Showing papers on "Non-equilibrium thermodynamics published in 1981"

On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state

Abstract: It is pointed out that chemical reactions which show an absorbing stationary state in the master-equation approach (e.g. Schlogl's first reaction) exhibit nevertheless a second order phase transition in non-zero dimensional macroscopic systems. The relation to Reggeon field theory is given more directly than by Grassberger et al. using the functional integral formalism of statistical dynamics. As a new result the correlation length exponent ν and the order parameter exponent β are found toO(e2) in an ɛ-expansion around the upper critical dimensiondc=4.

The principles of chemical equilibrium : with applications in chemistry and chemical engineering

Abstract: Preface to the first edition Preface to the fourth edition List of symbols Values of physical constants Part I. The Principles of Thermodynamics: 1. First and second laws 2. Auxiliary functions and conditions of equilibrium Part II. Reaction and Phase Equilibria: 3. Thermodynamics of gases 4. Equilibria of reactions involving gases 5. Phase rule 6. Phase equilibria in single component systems 7. General properties of solutions and the Gibbs-Duhem equation 8. Ideal solutions 9. Non-ideal solutions 10. Reaction equilibrium in solution Part III. Thermodynamics in Relation to the Existence of Molecules: 11. Statistical analogues of entropy and free energy 12. Partition function of a perfect gas 13. Perfect crystals and the third law 14. Configurational energy and entropy 15. Chemical equilibrium in relation to chemical kinetics Appendix Index.

Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: I. Generalized fluctuation-dissipation theorem

Abstract: The paper is devoted to the theory of thermal fluctuations in nonlinear macroscopic systems and to the derivation of variational principles of nonlinear nonequilibrium thermodynamics. In the first part of the paper rigorous universal fluctuation-dissipation relations for nonlinear classical and quantum systems, subjected to dynamic as well as thermodynamic perturbations, are derived and analyzed. General expressions for dissipative fluxes and nonlinear transfer coefficients with the help of fluctuation cumulants are found. The canonical structure of nonlinear evolution equations of macrovariables is derived and the rule of introducing langevinian random forces into these equations, in accordance with fluctuation-dissipation relations. A Markovian theory of fluctuations in a stationary nonequilibrium state is constructed.

Heat and thermodynamics : an intermediate textbook

Abstract: Part 1: fundamental concepts temperature and the Zeroth law of thermodynamics simple thermodynamic systems heat and the first law of thermodynamics ideal gas the second law of thermodynamics the Carnot cycle and the thermodynamic temperature scale entropy pure substances mathematical methods open systems. Part 2: applications of fundamental concepts statistical mechanics thermal properties of solids critical phenomena higher-order phase transitions chemical equilibrium ideal-gas reactions heterogenous systems answers to selected problems.

Fluctuations about simple nonequilibrium steady states

Abstract: The Langevin formalism that describes fluctuations about thermodynamic equilibrium is extended to study hydrodynamic nonequilibrium steady states. The limitations of our generalization are discussed as well as the connection between experimental and theoretical quantities which is more subtle than in equilibrium. The spectrum for Brillouin scattering from a fluid in a shear flow or temperature gradient is simply obtained by Langevin methods. The latter problem exhibits an asymmetry in the height of the peaks inversely proportional to the square of the scattering wave vector. We also construct a microscopic ensemble that is applicable to a variety of hydrodynamic nonequilibrium steady states, and then verify for a particular model that our extension of the Langevin method agrees with a fully microscopic calculation.

Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: II. Kinetic potential and variational principles for nonlinear irreversible processes

Abstract: On the basis of a complete system of fluctuation-dissipation relations, considered in the first part of this series, a variational principle for nonlinear irreversible processes is derived. According to this principle the virtual entropy production functional (analogous to the action in mechanics) has an absolute minimum meaning on the real trajectory of a system. The universal structure of the “kinetic potential” and the “lagrangian” of a system, each contain complete information about fluctuations of macrovariables. The connection of the lagrangian with the markovian kinetic operator of macrovariables is stated. Fundamental properties of dissipative potentials, reflecting microscopic reversibility, are considered. The derived variational principle can be applied to closed systems (the steady state of which is equilibrium) as well as to open ones (when external dynamic forces cause entropy flux through the system and put it into a steady non-equilibrium state). Canonical transformations of macrovariables are considered.

Thermodynamics of relativistic systems

Abstract: This paper will review recent progress in the covariant formulation of thermodynamics and statistical mechanics, with emphasis on two topics: (i) a consistent treatment of transient effects which avoids the paradox of an infinite speed of heat, and (ii) the thermodynamics of black holes.

Nonequilibrium fluctuations in μ space

Abstract: The properties of fluctuations inμ space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the Liouville or the Master equation. In particular we study the one-, two-, etc., time correlation functions that describe the spatial and temporal behavior of the fluctuations inμ space. Explicit solutions are obtained for a dilute gas. The Langevin approach is briefly discussed. Our results are compared with those obtained in the extensive literature, which is reviewed in some detail.

Free volume, excess entropy and mechanical behavior of polymeric glasses

Abstract: Free volume fraction of the Williams-Landel-Ferry(WLF)-Doolittle type has been applied to the analysis of the nonequilibrium state for the glassy polymers. The free volume fraction is a two parameter variable since it depends on the free volume and the occupied volume. The excess entropy is derived from the mixing of vacant and occupied sites, and for polymers a factor is added which corresponds to disordering the molecular segments. A relationship between the excess entropy and enthalpy is derived. For a given level of fractional free volume, there is a unique rate constant associated with changing that level of the fractional free volume. The reciprocal of this rate constant, which depends on the exponential order of the fractional free volume, can be considered as a time constant for changing the molecular conformational probability, and its value is in the order of the average dielectric relaxation time in the corresponding state. When mechanical deformation is. imposed with a rate which is too fast as compared to this time constant, the deformation without a change in the conformational probability, i.e., the reversible elastic deformation, will ensue. In contrast, a sufficiently slow deformation will be accompanied by a change in fractional free volume and the excess entropy, and the above-mentioned time constant will change with deformation. Since dilation will tend to shorten this time constant, tensile deformation will result in reducing the modulus accompanied by the increase in entropy. Shear deformation is considered as a mixture of compression and tension, where only tension contributes to a change in entropy, and the net result is the strain softening which can be predicted from the tensile behavior. Uniaxial compression is controlled by the shear behavior, and the excess entropy and the fractional free volume increase, while the occupied volume decreases with strain. A constitutive relationship has been proposed which accounts for the effects of temperature, pressure, strain rates and thermal history on nonlinear viscoelastic behavior of polymeric glass.

Thermodynamics of interfacial phenomena

Abstract: This paper reviews some of the problems associated with the formulation of the thermodynamics of interfacial phenomena. Special reference is made to the solid/liquid interface and stress is laid on the usefulness of making a thermodynamic analysis of experimental data before attempting an interpretation in terms of a molecular theory. An appropriate set of equations is developed, their application is discussed and a method of using adsorption data for the assessment of the relative wettability of surfaces is proposed. The thermodynamic characteristics, in terms of the surface tension, and the enthalpy and entropy of wetting, of some simple systems are presented and their relationship to current theories of adsorption from solution is discussed. INTRODUCTION There have been many expositions of the thermodynamics of interfacial phenomena emphasizing different aspects of the general problem. At one extreme are the most rigorous formulations which are not, however, always expressed in clearly operational terms, nor is it always easy to perceive their relationship to statistical mechanical models. On the other hand many treatments are linked either implicitly or explicitly to a molecular model of the interface, and it is then sometimes not easy to distinguish those features of the resulting equations which are independent of the chosen model from those which carry with them model— dependent characteristics. Since an increasing volume of experimental data on interfacial equilibria is becoming available, it is now an appropriate moment to establish the principles which should be followed in analysing and interpreting such information. One objective of the present paper is to emphasize the importance of identifying the thermodynamic quantities which can be derived unambiguously from experimental measurements. Only when this has been done should one seek the connection between such quantities and molecular concepts which provide a statistical mechanical interpretation of the observed phenomena. To this end we first discuss some general problems, some of which, despite the large literature on the subject, seem to have been relatively neglected. We then use the case of solid/liquid interfaces as an example of the application of thermodynamics to interfacial phenomena, and illustrate the methods by some experimental data on simple systems. Finally, a brief discussion is given of the problems of the molecular interpretation of adsorption. GENERAL THERMODYNAMIC PROBLEMS A very general thermodynamic analysis of adsorption, applicable to gas/solid, solid/liquid, liquid/liquid and liquid/gas interfaces was given by Schay (Ref.l) at the 1st International Conference on Colloid and Surface Science. As he pointed out this quite abstract and formal treatment needs further specification to make it operational. An appropriate choice of operational variables has to be made, the most expedient choice being dependent on the particular kind of interface under consideration. Thus, for example, in the case of liquid! gas and liquid/liquid interfaces accurate direct measurement of adsorption is difficult (except in the case of insoluble films) while the surface tension is directly measurable (Note a). In contrast, for the solid/liquid and solid/gas interfaces the adsorption can be Note a. It may be commented that for the liquid/gas interface it is in principle possible to determine the relative adsorption (defined later), although the experimental difficulties, in for example the McBain microtome method, are such that only a low accuracy is attainable.

Observability of hysteresis in first-order equilibrium and nonequilibrium phase transitions

Abstract: The general conditions under which a system undergoing a first-order phase transition will exhibit hysteresis behavior, rather than simple jump behavior, are obtained. These are expressed in terms of the intrinsic time scales of the system and the time scale of variation of the control parameter. The size of the critical region is estimated. Estimates of the characteristic times are made for some equilibrium and nonequilibrium systems to show hysteresis behavior.

Irreversible thermodynamics in petrology

Abstract: The formulation of reaction rates and transport rates from the point of view of entropy production can help elucidate petrologic processes. The theory of irreversible thermodynamics relates fluxes of heat or mass linearly to thermodynamic forces (temperature gradients or chemical potential gradients) near equilibrium. A consequence of the general theory of irreversible thermodynamics is that each flux may be influenced by any of the thermodynamic forces. This type of coupling leads to such effects as thermal diffusion, the Soret effect, and uphill diffusion. The theory, however, constrains the number and size of the coupling phenomenological coefficients. Estimates of the coupling phenomenological coefficients enable a calculation of the importance of these coupling effects. The linear theory of irreversible thermodynamics relates the rates of reactions to the free energy difference of the reaction. This relation can be used along with experimental data to obtain the individual rates of reactions in petrology. The behavior of systems far from equilibrium is shown to be different from that near equilibrium. In particular, the formation of spatial patterns so common in petrology, is intimately related to the action of a system, when far from equilibrium. The analysis of Liesegang type models as well as the spatialmore » patterns arising from autocatalytic effects can provide useful insights into the formation of differentiated layering in petrology. (JMT)« less

Mosaic nonequilibrium thermodynamics describes biological energy transduction.

Abstract: A procedure, called "mosaic nonequilibrium thermodynamics," for describing ion movement and energy transduction in biological membranes is tested in a model system: bacteriorhodopsin liposomes. The important steps in the theoretical derivations are summarized; one of the experimental tests of the postulated fundamental flow-force relationships is shown. Furthermore, how the quantitative method, even if used only qualitatively, facilitates analysis and understanding of experimental results (in this case, the effect of medium composition on the development of pH gradient and membrane potential in the bacteriorhodopsin liposomes) is shown. The main advantage of this method lies in its quantitative description of the effect of variation of system parameters on the performance of, in this case, the reconstituted proton pump bacteriorhodopsin. As an example, the method is shown to explain quantitatively the dependence of the steady-state pH gradient on the light intensity. Even in more refined analyses of experiments, the quantitative theoretical description is in full accordance with the experimental results; this is illustrated by considering the effect of valinomycin on the dependence of the initial rate of proton uptake into bacteriorhodopsin liposomes on light intensity. It is concluded that mosaic nonequilibrium thermodynamics describes ion movement and energy transduction in the model system of bacteriorhodopsin liposomes and, therefore, may be applied to any other biological system performing such processes.

Hydrodynamic and chemical stability of fluid—fluid reacting interfaces: I. General theory for aperiodic regimes

Abstract: Under nonequilibrium conditions, the coupling between surface chemical reactions and hydrodynamics can induce the onset of convection at an interface between two immiscible Newtonian fluids. A linear analysis of interfacial stability is performed for any number of fluctuating species. The uniform reference steady state is at rest. A nonequilibrium surface elasticity coefficient is defined in terms of the surface relaxation processes. The study is restricted to aperiodic regimes. It is qualitatively and quantitatively shown that unstable and marginal aperiodic regimes can occur only for negative values of the surface elasticity. The instability is due to the self-amplification of the fluctuations of the surface tension. The chemical kinetic conditions necessary for the occurrence of this phenomenon are discussed. Intrinsically (i.e., without convection) unstable—aperiodic regimes with respect to time—surface chemical reactions always induce nonoscillatory unstable mechanochemical regimes, for the same values of the chemical parameters, when these processes are coupled with hydrodynamics. The chemical positive feedback which is responsible for the intrinsic chemical instability is then the fundamental destabilizing factor for the interfacial instability. In the absence of feedback loops in the chemical scheme, unstable mechanochemical regimes are also possible owing to the competition between interfacial chemical and convective processes. The qualitative behavior of the solutions of the dispersion equation is discussed, as well as the roles of the viscosities in the bulk phases and in the surface. New and general stability conditions are obtained.

Nonlinear transport equations in statistical mechanics

Abstract: A simple projection operator method is developed for computing nonequilibrium ensemble averages for systems that are close to a state of local equilibrium. The formalism used here is a straight-forward generalization of the Mori-Zwanzig techniques used in linear response theory and it avoids many of the technical difficulties associated with time-dependent projection operators. The method is used here to derive gradient expansions for nonequibrium average values about their values in local equilibrium. This is used to derive the nonlinear hydrodynamic equations for a pure fluid, to Burnett order.

Higher-order Einstein relations for nonlinear charge transport

Abstract: Nonlinear terms in relations for current densities are treated macroscopically, semimicroscopically and microscopically. In the macroscopic treatment, terms in phi 2, E2, (grad n)2,(del)2n, and E.grad n are included, where phi is the electrostatic potential, n is the carrier concentration and E is the electric field. The power series expansion of the current density is valid for equilibrium and yields conductivity-diffusion type Einstein relations. In the semimicroscopic approach, a perturbation theory for the density matrix is used, and Einstein relations are then derived by equating the average of the current density operator to zero. In the microscopic approach a Kubo formalism is developed, based on a local nonequilibrium distribution function due to Mori (1958). This leads to Einstein relations via correlation functions and Liouville's equation. A set of such relations which emerge consistently from such a treatment is given.

Nonequilibrium Phase Transitions and Chemical Instabilities

Abstract: The effect of inhomogeneous fluctuations on instabilities in various nonlinear chemical models is studied in terms of concepts developed in the theory of equilibrium phase transitions.

The modified moment method, irreversible thermodynamics, and the nonlinear viscosity of a dense fluid

Abstract: The extended Gibbs relation is derived for dense fluids in a nonequilibrium state from the kinetic equation for dense fluids proposed in a previous paper. The method used for derivation is basically the same as that used in the case of dilute (ideal) gases described by the Boltzmann equation. The extended Gibbs relation derived is, as it should be, in the same form as for ideal gases, but the evolution equations for macroscopic variables involved contain contributions due to molecular interactions. This derivation together with that of the corresponding relation for ideal gases previously reported provides us with a mathematical basis to study irreversible thermodynamics for systems at any nonequilibrium state without making the assumption of local equilibrium. The non‐Newtonian viscosity is also studied for a dense fluid with the stationary solution of the evolution equation for stress tensor and viscosity formulas are obtained as extensions of the formulas for ideal gases reported previously.

Einstein and statistical thermodynamics. I. Relativistic thermodynamics

Abstract: The influence of Einstein on statistical thermodynamics is illustrated by considering, from both the historical and a modern point of view, the relativistic transformation of thermodynamic quantities.

Two continuum approaches to a wavelength-dependent description of heat conduction

Abstract: Heat conduction in rigid solids is examined with the purpose of setting up a systematic thermodynamic description accounting for frequency- and wavelength-dependent phenomena. Such a scheme is exhibited in two versions, namely extended irreversible thermodynamics and hidden variable thermodynamics. Though starting from different assumptions, the two versions lead to the same practical conclusions, which in turn may be identified with Chester's microscopic results on high-frequency thermometry. Also a generalization compatible with discontinuity propagation is proposed.