational thermodynamics because some of its formal aspects are interesting as well as convenient if a mathematical presentation is aimed at. In other words, we shall see how far the classical theory of irreversible processes, with appropriate modifications, becomes equivalent to a description in terms of functional [3,5,6]. 1. Preliminary Assumptions To keep the discussion simple, we shall restrict attention to thermomechanical processes taking place in non-polar media and will exclude electromagnetic phenomena, diffusion, volumetrically distributed heat sources or, generally, external force fields. We shall also leave out of account the more recent discipline of non-local thermodynamics (see, for example, [29]) which may well have practical applications in certain cases. Within the preceeding constraints, each material particle undergoes an autonomous thermomechanical process and it makes sense to speak about the thermodynamic state of an element of volume thought of as isolated from the rest. In particular, we shall apply to it the laws of conservation of mass, momentum, moment of momentum and energy. These can be written in the following local forms:

The maxwell-stefan formulation of irreversible thermodynamics for simultaneous heat and mass transfer

Abstract: We consider constitutive relations for diffusion and simultaneous heat conduction in an n-coraponent non-ideal fluid mixture. Using the ideal gas treatment of Hirschfelder, Curtiss and Bird as a basis, we develop the generalization of the Maxwell-Stefan diffusion equations. The application of the second law of thermodynamics is shown to impose non-negativity constraints on the defined diffusion coefficients, D ik The practicalusefulness of the Generalized Maxwell-Stefan formulation is demonstrated by a few examples.

Stability of motions of thermoelastic fluids

Abstract: It is shown that the second law of thermodynamics induces uniqueness and continuous dependence upon initial-state and supply terms of smooth thermodynamic processes of thermoelastic fluids within the broader class of thermodynamic processes with shock waves.

Low-temperature plasmas with nonequilibrium ionization

Abstract: Low-temperature plasmas are frequently not in thermodynamic equilibrium. External fields, the emission of radiation, gradients of various physical properties, and the finite rates of various processes can all prevent the attainment of equilibrium. In nonequilibrium conditions the ionization state, the distribution of atomic excited states, and the electron energy distribution all become complicated functions of the factors responsible for the deviation from equilibrium. Since the components of the plasma—the electrons, atoms, and ions—are strongly coupled, a departure from equilibrium in one component causes departure in the others. The criteria for a deviation from local thermodyamic equilibrium are given. A study is made of plasmas far from equilibrium, in which the electron density is not described by the Saha equation, the atoms do not have a Boltzmann energy-level distribution, and the electrons do not have a Maxwellian energy distribution. A steady-state nonequilibrium plasma and time-dependent relaxation phenomena are studied. The theory is compared with the extensive experimental data available.

Dynamics of nuclear fluid. V. Extended time-dependent Hartree-Fock approximation illuminates the approach to thermal equilibrium

Abstract: In the time-dependent Hartree-Fock approximation, the fermions are assumed to interact only through the mean field and the collisions between particles are neglected. We formulate an extended time-dependent Hartree-Fock approximation which incorporates particle collisions due to the residual interaction, with the usual time-dependent Hartree-Fock approximation as the collisionless limit. It is obtained by a truncation of the Martin-Schwinger hierarchy at the second level and by using a simple representation of the one-body Green's function in terms of time-dependent occupation numbers. The final set of coupled equations consists of a modified time-dependent Hartree-Fock equation and a master equation for the occupation numbers. These results are physically transparent and describe properly the physics of the collision process. They may also be simple enough to be of practical use to study heavy-ion collisions or the dynamics of other fermion systems. Furthermore, as the configuration-space analog of the quantum Boltzmann equation, many important results concerning statistical dynamics are obtained. Concepts such as entropy, temperature, and local and thermal equilibrium can be quantitatively introduced. The well-known $H$ theorem that entropy never decreases can be readily recovered. With the collision term explicitly exhibited, the macroscopic equations (equations of continuity, momentum flux, and energy) and their associated conservation theorems can also be derived. Analytic solutions for the master equation for simple cases lead to new "level crossing" formulas having characteristics distinctly different from the Landau-Zener level-crossing formula and illuminate the salient features as to how a nonequilibrium fermion system approaches thermal equilibrium.NUCLEAR REACTIONS Extension of time-dependent Hartree-Fock approximation. Collisions between particles. Master equation for occupation probabilities. Entropy, temperature, and thermal equilibrium. $H$ theorem. Analytic solution of the master equation. New types of level crossing formula.

Statistical mechanics of systems nonlinearly displaced from equilibrium I

Abstract: A graphical approach is used to extend the response theory expression for nonequilibrium averages to any arbitrry order in deviations from equilibrium. Various ways in which the perturbation series about equilibrium can be resummed into gradient or Chapman-Enskog like expansions are presented. As a matter of illustration, examples from the hydrodynamics of simple fluids and the motion of a Brownian particle are considered. Specifically the normal stresses, shear dependent viscosity and velocity dependent friction constant are examined.

An axiomatic thermodynamics of open systems

Abstract: The axiomatic thermodynamics of Giles (1964) is extended in such a way that direct applications to open systems are possible. The Helmholtz and other generalised Massieu function representations of thermodynamics are discussed without specialising to equilibrium. Quasi, 'ordinary', and absolute Helmholtz and generalised Massieu functions are introduced and shown to exist. 'Uniqueness' theorems for these quantities are established. A fundamental theorem is proved for each of the above representations of thermodynamics. This theorem provides quantitative conditions which are necessary and sufficient for one arbitrary state of a system A to be accessible from another state of A in a natural process which involves not only A but also certain reservoirs. It is verified that, when the theory is specialised to equilibrium, the result is the well known partial Legendre transform 'picture' of the Helmholtz and Massieu function representations.

Comments on ``THE Diffusion and Nonequilibrium Thermodynamic Equations of Water Vapor in Soils Under Temperature Gradients''

Abstract: Based on the observation that temperature is a function of distance, Fick's law of diffusion is extended as widely as possible to apply to the movement of water vapor in soils under temperature gradients. The general equations developed as a result are expressed using (1) water vapor pressure, (2) water vapor density, (3) the Clapeyron equation, and (4) the form of phenomenological equations in nonequilibrium thermodynamics. From comparisons with the equations derived in several previous reports, we conclude that the earlier results may be valid only under the condition that the total water potential is larger than −106 centimeters.

Non-equilibrium thermodynamics of interfaces including electromagnetic effects

Abstract: The application of non-equilibrium thermodynamics to a system consisting of two bulk phases and their interface is extended to include electromagnetic effects. The interface is assumed to carry singular mass, energy, and entropy densities as well as singular electric charge, electric current, polarization and magnetization. Electric and magnetic fields are allowed to be discontinuous across the interface, but not singular. Maxwell's equations are used to derive relationships among electromagnetic quantities on the surface and boundary conditions for the bulk phases. An expression for the surface entropy production including electromagnetic effects is obtained, and the resulting linear laws relating thermodynamic forces and fluxes are investigated.

Entropy and black-hole thermodynamics

Abstract: The concept of entropy is examined with an eye toward gaining insight into the nature of black-hole thermodynamics. Definitions of entropy are given for ordinary classical and quantum-mechanical systems which lead to plausibility arguments for the ordinary laws of thermodynamics. The treatment of entropy for a classical system is in the spirit of the information-theory viewpoint, but by explicitly incorporating the coarse-grained observable into the definition of entropy, we eliminate any nonobjective features. The definition of entropy for a quantum-mechanical system is new, but directly parallels the classical treatment. We then apply these ideas to a self-gravitating quantum system which contains a black hole. Under some assumptions: which, although nontrivial, are by no means exotic: about the nature of such a system, it is seen that the same plausibility arguments which lead to the ordinary laws of thermodynamics for ordinary systems now lead to the laws of black-hole mechanics, including the generalized second law of thermodynamics. Thus, it appears perfectly plausible that black-hole thermodynamics is nothing more than ordinary thermodynamics applied to a self-gravitating quantum system.

Statistical mechanics of stationary states. IV. Far-from-equilibrium stationary states and the regression of fluctuations

Abstract: The authors present a microscopic theory for the averages of any dynamical variable and in particular of fluctuations in nonequilibrium stationary states that are arbitrarily far from equilibrium, as long as the macroscopic gradients are sufficiently small. It is argued that the dynamics of the fluctuations are governed by the linearized macroscopic equations of motion (analogous to Onsager's hypotheses for equilibrium fluctuations). The fluctuation-dissipation theorem is examined and it is found that it does not hold in its equilibrium form. The authors find that the dissipation does not contain an important part of the information about the fluctuation, and attempt an interpretation of this fact.

Isothermal diffusion and quasielastic light-scattering of macromolecular solutes at finite concentration

Abstract: The Brownian motion of a group of hydrodynamically interacting particles suspended in a low‐Reynolds‐number fluid is described by a generalization of the Einstein diffusion relation. The time integral of each velocity self‐ or cross‐correlation function is found to be equal to one of the mobility tensors governing steady movement of the particles through the fluid. Using the approach of nonequilibrium thermodynamics and linear response theory, this result allows formulation of an expression for the concentration dependence of the Fick’s law diffusion coefficient for mutual binary diffusion in terms of the mobility tensors. The relationship between the concentration dependence of the solute chemical potential, sedimentation rate and mutual diffusion coefficient D is proved. A distinction is made between D and the mean self‐diffusion coefficient Ds for solute molecules, thus allowing interpretation of results obtained using different experimental techniques. An argument is presented which indicates that qua...