Showing papers on "Non-equilibrium thermodynamics published in 1997"

Nonequilibrium Equality for Free Energy Differences

Abstract: An expression is derived for the equilibrium free energy difference between two configurations of a system, in terms of an ensemble of finite-time measurements of the work performed in parametrically switching from one configuration to the other. Two well-known identities emerge as limiting cases of this result.

Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach

Abstract: In has recently been shown that the Helmholtz free-energy difference between two equilibrium configurations of a system may be obtained from an ensemble of finite-time (nonequilibrium) measurements of the work performed in switching an external parameter of the system. Here this result is established, as an identity, within the master equation formalism. Examples are discussed and numerical illustrations provided.

Thermodynamics and Kinetics of a Brownian Motor

Abstract: Nonequilibrium fluctuations, whether generated externally or by a chemical reaction far from equilibrium, can bias the Brownian motion of a particle in an anisotropic medium without thermal gradients, a net force such as gravity, or a macroscopic electric field. Fluctuation-driven transport is one mechanism by which chemical energy can directly drive the motion of particles and macromolecules and may find application in a wide variety of fields, including particle separation and the design of molecular motors and pumps.

Dynamics and thermodynamics of complex fluids. I. Development of a general formalism

Abstract: We recognize some universal features of macroscopic dynamics describing the approach of a well-established level of description (that is, successfully tested by experimental observations) to equilibrium. The universal features are collected in a general equation for the nonequilibrium reversible-irreversible coupling (abbreviated as GENERIC). In this paper we formulate a GENERIC, derive properties of its solutions, and discuss their physical interpretation. The relation of the GENERIC with thermodynamics is most clearly displayed in a formulation that uses contact structures. The GENERIC is also discussed in the presence of noise. In applications we either search for new governing equations expressing our insight into a particular complex fluid or take well-established governing equations and cast them into the form of a GENERIC. In the former case we obtain the governing equations as particular realizations of the GENERIC structure; in the latter case we justify the universality of the GENERIC and derive some properties of solutions. Both types of applications are discussed mainly in the following paper [Phys. Rev. E 56, 6633 (1997)].

Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism

Abstract: For a number of well-known time-evolution equations for nonequilibrium systems we extract a common structure from these equations, referred to as a general equation for the nonequilibrium reversible-irreversible coupling (GENERIC). This fundamental structure is determined by four building blocks, two ``potentials'' (total energy and entropy) and two ``matrices.'' We illustrate for various examples how three of the four building blocks can be determined in a rather straightforward manner so that, within our GENERIC approach to nonequilibrium dynamics, understanding of a given nonequilibrium system is reduced to determining a single ``metric matrix,'' or friction matrix, either empirically or by more microscopic considerations. In formulating nonisothermal polymer kinetic theories, we show how the general structure provides a clear distinction between spring potentials of energetic and entropic origins in the various time-evolution equations.

Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics

Abstract: We show that, in nonequilibrium systems with small heat flows, there is a time-scale-dependent effective temperature that plays the same role as the thermodynamical temperature in that it controls the direction of heat flows and acts as a criterion for thermalization. We simultaneously treat the case of stationary systems with weak stirring and of glassy systems that age after cooling and show that they exhibit very similar behavior provided that time dependences are expressed in terms of the correlations of the system. We substantiate our claims with examples taken from solvable models with nontrivial low-temperature dynamics, but argue that they have a much wider range of validity. We suggest experimental checks of these ideas.

Thermodynamics and the measure of entanglement

Abstract: We point out formal correspondences between thermodynamics and entanglement. By applying them to previous work, we show that entropy of entanglement is the unique measure of entanglement for pure states.

Thermodynamics and Rheology

Abstract: Introduction. I. Kinematics. II. Dynamics. III. Deformation and Stress. IV. Non-Equilibrium Thermodynamics. V. Thermodynamics of Deformation. Systems Close to Equilibrium. VI. Thermodynamics of Deformation. Systems Far From Equilibrium. VII. Electric Polarization in Flowing Media. VIII. Applications of the Theory. Appendix: A.1. The Basic Operations. A.2. Symmetric and Antisymmetric Tensors. A.3. Tensor Products. A.4. Eigenvalues and Invariants. A.5. Orthogonal Tensors. A.6. Isotropic Tensors. A.7. Derivatives. A.8. Integral Theorems. References.

Modified nonequilibrium molecular dynamics for fluid flows with energy conservation

Abstract: The nonequilibrium molecular dynamics generated by the SLLOD algorithm [so called due to its association with the DOLLS tensor algorithm (D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic, New York, 1990)] for fluid flow is considered. It is shown that, in the absence of time-dependent boundary conditions (e.g., shearing boundary conditions via explicit cell dynamics or Lees–Edwards boundary conditions), a conserved energy, H exists for the equations of motion. The phase space distribution generated by SLLOD dynamics can be explicitly derived from H. In the case of a fluid confined between two immobile boundaries undergoing planar Couette flow, the phase space distribution predicts a linear velocity profile, a fact which suggests the flow is field driven rather than boundary driven. For a general flow in the absence of time-dependent boundaries, it is shown that the SLLOD equations are no longer canonical in the laboratory momenta, and a modified form of the SLLOD dynamics is presented which is valid arbitrarily far from equilibrium for boundary conditions appropriate to the flow. From an analysis of the conserved energy for the new SLLOD equations in the absence of time-dependent boundary conditions, it is shown that the correct local thermodynamics is obtained. In addition, the idea of coupling each degree of freedom in the system to a Nose–Hoover chain thermostat is presented as a means of efficiently generating the phase space distribution.

Irreversibility of classical fluctuations studied in analogue electrical circuits

Abstract: Fluctuations around some average or equilibrium state arise universally in physical systems. Large fluctuations — fluctuations that are much larger than average — occur only rarely but are responsible for many physical processes, such as nucleation in phase transitions, chemical reactions, mutations in DNA sequences, protein transport in cells and failure of electronic devices. They lie at the heart of many discussions1,2,3,4,5 of how the irreversible thermodynamic behaviour of bulk matter relates to the reversible (classical or quantum-mechanical) laws describing the constituent atoms and molecules. Large fluctuations can be described theoretically using hamiltonian6,7 and equivalent path-integral8,9,10,11,12 formulations, but these approaches remain largely untested experimentally, mainly because such fluctuations are rare and also because only recently was an appropriate statistical distribution function formulated11. It was shown recently, however, that experiments on fluctuations using analogue electronic circuits allow the phase-space trajectories of fluctuations in a dynamical system to be observed directly12. Here we show that this approach can be used to identify a fundamental distinction between two types of random motion: fluctuational motion, which takes the system away from a stable state, and relaxational motion back towards this state. We suggest that macroscopic irreversibility is related to temporal asymmetry of these two types of motion, which in turn implies a lack of detailed balance and corresponds to non-differentiability of the generalized nonequilibrium potential in which the motion takes place.

Towards granular hydrodynamics in two dimensions

Abstract: We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions compare well with numerical simulations in the nearly elastic limit. It is also seen that the system can achieve a nonequilibrium steady-state with asymmetric velocity distributions, and we discuss the conditions under which such situations occur.

On the thermodynamics of fractional damping elements

Abstract: Constitutive models of viscoelasticity in combination with fractional differential operators are successfully used by many authors to describe the mechanical properties of polymers. The topic of the present paper is the investigation of rheological models incorporating fractional damping elements from the point of view of thermodynamics. We take the Clausius Duhem inequality as admissibility criterion and investigate uniaxial and three-dimensional deformation processes at constant temperature. We specify sufficient conditions and show that rheological models, which consist of springs in combination with fractional dashpots, are compatible with the dissipation principle. As a new aspect of the subject, we present a systematic method for deriving the free energy functionals. With the help of two examples we demonstrate that the free energy of fractional systems can be derived as a generalisation of related discrete systems. To illustrate this method, we study in detail an isolated fractional dashpot (also known as a power-law model) and a fractional standard solid (Zener model). Finally, we propose a three-dimensional formulation of the fractional Zener model and specify the corresponding free energy functional.

Directionality principles in thermodynamics and evolution

Abstract: Directionality in populations of replicating organisms can be parametrized in terms of a statistical concept: evolutionary entropy. This parameter, a measure of the variability in the age of reproducing individuals in a population, is isometric with the macroscopic variable body size. Evolutionary trends in entropy due to mutation and natural selection fall into patterns modulated by ecological and demographic constraints, which are delineated as follows: (i) density-dependent conditions (a unidirectional increase in evolutionary entropy), and (ii) density-independent conditions, (a) slow exponential growth (an increase in entropy); (b) rapid exponential growth, low degree of iteroparity (a decrease in entropy); and (c) rapid exponential growth, high degree of iteroparity (random, nondirectional change in entropy). Directionality in aggregates of inanimate matter can be parametrized in terms of the statistical concept, thermodynamic entropy, a measure of disorder. Directional trends in entropy in aggregates of matter fall into patterns determined by the nature of the adiabatic constraints, which are characterized as follows: (i) irreversible processes (an increase in thermodynamic entropy) and (ii) reversible processes (a constant value for entropy). This article analyzes the relation between the concepts that underlie the directionality principles in evolutionary biology and physical systems. For models of cellular populations, an analytic relation is derived between generation time, the average length of the cell cycle, and temperature. This correspondence between generation time, an evolutionary parameter, and temperature, a thermodynamic variable, is exploited to show that the increase in evolutionary entropy that characterizes population processes under density-dependent conditions represents a nonequilibrium analogue of the second law of thermodynamics.

Local non-equilibrium transport models

Abstract: Local non-equilibrium models of heat and mass transport processes are considered and shown to form a hierarchy of parabolic and hyperbolic equations whose order increases with deviation from local equilibrium. The basic features of these models, in particular their relationship to generalized irreversible thermodynamics, are discussed.

``Nernst theorem'' and black hole thermodynamics

Abstract: The Nernst formulation of the third law of ordinary thermodynamics (often referred to as the ``Nernst theorem'') asserts that the entropy, $S$, of a system must go to zero (or a ``universal constant'') as its temperature, $T$, goes to zero. This assertion is commonly considered to be a fundamental law of thermodynamics. As such, it seems to spoil the otherwise perfect analogy between the ordinary laws of thermodynamics and the laws of black hole mechanics, since rotating black holes in general relativity do not satisfy the analog of the ``Nernst theorem''. The main purpose of this paper is to attempt to lay to rest the ``Nernst theorem'' as a law of thermodynamics. We consider a boson (or fermion) ideal gas with its total angular momentum, $J$, as an additional state parameter, and we analyze the conditions on the single particle density of states, $g(\epsilon,j)$, needed for the Nernst formulation of the third law to hold. (Here, $\epsilon$ and $j$ denote the single particle energy and angular momentum.) Although it is shown that the Nernst formulation of the third law does indeed hold under a wide range of conditions, some simple classes of examples of densities of states which violate the ``Nernst theorem'' are given. In particular, at zero temperature, a boson (or fermion) gas confined to a circular string (whose energy is proportional to its length) not only violates the ``Nernst theorem'' also but reproduces some other thermodynamic properties of an extremal rotating black hole.

Nonlinear bulk viscosity and inflation

Abstract: We develop a nonlinear generalization of the causal linear thermodynamics of bulk viscosity, incorporating the positivity of the entropy production rate and the effective specific entropy. The theory is applied to viscous fluid inflation (which is necessarily far from equilibrium), and we find thermodynamically consistent inflationary solutions, both exponential and power law.

Vibrational favoring effect in DSMC dissociation models

Abstract: Several common models for dissociation reactions in direct simulation Monte Carlo calculations are analyzed quantitatively under general equilibrium and nonequilibrium conditions. The models differ in the degree to which the internal energy of the colliding particles contributes to the probability of dissociation. Test calculations in an equilibrium bath show that the temperature dependence of the predicted equilibrium rate constant, a commonly used measure of accuracy, is dominated by the collision selection algorithm, rather than the details of the dissociation model, and is thus a poor measure of physical validity or accuracy. The distribution of internal energy states of molecules selected for dissociation under the bath conditions, as used for analysis here, is a preferred means to assess accuracy, and is available qualitatively from existing theory. Recent state-specific quasi-classical trajectory calculations allow for quantitative assessment for certain molecules. Certain singularities present in ...

Dynamics and thermodynamics of delayed population growth

Abstract: Grup de Fi ´sica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, E-08193 Bellaterra, Spain~Received 31 January 1997!The dynamic and thermodynamic properties of delayed nonlinear reaction-diffusion equations describingpopulation growth with memory are analyzed. In the dynamic study we first apply the speed selection mecha-nisms for wave fronts connecting two steady states obtaining, on one hand, a decrease in the lower boundspeed, and also an upper bound velocity; we also calculate an exact wave front solution. In the thermodynamicstudy, we show an agreement between the stochastic description and extended irreversible thermodynamics inthe presence of a source of particles. @S1063-651X~97!10205-7#PACS number~s!: 05.70.2a, 05.40.1jI. INTRODUCTION

A study of viscosity inhomogeneity in porous media

Abstract: The theory of transport in highly inhomogeneous systems, developed recently by Pozhar and Gubbins, and the nonequilibrium molecular dynamics (NEMD) technique are employed to study the viscosity of WCA fluids confined in narrow slit pores of width 5.1 and 20σ at reduced densities ρσ3 of 0.422–0.713. Calculated quantities include the equilibrium and nonequilibrium density profiles, equilibrium pair correlation functions, flow velocity profiles, and the viscosity profiles. NEMD simulation results are compared with the theoretical predictions. The agreement is good except for the region within one molecular diameter from the walls. The viscosity was found to vary with position across the pore.

Crystal Growth of the Lennard-Jones (100) Surface by Means of Equilibrium and Nonequilibrium Molecular Dynamics

Abstract: On the basis of Onsager's hypothesis a new method is presented to calculate growth rate constants of various crystal faces from the fluctuations of interfaces during NVT simulations. The method is applied to the (100) face of a Lennard-Jones crystal grown from the melt. The results are in perfect agreement with those obtained by means of NPT nonequilibrium simulations. The new method allows for much better statistics at the cost of much less computation time. The use of Onsager's hypothesis to derive the microscopic expression for the growth rate constant may serve as an example for applications in other fields.

Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium

Abstract: Analytical Fokker–Planck calculations are used to accurately determine the minimum power that must be recycled in order to maintain a plasma out of thermodynamic equilibrium despite collisions. For virtually all possible types of fusion reactors in which the major particle species are significantly non-Maxwellian or are at radically different mean energies, this minimum recirculating power is substantially larger than the fusion power. Barring the discovery of methods for recycling the power at exceedingly high efficiencies, grossly nonequilibrium reactors will not be able to produce net power.

Effects of Mass Action Equilibria on Fixed-Bed Multicomponent Ion-Exchange Dynamics

Abstract: A generalized parallel pore and surface diffusion model and associated dynamic simulation program have been developed for multicomponent fixed-bed ion-exchange processes. Both equilibrium and nonequilibrium mass action laws are used to describe stoichiometric ion exchange. Model equations are solved numerically for frontal, pulse, or sequential loading processes. Analytical solutions obtained from a local equilibrium theory for binary systems and experimental data of two multicomponent systems served as benchmarks for the numerical solutions. The results indicate that the parallel pore and surface diffusion model should be considered for nonlinear large-particle systems. A parametric study shows that a major difference in fixed-bed dynamics between mass action and Langmuir systems lies in the propagation of diffuse waves of multivalent ions. Generally, the higher the valence or mass action equilibrium constant, the more pronounced the tailing of diffuse waves, which results in apparent adsorption hysteres...

The Dynamic Response

Abstract: For the nonequilibrium response the second law takes the form of the internal dissipation inequality (9.2.4) and the combination of the frame indifference with the symmetry leads to explicit representations of the nonequilibrium response functions. As these depend on more vectorial and tensorial variables (namely on F,θ D g or on F θ F G ), the representation theorems are necessarily more complicated. Since there are essentially no new ideas in them, and since some parts of the development are closely parallel to those concerning the equilibrium response, the material will be presented only briefly. The rest of the chapter deals with the nonequilibrium response from a broader point of view. First, the classical linear irreversible thermodynamics, based on Onsager’s relations, will be briefly described in view of its obvious historical importance. Then a possible nonlinear generalization of the Onsager relations, namely, the assumption of the existence of the convex dissipation potential, will be presented. Finally, the relaxation models including those studied by the extended linear irreversible thermodynamics will be examined from the point of view of the thermodynamics based on the Clausius—Duhem inequality.

Reheating and causal thermodynamics

Abstract: The reheating process in inflationary universe models is considered as an out-of-equilibrium mixture of two interacting and reacting fluids, and studied within the framework of causal, irreversible thermodynamics. The evolution of the temperature and the decay rate as determined by causal thermodynamics are estimated at different stages of the process. A simple model is also used to find the perturbations of the expansion rate, including the possibility of damped oscillations.

Point defects and diffusion in thin films of GaAs

Abstract: Impurity diffusivity in thin films of GaAs is affected by native defect concentrations which were grown into the film, and which enter the film from both the substrate and the external ambient. Variations in measured diffusivity are related to native defects whose concentrations gradually relax to equilibrium values via different kinetic pathways. The time required for native defects to equilibrate depends upon the experimental design which in turn determines which region of the phase diagram that an annealing experiment begins and ends in. The Gibbs phase rule is applied to several commonly used experimental designs to show why the equilibrium native defect concentrations are generally not defined solely by temperature. The necessary conditions which define an equilibrium state, and the sufficient conditions which determine whether that equilibrium state can be approximated within a short time, are explicitly discussed. Experiments begun far from equilibrium are often associated with unusually high or low time-dependent diffusivities, but the results are often irreproducible as the native defect concentrations drift for extended periods of time. Experiments begun close to equilibrium are generally associated with reproducible diffusivities because the native defect concentrations reach constant values in a time which is short compared with the anneal period. Some diffusion results can be adequately described by equilibrium models, and the so-called ‘Fermi-level effect’ model is shown to apply as a special case of solid-vapor equilibrium. Near-equilibrium, results from several groups provide strong evidence that a Ga vacancy, with a charge of −1, controls group III element marker diffusion in n-type, intrinsic, and p-type GaAs at T > 800 °C. By relating an anneal ambient to a region of the ternary phase diagram, it becomes clear why the group II-related diffusion and other variables are extremely sensitive to the experimental design. Pinning of the Fermi energy at the surface during vapor phase epitaxy appears to explain why nonequilibrium concentrations of dopants and charged point defects can be grown into GaAs and affect diffusion in post-growth anneals. The relatively large random measurement noise often accompanying interdiffusion appears to be largely associated with the presence of Al in GaAs. We conclude that this behavior is associated with a residual contaminant, most likely oxygen. It also appears likely that small amounts of an oxidant have been present in many closed ampoule anneals and affected the reported interdiffusion results. We conclude that poorly understood metallurgical reactions are probably responsible for the enormous range of interdiffusion observed in device structures annealed under SiO 2 and Si 3 N 4 glass caps.

Thermodynamic variables in the context of a nonequilibrium statistical ensemble approach

Abstract: We consider the question of the definition of thermodynamic-like variables in the context of a statistical thermodynamics, which is a large generalization of Gibbs statistical thermostatics and linear and local-equilibrium classical irreversible thermodynamics. It is based on a nonequilibrium ensemble approach known as the nonequilibrium statistical operator method. Some of these quasithermodynamic variables are characteristic of the nonequilibrium state and go to zero in the limit of local or global equilibrium, but others go over the thermodynamic variables that are present in such a limit. We consider in particular temperature-like variables for the different subsystems of the sample. For illustration we apply the theory to the study of optical properties of highly photoexcited plasma in semiconductors, following a good agreement between theory and experimental data. It is shown that high-resolution spectroscopy provides an excellent experimental testing ground for corroboration of the theoretical concepts, and a quite appropriate way for characterizing and measuring nonequilibrium thermodynamic-like variables.