Showing papers on "Non-equilibrium thermodynamics published in 1982"

Victims of History—A Nonequilibrium Approach to Evolution

Abstract: Wiley, E. O., and D. R. Brooks (Museum of Natural History, University of Kansas, Lawrence, Kansas 66045; Department of Zoology, University of British Columbia, Vancouver, British Columbia V6T 2A9, Canada.) 1982. Victims of history-a nonequilibrium approach to evolution. Syst. Zool., 31:1-24.-Evolution may be described as a nonequilibrium process involving the conversion of information from one form to another and the maintenance of old or forging of new reproductive networks. Species participate in nonequilibrium processes because they have properties of closure and because evolution is a historically irreversible phenomenon. Speciation is a process which consolidates available potential information into two or more stored information systems. Character change and the history of a clade are highly correlated because potential information is constrained by its own evolutionary history. Thus new and potential information may be converted into stored information only to the extent that this new and potential information is compatible with the ancestral information system or can find expression in an alternate ontogenetic pathway. All modes of speciation as well as anagenesis follow the second law of thermodynamics and may be described by a summary equation which charts the changes of entropy states of information and cohesion over time. We suggest that some empirical evidence corroborates our theory and that the research programs involved in further studying nonequilibrium evolution are largely in place now. [Evolution; nonequilibrium evolution; speciation; entropy; second law of thermodynamics; information theory.] In a previous paper (Brooks and Wiley, 1982), we suggested that evolution is best explained as an irreversible nonequilibrium phenomenon, and not, as present theories describe, as an equilibrium or punctuated equilibrium phenomenon. We suggested nonequilibrium thermodynamics, as developed by Ilya Prigogine and his colleagues (Prigogine, 1947, 1961, 1978, 1980; Glansdorff and Prigogine, 1971; for a readable summary see Prigogine et al., 1972 and Prigogine, 1980). We did so by considering three aspects of populations and species: information specifying successful growth and ontogeny, cohesion resulting from mating bonds between parts of species (i.e., individual organisms), and energy flow. Our application of information theory followed the conceptual developments of Gatlin (1972), Wicken (1979), Ho and Saunders (1979) and Saunders and Ho (1981). We concluded that speciation, the evolution of diversity in a clade, is accomplished by individual species acting as open-ended, closed, thermodynamic systems-open-ended in terms of energy and closed (or partly closed) in terms of information and cohesion. We suggested that our theory is sufficient to explain variation within species and how speciation is accomplished. We also suggested that extinction could be described using the same parameters. In this paper, we take the opportunity to more fully discuss our thesis. We shall not dwell on competing theories such as neo-Darwinism (the synthetic theory) or punctuated equilibrium except where these theories conflict with or illuminate our own. We will say that if the evolutionary process is, indeed, a nonequilibrium phenomenon and if species, like individual organisms, are dissipative energy structures far from equilibrium, then the assumptions of equilibrium inhibit these theories from fully explaining the phenomenon. In spite of this, we predict that neo-Darwinism and punctuated equilibrium (at least as an empirical observation) will come to rest comfortably within our theory.

Thermodynamic Bond Graphs and the Problem of Thermal Inertance

Abstract: It is shown that an isolated thermal inertance does not obey the second law of thermodynamics. Consequently, such an element should not be used in physical systems theory. To eliminate the structural gap in the thermal domain of current physical systems theory, a new framework is introduced using Bond Graph concepts. These Thermodynamic Bond Graphs are the result of synthesis of methods used in thermodynamics and in mechanics.

Maximization of entropy, kinetic equations, and irreversible thermodynamics

Abstract: By an extension to the dense-fluid regime of a method based upon maximization of entropy subject to constraints, first exploited by Lewis to obtain the Boltzmann equation, kinetic equations for one-particle and two-particle classical distribution functions are obtained. For the hard-sphere potential and a one-particle constraint, the kinetic equation (for the one-particle distribution function) of the revised Enskog theory is obtained; for a two-particle constraint a more general kinetic equation (for the two-particle distribution function) than that studied by Livingston and Curtiss is obtained. For a pair potential with hard-sphere core plus smooth attractive tail, a new mean-field kinetic equation is obtained on the one-particle level. In the Kac-tail limit the equation takes the form of an Enskog-Vlasov equation. The method yields an explicit entropy functional in each case. Explicit demonstration of an $H$ theorem is made for the one-particle theories in a novel way that illustrates the roles of the reversible and irreversible parts of the hard-sphere piece of the collision integral. The latter part leads to the classical form of entropy-production density as described by linear irreversible thermodynamics and so possesses many of the features of the Boltzmann collision integral. The former part introduces new elements into the entropy-production term. It is noted that the kinetic coefficients of the revised Enskog theory exhibit Onsager reciprocity in the linear regime. Upon consideration of the standard Enskog theory in the linear regime, we construct an entropy-production density and identify conjugate fluxes and forces and also kinetic coefficients which are shown to exhibit Onsager reciprocity. The standard theory is in disagreement, however, with the results of phenomenological irreversible thermodynamics for the conventional forms of fluxes and forces.

Nonequilibrium Thermodynamics and its Statistical Foundations

Abstract: H J Kreuzer 1980 Clarendon Press: Oxford University Press vii + 438 pp price £45 This is a welcome addition to the small number of books which deal with the principles of nonequilibrium statistical physics at a level suitable for the theoretically inclined but nonspecialist reader. The early part is concerned with irreversible thermodynamics.

Irreversible-thermodynamic approach to nonequilibrium heat fluctuations

Abstract: Starting from a generalized nonequilibrium entropy, and from an extension of the Einstein formula for the probability of the fluctuations, we obtain the second moments of nonequilibrium fluctuations of the specific energy and the heat flux in rigid heat conductors. This approach leads to nonequilibrium corrections to the usual fluctuationdissipation expressions for the heat fluctuations. The corresponding numerical corrections are found for phonon heat transport in dielectric solids and for electronic heat transport in metals. The macroscopic results share common features with those obtained for heat transport in harmonic chains by an information-theoretical approach.

Magnetohydrodynamic equilibrium. III - Helically symmetric fields. IV - Nonequilibrium of nonsymmetric hydrodynamic topologies

Abstract: It is pointed out that plasma confinement in stable equilibrium states constitutes a fundamental and still unresolved question in plasma astrophysics and thermonuclear fusion research. The problem has two parts related to the equilibrium states themselves and their mechanical stability. The question of the existence of general solutions of the field and fluid equations for the steady dynamical interaction of inviscid compressible fluids of high electrical conductivity with magnetic and gravity fields is considered. In the absence of fluid motions, the presented equations become the familiar equations of magnetostatics supplemented by an equation of state. Starting from this simplest case of magnetostatic equilibrium, the investigation proceeds to the more complex case of magnetohydrodynamic equilibrium. Examples of helically symmetric fields are presented to illustrate the use of the formulation for treating the dynamics of helically symmetric hydromagnetic flows.

Current layers and filaments in a semiconductor model with an impact ionization induced instability

Abstract: Dissipative structures associated with an instability in a semiconductor far from equilibrium are studied. A generation-recombination mechanism, which effects anS-shaped current-voltage characteristics, is coupled to diffusion and drift of the electrons. The spectrum of linear recombination-diffusion modes is computed for the homogeneous steady state with negative differential conductivity. The obtained soft mode instability gives rise to the bifurcation of a family of transversally modulated inhomogeneous steady states and longitudinal travelling waves. The inhomogeneous steady states are calculated from the full nonlinear transport equations for plane and cylindrical geometries. They correspond to oscillatory and solitary concentration profiles, including depletion and accumulation layers and cylindrical filaments. Conditions for the formation of kink-shaped coexistence profiles are established in terms of equal area rules. The current-voltage characteristics are extended to include inhomogeneous current states. Nonequilibrium phase transitions between various branches of these characteristics are associated with switching through filamentation.

Mode coupling theory of hydrodynamics and steady state systems

Abstract: We construct a formal mode coupling theory for hydrodynamic systems which includes contributions from all powers of the hydrodynamic variables. This theory is applied to nonequilibrium steady state systems. A generalization of the local equilibrium distribution is used to describe the nonequilibrium state. This distribution independently constrains all moments of the hydrodynamic variables. The infinite hierarchy of equations for the moments of the hydrodynamic variables is truncated using an inverse system size expansion. Explicit results are obtained for the time correlation functions of fluids with a linear temperature gradient or a linear shear. These results agree with previous studies of these steady states.

The linear Onsager coefficients for biochemical kinetic diagrams as equilibrium one-way cycle fluxes

Abstract: In a biochemical kinetic diagram1, the various discrete states of an enzyme or enzyme complex are represented by points, and interstate transitions are represented by lines. Figure 1 is an example. I show here that, for steady states near equilibrium, the phenomenological Onsager coefficients in the linear flux–force equations that are a consequence of any such diagram have a transparent physical interpretation: these coefficients are simple combinations of one-way cycle fluxes1 at equilibrium. The existence of this kind of relationship was pointed out recently in an appendix of a paper2 on another subject. I present here the explicit connection between the phenomenological coefficients and the one-way cycle fluxes of the diagram. These coefficients are considered by many scientists to be strictly empirical and incomprehensible. My report provides a simple interpretation of them, at the molecular level, for any biochemical kinetic diagram. This is analogous to the molecular interpretation of phenomenological equilibrium thermodynamics that is provided by statistical mechanics.

A kinetic derivation of extended irreversible thermodynamics

Abstract: The basic postulates of the extended irreversible thermodynamics are derived from the kinetic model for a dilute monoatomic gas Using the Grad 13-moment method to solve the full nonlinear Boltzmann equation for molecules conceived as soft spheres we obtain the microscopic expressions for the entropy flux, the entropy production, and the generalized Pfaffian for the extended definition of entropy as required by such a theory Some of the physical implications of these results are discussed

A nonclassical thermodynamic description of heat conducting viscous fluids

Abstract: Classically, the description of a fluid is assumed to be governed by the usual variables: density, temperature, and velocity. Here it is postulated that such a system requires supplementary variables, namely, the heat flux vector and the viscous part of the pressure tensor. Starting from this hypothesis, a general theory of thermoviscous fluids is proposed. Balance equations and constitutive equations necessary to its description are given. Restrictions on the form of the constitutive equations are placed by the second law. The relaxation times associated with the various dissipative fluxes are interpreted in terms of the theory of fluctuations. This is achieved by extending Einstein’s theory of fluctuations. The corresponding expressions for the second moments and the time correlations of the fluctuations of the dissipative fluxes are derived. In the limit of vanishing relaxation times, the classical results are recovered.

The Burnett Equations in Extended Irreversible Thermodynamics

Abstract: In this paper we show that the non-linear stationary state solutions of the time evolution equations for the fast or non-conserved quantities appearing in the generalized Gibbs relation of extended irreversible thermodynamics correspond, to second order in the gradients, to the Burnett constitutive equations of hydrodynamics. The proof is explicitly written down for the case of a simple Isotropie fluid. Introduction In recent years an extension of linear irreversible thermodynamics which is based on the local equilibrium assumption, has been proposed by raising the thermodynamic fluxes to the status of independent variables [1—3]. Using a more descriptive language, the new form which is proposed for the Gibbs equation contains the conventional slow or conserved quantities such as the mass and internal energy densities plus new terms in which \"fast, non conserved\" quantities are added. Among them one may include the heat flux q, the symmetrical traceless part of the viscous tensor I, its trace I, and so on. With such a proposal, one encounters first the problem to derive the time evolution equations for such quantities, and secondly to find what their physical meaning is. These questions have been discussed by Jou et al. [2—3], in several contexts and we shall not repeat them here. What we want to stress about their results is that such time evolution equations are, as expected, relaxation equations with relaxation times which may be computed either from experimental data or from microscopic theories. For the case of a linear theory they have the structure of the so called MaxwellCattaneo equations whose stationary solutions lead precisely to the well known constitutive relations between forces and fluxes, namely Fourier's equation for heat conduction and the Navier-Newton equation for the momentum flow. However, nothing has been said in the literature about the generalization of these equations to non-linear cases. What we want to show in this paper is that if one suitably generalizes the arguments leading to the relaxation equations for the \"fast variables\" and performs a systematic expansion in powers of the gradients, then to 0340-0204/82/0007-0095$02.00 © Copyright by Walter de Gruyter & Co. Berlin New York 96 L. S. Garcia-Colin, M. Lopez de Haro each order in the gradients, the stationary solutions are precisely the Burnett and higher order constitutive equations of hydrodynamics. And, furthermore, since these equations correspond to the case in which the fast variables are no longer present in the system's description, they are consistent with the ordinary Gibbs equation, that is with the local equilibrium assumption, and consequently with an entropy balance equation. These results have recently been obtained [4—6], using an entirely independent method. Since both derivations of the Burnett and higher order equations are completely phenomenological, we can consider the long sought \"physically transparent\" derivation of such equation [7—8] somewhat clarified. To avoid writing an unneccesary lengthy paper we shall devote Sect. 1 to a brief discussion of the main steps leading to the Maxwell-Cattaneo equations. Section 2 contains the main body of the paper and in Sect. 3 a few concluding remarks will be given. 1. Relaxation equations for fast variables The starting point of the extended theory for non-equilibrium thermodynamics is to assume that the local equilibrium assumption must be replaced, for a simple isotropic fluid, by the equation

Thermodynamic aspects of nonequilibrium current fluctuations

Abstract: Starting from a macroscopic nonequilibrium entropy, we obtain an expression for the nonequilibrium fluctuations of the electric current in a metallic resistor. Our method goes further than previous theories of irreversible thermodynamics and, as well as microscopic entropies, it leads to results of the same order of magnitude but not completely coincident with the full nonequilibrium corrections obtained from kinetic methods by Tremblay et al.

Relaxation of some fermion nonequilibrium momentum distributions

Abstract: We study the time evolution of momentum distribution for an infinite, dilute, and spatially homogeneous system of fermions by solving the Uehling-Uhlenbeck equation. The initial nonequilibrium distributions examined are taken to be (i) a Fermi sphere with an outer spherical shell, and (ii) a Fermi bisphere. It is found that the entropy of the system approaches its equilibrium value in a nearly exponential manner. Such a behavior allows an extraction of the relaxation times. The relaxation times decrease with increasing size of the perturbation and depend on the shape of the perturbation. Deviations from equilibrium in the initial momentum distribution persist into the late stages of the relaxation process.

Hidden supersymmetry of stochastic dissipative dynamics

Abstract: It is shown that the generating functional of dissipative dynamics in a potential force field can be reduced to the form of the functional integral of Euclidian supersymmetric field theory. The existence of a nonequilibrium (current) steady state is related to spontaneous supersymmetry breaking in the corresponding field theory. A variational principle of minimum entropy production is formulated. A supersymmetric diagrammatic technique is developed which is a compact invariant formulation of the well-known diagrammatic technique for dynamical problems. The nonlinear-dynamics problem for the fluctuating pendulum is considered in detail. The coefficient of angular diffusion under essentially nonequilibrium conditions, which determines, in particular, the line width of a synchronized self-excited oscillator, is computed.

On Thermodynamics of Non-Equilibrium Processes

Abstract: A statement of the second law of thermodynamics formulated in the spirit of the classics of the 19th century is shown to yield the existence of the non-equilibrium absolute temperature and non-equilibrium entropy which satisfy the Clausius-Planck dissipation inequality for general processes. A non-traditional form of the first law of thermodynamics employed here is expressed in terms of inequalities analogous to those of the second law. Deep similarities as well as differences between the two laws are thereby revealed.

Thermodynamic Criteria Governing Irreversible Processes under the Influence of Small Thermal Fluctuations

Abstract: The Ventsel'-Freidlin probability estimates for small random perturbations of dynamical systems are used to generalize and justify the Onsager-Machlup irreversible thermodynamic variational description of Gaussian statistical distributions in the limit where Boltzmann's constant tends to zero for non-Gaussian diffusion processes. A Hamiltonian formulation is used to determine the maximum likelihood paths for the growth and decay of nonequilibrium fluctuations, in the same limit, subject to the imposed constraints. The paths of maximum likelihood manifest a symmetry in past and future and are the stationary conditions of the constrained thermodynamic variational principle of least dissipation of energy. The power balance equations supply the required constraints and the most likely path for the growth of a fluctuation is characterized by a negative entropy production. The entropy plays the role of the quasipotential of Ventsel' and Freidlin and exit from a bounded domain containing a deterministically stable steady state is made at that state on the boundary with maximum entropy.

Self-Consistent Nonequilibrium Description of Phase-Slip States in Superconducting Filaments

Abstract: Inhomogeneous dissipative states found in a current-driven superconducting filament have been investigated with explicit allowance for depairing and coupling between pairs and quasiparticles off equilibrium. The resulting charge imbalance is insensitive to the gapless approximation used over a wide range of parameters; it can induce additional synchronized phase-slip centers, and leads to novel effects related to a mismatch between the core and the wings of each phase-slip center if local equilibrium cannot be maintained.