Showing papers on "Non-equilibrium thermodynamics published in 1987"

Statistical Thermodynamics of Nonequilibrium Processes

Abstract: The structure of the theory ofthermodynamics has changed enormously since its inception in the middle of the nineteenth century. Shortly after Thomson and Clausius enunciated their versions of the Second Law, Clausius, Maxwell, and Boltzmann began actively pursuing the molecular basis of thermo dynamics, work that culminated in the Boltzmann equation and the theory of transport processes in dilute gases. Much later, Onsager undertook the elucidation of the symmetry oftransport coefficients and, thereby, established himself as the father of the theory of nonequilibrium thermodynamics. Com bining the statistical ideas of Gibbs and Langevin with the phenomenological transport equations, Onsager and others went on to develop a consistent statistical theory of irreversible processes. The power of that theory is in its ability to relate measurable quantities, such as transport coefficients and thermodynamic derivatives, to the results of experimental measurements. As powerful as that theory is, it is linear and limited in validity to a neighborhood of equilibrium. In recent years it has been possible to extend the statistical theory of nonequilibrium processes to include nonlinear effects. The modern theory, as expounded in this book, is applicable to a wide variety of systems both close to and far from equilibrium. The theory is based on the notion of elementary molecular processes, which manifest themselves as random changes in the extensive variables characterizing a system. The theory has a hierarchical character and, thus, can be applied at various levels of molecular detail."

Thermodynamics and Control of Biological Free-Energy Transduction

Abstract: Chapter 1. The basis for mosaic non-equilibrium thermodynamics. Equilibrium statistical mechanics: a basis for thermodynamics in (quantum) mechanics and statistics. Equilibrium thermodynamics. 'Classical' or 'phenomenological' non-equilibrium thermodynamics. The master equation approach to non-equilibrium systems. The Langevin approach: near-equilibrium statistical mechanics. An extension to far from equilibrium systems. Kinetics. Stability of metabolic states as the basis for thermodynamic and control properties of systems. The theory of metabolic control. The biology of some systems. Introduction to some biochemical methods. Chapter 2. The core of mosaic non-equilibrium thermodynamics. The principles. Flow-force relationships for elementary processes close to equilibrium. Force-flow relations for elementary processes far from equilibrium. Reciprocity of flow-force relations. Steady-state criteria. Towards the mosaic of elemental processes: examples. Chapter 3. Applications of mosaic non-equilibrium thermodynamics. Ion transport in bacteriorhodopsin liposomes. Mitochondrial oxidative phosphorylation. Microbial growth. Efficiency and optimisation of biological free-energy converters. Chapter 4. Control of free energy transduction . Thermodynamics and metabolic control. Control in compartmented systems. The analysis of the control of free-energy transduction in practice. Appendix A. The thermodynamics of the light-driven process. Appendix B. Statistical aspects of protonic energy coupling and metabolic chanelling. References. Subject Index.

Linearized microscopic theories of nonequilibrium solvation

Abstract: Linearized microscopic theories of equilibrium solvation can be straightforwardly extended to treat the dynamic situation. A particular example, the solvation of a newly formed ion, is developed within the mean spherical approximation. The MSA exhibits significant deviations from the Born–Marcus formula for nonequilibrium solvation energies. The solvation dynamics proceeds on several time scales. The solvation structure first forms distant from the ion, in harmony with a remark of Onsager and with previous numerical calculations of Calef and Wolynes [J. Chem. Phys. 78, 4145 (1983)].

Diffusion in a periodic Lorentz gas

Abstract: We use a constant “driving force”F d together with a Gaussian thermostatting “constraint force”F d to simulate a nonequilibrium steady-state current (particle velocity) in a periodic, two-dimensional, classical Lorentz gas. The ratio of the average particle velocity to the driving force (field strength) is the Lorentz-gas conductivity. A regular “Galton-board” lattice of fixed particles is arranged in a dense triangular-lattice structure. The moving scatterer particle travels through the lattice at constant kinetic energy, making elastic hard-disk collisions with the fixed particles. At low field strengths the nonequilibrium conductivity is statistically indistinguishable from the equilibrium Green-Kubo estimate of Machta and Zwanzig. The low-field conductivity varies smoothly, but in a complicated way, with field strength. For moderate fields the conductivity generally decreases nearly linearly with field, but is nearly discontinuous at certain values where interesting stable cycles of collisions occur. As the field is increased, the phase-space probability density drops in apparent fractal dimensionality from 3 to 1. We compare the nonlinear conductivity with similar zero-density results from the two-particle Boltzmann equation. We also tabulate the variation of the kinetic pressure as a function of the field strength,

Statistical theories of atomic transport in crystalline solids

Abstract: This review is concerned with the fundamentals of the theory of the transport of atoms through crystalline solids, such as may result from the existence of gradients of chemical and isotopic composition, electrical potential, stress, temperature, etc. The main emphasis is on the statistical description of these processes via the theory of mobile lattice imperfections-vacancies and interstitial atoms. Only processes taking place in the bulk of the solid are considered, i.e. enhanced diffusion and migration in the vicinity of dislocations, grain boundaries and other interfaces are not discussed. The various statistical theories available at the present time are reviewed against the phenomenological framework provided by nonequilibrium thermodynamics. One object of this work is to demonstrate the interrelations among the different theories and to disclose where they are equivalent. Another is to show that the means are now available to calculate all the phenomenological transport coefficients which arise in the nonequilibrium thermodynamics of these processes in terms of the assumed properties of the defects, their interactions with solute atoms, etc. Although this review is thus primarily concerned with the theory of atomic transport at an abstract level, the physical aspects of the subject are referred to throughout. Explicit solutions of the transport equations, however, are not considered.

Thermodynamics of ion hydration and its interpretation in terms of a common model

Abstract: The relationship between the conventional standard molar thermodynamic quantities of hydration of an ion and the correspon— ding quantities of solvation, that are due entirely to its inter— actions with its aqueous environment, is presented. The TATB assumption, i.e., that quantities pertaining to the tetraphenyl— arsonium cation equal those pertaining to the tetraphenylborate anion, is applied to the standard enthalpy, entropy, and Gibbs energy of hydration of ions, and to the standard partial molar heat capacity and volume of aqueous ions. A model of the hydrated ion, consisting of a layer of completely immobilized water molecules surrounded by a dielectric continuum affected by the field of the ion and water the structure of which is modified, is presented. The thickness of the first layer and the number of water molecules in it is proportional to the radius of the ion. The model is shown to be compatible with all these thermodynamic quantities.

Stable and metastable phase equilibria in the Al-Mn system

Abstract: The aim of the present investigation was resolution of certain obscure features of the Al-Mn phase diagram. The experimental approach was guided by assessment of the previous literature and modeling of the thermodynamics of the system. It has been shown that two phases of approximate stoichiometry “Al4Mn” (λ and μ) are present in stable equilibrium, λ forming by a peritectoid reaction at 693 ± 2 °C. The liquidus and stable equilibrium invariant reactions as proposed by Goedecke and Koester have been verified. A map has been made of the successive nonequilibrium phase transformations of as-splat-quenched alloys. Finally, the thermodynamic calculation of the phase diagram allows interpretation of complex reaction sequences during cooling in terms of a catalogue of all the metastable invariant reactions involving (Al), Al6Mn, λ, μ, ϕ, and Al11Mn4 phases.

Application of transient correlation functions to shear flow far from equilibrium

Abstract: Morriss and Evans recently developed a generalization of the Green-Kubo relations which is valid for nonequilibrium steady states far from equilibrium. This formalism relates the nonequilibrium response to transient time correlation functions which connect the nonequilibrium steady state to the equilibrium state. In the linear regime, the transient time correlation functions reduce to simple equilibrium Green-Kubo relations. The transient time correlation function method thus provides a long-sought-after fundamental relation between nonequilibrium molecular dynamics algorithms and the Green-Kubo formalism which is only valid close to equilibrium. In this paper we demonstrate the use of the transient time correlation function formalism for isothermal planar Couette flow. The results show that the nonlinear steady-state response can be calculated by integrating the appropriate transient response time correlation function. In particular, the nonlinear shear stress and pressure calculated in this way agree with the values calculated directly.

Thermodynamics of Nitinol

Abstract: A self‐consistent macroscopic thermodynamics is developed for the calculation of work, heat, and dissipation for thermodynamic paths of the shape memory alloy, Nitinol. The thermodynamic system analyzed is a Nitinol helix for which extensive force–length–temperature (FLT) equation of state measurements have been made. The Nitinol system exhibits significant hysteresis and is determined to be a nonequilibrium thermostatic system. A set of equations of state are provided which correlate all reversible and irreversible Nitinol thermodynamic paths to both the set of helix (FLT) thermodynamic state variables and to new ‘‘history’’ state variables. It is shown that these equations predict observed cyclic behaviors not previously interpreted. In the absence of calorimetric measurements for the Nitinol helix system, a physical assumption is made that reversible paths are of constant phase. This assumption is used to estimate the reversible path thermal and mechanical heat capacities for the Nitinol system. With t...

Quantum thermodynamics of nonequilibrium. Onsager reciprocity and dispersion-dissipation relations

Abstract: A generalized Onsager reciprocity theorem emerges as an exact consequence of the structure of the nonlinear equation of motion of quantum thermodynamics and is valid for all the dissipative nonequilibrium states, close and far from stable thermodynamic equilibrium, of an isolated system composed of a single constituent of matter with a finite-dimensional Hilbert space. In addition, a dispersion-dissipation theorem results in a precise relation between the generalized dissipative conductivity that describes the mutual interrelation between dissipative rates of a pair of observables and the codispersions of the same observables and the generators of the motion. These results are presented together with a review of quantum thermodynamic postulates and general results.

Self-synchronization of populations of nonlinear oscillators in the thermodynamic limit

Abstract: A population of identical nonlinear oscillators, subject to random forces and coupled via a mean-field interaction, is studied in the thermodynamic limit. The model presents a nonequilibrium phase transition from a stationary to a time-periodic probability density. Below the transition line, the population of oscillators is in a quiescent state with order parameter equal to zero. Above the transition line, there is a state of collective rhythmicity characterized by a time-periodic behavior of the order parameter and all moments of the probability distribution. The information entropy of the ensemble is a constant both below and above the critical line. Analytical and numerical analyses of the model are provided.

Small Systems: When Does Thermodynamics Apply?

Abstract: The validity of using temperature to describe quantitatively the state of excitation of an isolated nucleus is examined. The problem arises because of the small number of particles in a nucleus. As a consequence, it is possible to construct a heat bath and so fix the temperature. Another definition is used that leads to an uncertainty in the measured temperature which tends to zero as the number of particles in the system increases. The emphasis is on the nuclear problem but it is presumed that similar considerations apply to other small isolated systems such as single molecules, atomic clusters containing two to several hundred atoms, helium droplets, etc. >

Steepest entropy ascent in Quantum Thermodynamics

Abstract: Quantum Thermodynamics [I] is a unified quantum theory that includes within a single uncontradictory nonstatistical structure the whole of Quantum Mechanics and Classical Equilibrium Thermodynamics, as well as a general description of nonequilibrium states, their entropy, and their irreversible motion towards stable equilibrium. Quantum Thermodynamics postulates that a system has access to a much broader set of states than contemplated in Quantum Mechanics. Specifically, for a system that is strictly uncorrelated from any other system, namely, a system for which Quantum Mechanics contemplates only states that are described by a state vector I~>, Quantum Thermodynamics postulates that in addition to the quantum mechanical states there exist many other states that cannot be described by a vector I~> but must be described by a self-adjoint, unit-trace, nonnegative-definite linear operator p that we call the state operator.

Generalized Onsager symmetry.

Abstract: Onsager's symmetry theorem for transport near equilibrium is extended in two directions. A corresponding symmetry is obtained for linear transport near nonequilibrium stationary states, and the class of transport laws is extended to include nonlocality in both space and time. The results are formally exact and independent of any specific model for the nonequilibrium state.

Extended thermodynamics of non-ideal gases

Abstract: A phenomenological extended thermodynamics theory for non-ideal gases is formulated. In this theory 13 basic fields of density, velocity, pressure tensor and heat flux are considered. The coefficients in the representations of the constitutive quantities are obtained in terms of the virial coefficients of the thermal equation of state and of the free energy density. The laws of Fourier and Navier-Stokes follow from an iteration method akin to the Maxwellian iteration in the kinetic theory of gases.

Advanced classical thermodynamics

Abstract: This graduate-level text begins with basic concepts of thermodynamics and continues through the study of Jacobian theory, Maxwell equations, stability, theory of real gases, critical point theory, and chemical thermodynamics.

A comprehensive interpretation of mixing effects on stationary states and dynamical behavior of the bistable ClO−2–I− reaction in a flow reactor

Abstract: We propose an interpretation of mixing effects on temporal dissipative structures in CSTR in terms of micromixing. The bistability of the ClO−2 –I− reaction is extensively discussed. The micromixing process is successively represented by a mean field model and a coalescence redispersion model, together with a realistic kinetic scheme of the reaction. The latter was found more suited to the problem. The results are in good agreement with experimental observations previously reported, accounting for shifts in the transitions from thermodynamic branch to flow branch both in premixed and nonpremixed mode. It also accounts for dynamical behavior in the vicinity of the transition, including oscillatory fluctuations. It is finally suggested that micromixing processes could induce oscillations in otherwise nonoscillating conditions if the system was perfectly homogeneous.

Nonlinear effects in macroscopic kinetics

Abstract: Macroscopic kinetics describes relaxation in terms of macroscopic states, i.e., the distributions of density, temperature, and so on. Two types of system are examined in this review, namely, (1) closed systems (or systems interacting exclusively with a thermostat) and (2) flow systems in which the nonequilibrium state is maintained by an external agency (source of supply or pump). In both cases, states are established that do not depend (in a particular range) on the initial conditions. These are the attractor states. Spatially homogeneous states (kinetic phases) are discussed for flow systems, together with transitions between them that are the analogs of the motion of interphase boundaries. In closed systems, the establishment of equilibrium can be preceded by the appearance of other attractors in the form of intermediate asymptotic behavior. A comparison is made between similar states in different processes (chemical reactions, viscous flows, absorption of light, and so on). Stability conditions are discussed.

Dissipation in steady states of chemical systems and deviations from minimum entropy production

Abstract: According to the linear thermodynamic theory of irreversible processes, entropy production is minimized at the steady states of nonequilibrium systems. The principle of minimum entropy production is obtained if the dissipation is expanded in the deviation δ from equilibrium, truncated to lowest order (δ 2 ), and then differentiated. At this level of apprximation, the derivative of the dissipation is linear in δ and vanishes at the steady state. For a simple chemical reaction mechanism in a well-defined model system, we have derived the corrections to this approximation, by first evaluating the dissipation and its derivative exactly, and then expanding as a series in δ. To leading order in δ, the ratio of the derivative to the dissipation at the steady state is 1 2 (in dimensionless units), and this ratio does not decrease as equilibrium is approached. The steady state coincides with the state of minimum entropy production only at equilibrium. Given sufficient accuracy in measurements of species concentrations, the breakdown of the principle of minimum entropy production can be detected experimentally when the relative standard deviation in measurements of the dissipation is less than δ. Our example shows that the dissipation in a reaching chemical system may increase in time, in the later stages of relaxation toward a near-equilibrium steady state.

Entropy in the teaching of introductory thermodynamics

Abstract: An elementary physics course on thermodynamics is presented. It uses entropy and temperature as fundamental, undefined objects. Suggestions on how to do this can be traced back to H. L. Callendar [Proc. Phys. Soc. (London) 23, 153 (1911)].

Algebraic symmetry in chemical reaction systems at stationary states arbitrarily far from thermodynamic equilibrium

Abstract: For systems of chemical reactions the phenomenological equations of nonequilibrium thermodynamics display the differential symmetry of Onsager reciprocity in general only for stationary states in the vicinity of thermodynamic equilibrium, as is well known. It will be shown here, however, that systems of chemical reactions, on the macroscopic, phenomenological level of chemical kinetics, do show a less stringent symmetry at all stationary states arbitrarily far from equilibrium. The key is a reformulation of the kinetic equations for single chemical reactions as resistive laws relating the force driving a reaction to the rate of the reaction through a (nonlinear) generalized chemical resistance; these laws are analogous to the ‘‘voltage=current times resistance’’ laws for resistive elements in electrical networks. The resistive laws for single reactions then lead naturally to stationary state relations for systems of coupled chemical reactions of the form of the phenomenological equations of nonequilibrium thermodynamics, and these relations display algebraic symmetry at stationary states arbitrarily far from equilibrium, although the differential symmetry of Onsager reciprocity is in general not valid. An example illustrates the relation of the symmetry property for chemical reactions to that displayed by RC electrical networks and how the chemical symmetry follows from analogs of Kirchhoff’s laws obeyed by systems of chemical reactions.

Critical behavior in nonequilibrium phase transitions.

Abstract: The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.

Fluids with internal degrees of freedom. I. Extended thermodynamics approach

Abstract: Extended irreversible thermodynamics (EIT) is used to derive a complete set of time evolution equations for the state variables describing a general polyatomic fluid. The internal degrees of freedom of the fluid are represented by suitable nonconserved variables. In particular, these time evolution equations are shown to resemble relaxation‐type equations. The sign of the unknown coefficients included in such equations is undetermined. However, when a comparison is made with the results obtained from the moment solution method of a kinetic equation for a dilute polyatomic fluid, several of the general features of the phenomenological results are clarified. Indeed, the predictions of kinetic theory fully agree with the basic equations of EIT. This provides a mesoscopic foundation for the theory. The sign of the unknown coefficients appearing in the relaxation‐type equations for the nonconserved variables is such that the corresponding relaxation times are positive definite. Therefore, such equations are indeed relaxation equations. Other features of the phenomenological theory are also discussed on the light of the kinetic theoretical results. Further, the usefulness of the theory will be addressed in connection with a subsequent paper where the results here obtained will be used to compute the Rayleigh–Brillouin spectrum for a polyatomic fluid.