Showing papers on "Non-equilibrium thermodynamics published in 2008"

Introduction to the Thermodynamics of Materials

Abstract: Preface. Introduction and Definition of Terms. The First Law of Thermodynamics. The Second Law of Thermodynamics. The Statistical Interpretation of Entropy. Auxiliary Functions. Heat Capacity, Enthalpy, Entropy, and the Third Law of Thermodynamics. Phase Equilibrium in a One-Component System. The Behavior of Gases. The Behavior of Solutions. Gibbs Free Energy-Composition and Phase Diagrams of Binary Systems. Reactions Involving Gases. Reactions Involving Pure Consensed Phases and a Gaseous Phase. Reaction Equilibria in Systems Containing Components in Condensed Solutions. Phase Diagrams for Binary Systems in Pressure-Temperature-Composition Space. Electrochemistry. Appendix A: Selected Thermodynamic and Thermochemical Data. Appendix B Exact Differential Equations. Appendix C The Generation of Auxiliary Functions as Legendre Transformations. Nomenclatures. Answers. Index.

An introduction to phase-field modeling of microstructure evolution

Abstract: The phase-field method has become an important and extremely versatile technique for simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface approach, it allows us to study the evolution of arbitrary complex grain morphologies without any presumption on their shape or mutual distribution. It is also straightforward to account for different thermodynamic driving forces for microstructure evolution, such as bulk and interfacial energy, elastic energy and electric or magnetic energy, and the effect of different transport processes, such as mass diffusion, heat conduction and convection. The purpose of the paper is to give an introduction to the phase-field modeling technique. The concept of diffuse interfaces, the phase-field variables, the thermodynamic driving force for microstructure evolution and the kinetic phase-field equations are introduced. Furthermore, common techniques for parameter determination and numerical solution of the equations are discussed. To show the variety in phase-field models, different model formulations are exploited, depending on which is most common or most illustrative.

Exact relaxation in a class of nonequilibrium quantum lattice systems.

Abstract: A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we introduce an experimentally accessible setting where relaxation to a steady state is exact, namely, for the Bose-Hubbard model quenched from a Mott quantum phase to the free strong superfluid regime. We rigorously prove that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments--thus maximizing the entanglement. Remarkably, for this to be true, no time average is necessary. Our argument includes a central limit theorem and exploits the finite speed of information transfer. We also show that for all periodic initial configurations (charge density waves) the system relaxes locally, and identify experimentally accessible signatures in optical lattices as well as implications for the foundations of statistical mechanics.

Non-Equilibrium Thermodynamics of Heterogeneous Systems

Abstract: General Theory: The Entropy Production for a Homogeneous Phase The Excess Entropy Production for the Surface Flux Equations and Onsager Relations Transport of Heat and Mass Transport of Mass and Charge Applications: Evaporation and Condensation A Non-Isothermal Concentration Cell Adiabatic Electrode Reactions The Formation Cell Modeling the Polymer Electrolyte Fuel Cell The Impedance of an Electrode Surface The Non-Equilibrium Two-Phase van der Waals Model and other chapters.

Fully integrated transport approach to heavy ion reactions with an intermediate hydrodynamic stage

Abstract: We present a coupled Boltzmann and hydrodynamics approach to relativistic heavy ion reactions. This hybrid approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. Event-by-event fluctuations are directly taken into account via the nonequilibrium initial conditions generated by the initial collisions and string fragmentations in the microscopic UrQMD model. After a (3+1)-dimensional ideal hydrodynamic evolution, the hydrodynamical fields are mapped to hadrons via the Cooper-Frye equation and the subsequent hadronic cascade calculation within UrQMD proceeds to incorporate the important final state effects for a realistic freeze-out. This implementation allows us to compare pure microscopic transport calculations with hydrodynamic calculations using exactly the same initial conditions and freeze-out procedure. The effects of the change in the underlying dynamics--ideal fluid dynamics versus nonequilibrium transport theory--is explored. The freeze-out and initial state parameter dependencies are investigated for different observables. The time evolution of the baryon density and particle yields are also discussed. We find that the final pion and proton multiplicities are lower in the hybrid model calculation owing to the isentropic hydrodynamic expansion whereas the yields for strange particles are enhanced owing to the localmore » equilibrium in the hydrodynamic evolution. The results of the different calculations for the mean transverse mass excitation function, rapidity, and transverse mass spectra for different particle species at three different beam energies are discussed in the context of the available data.« less

Evolution of entanglement entropy following a quantum quench : Analytic results for the XY chain in a transverse magnetic field

Abstract: The nonequilibrium evolution of the block entanglement entropy is investigated in the $XY$ chain in a transverse magnetic field after the Hamiltonian parameters are suddenly changed from and to arbitrary values. Using Toeplitz matrix representation and multidimensional phase methods, we provide analytic results for large blocks and for all times, showing explicitly the linear growth in time followed by saturation. The consequences of these analytic results are discussed and the effects of a finite block length is taken into account numerically.

Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states

Abstract: We give the explicit structure of the functional governing the dynamical density and current fluctuations for a mesoscopic system in a nonequilibrium steady state. Its canonical form determines a generalised Onsager-Machlup theory. We assume that the system is described as a Markov jump process satisfying a local detailed balance condition such as typical for stochastic lattice gases and for chemical networks. We identify the entropy current and the traffic between the mesoscopic states as extra terms in the fluctuation functional with respect to the equilibrium dynamics. The density and current fluctuations are coupled in general, except close to equilibrium where their decoupling explains the validity of entropy production principles.

Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow.

Abstract: The standard lattice Boltzmann equation (LBE) is inadequate for simulating gas flows with a large Knudsen number. In this paper we propose a generalized lattice Boltzmann equation with effective relaxation times based on a recently developed generalized Navier-Stokes constitution [Guo et al., Europhys Lett. 80, 24001 (2007)] for nonequilibrium flows. A kinetic boundary condition corresponding to a generalized second-order slip scheme is also designed for the model. The LBE model and the boundary condition are analyzed for a unidirectional flow, and it is found that in order to obtain the generalized Navier-Stokes equations, the relaxation times must be properly chosen and are related to the boundary condition. Numerical results show that the proposed method is able to capture the Knudsen layer phenomenon and can yield improved predictions in comparison with the standard lattice Boltzmann equation.

Efficient and direct generation of multidimensional free energy surfaces via adiabatic dynamics without coordinate transformations.

Abstract: Adiabatic free energy dynamics (AFED) was introduced by Rosso et al. [J. Chem. Phys. 2002, 116, 4389] for computing free energy profiles quickly and accurately using a dynamical adiabatic separation between a set of collective variables or reaction coordinates and the remaining degrees of freedom of a system. This approach has been shown to lead to a significant gain in efficiency versus traditional methods such as umbrella sampling, thermodynamic integration, and free energy perturbation for generating one-dimensional free energy profiles. More importantly, AFED is able to generate multidimensional free energy surfaces efficiently via full sweeps of the surface that rapidly map out the locations of the free energy minima. The most significant drawback to the AFED approach is the need to transform the coordinates into a generalized coordinate system that explicitly contains the collective variables of interest. Recently, Maragliano and Vanden-Eijnden built upon the AFED approach by introducing a set of extended phase-space variables, to which the adiabatic decoupling and high temperature are applied [Chem. Phys. Lett. 2006, 426, 168]. In this scheme, which the authors termed "temperature accelerated molecular dynamics" or TAMD, the need for explicit coordinate transformations is circumvented. The ability of AFED and TAMD to generate free energy surfaces efficiently depends on the thermostatting mechanism employed, since both approaches are inherently nonequilibrium due to the adiabatic decoupling. Indeed, Maragliano and Vanden-Eijnden did not report any direct generation of free energy surfaces within the overdamped Langevin dynamics employed by these authors. Here, we show that by formulating TAMD in a manner that is closer to the original AFED approach, including the generalized Gaussian moment thermostat (GGMT) and multiple time-scale integration, multidimensional free energy surfaces for complex systems can be generated directly from the probability distribution function of the extended phase-space variables. The new TAMD formulation, which we term driven AFED or d-AFED, is applied to compare the conformational preferences of small peptides both in gas phase and in solution for three force fields. The results show that d-AFED/TAMD accurately and efficiently generates free energy surfaces in two collective variables useful for characterizing the conformations, namely, the radius of gyration, R(G), and number of hydrogen bonds, N(H).

Nonequilibrium work relations: foundations and applications

Abstract: When a macroscopic system in contact with a heat reservoir is driven away from equilibrium, the second law of thermodynamics places a strict bound on the amount of work performed on the system. With a microscopic system the situation is more subtle, as thermal fluctuations give rise to a statistical distribution of work values. In recent years it has been realized that such distributions encode surprisingly more information than one might expect from traditional thermodynamic arguments. I will discuss a number of exact results that relate equilibrium properties of the system, in particular free energy differences, to the fluctuations in the work performed during such a nonequilibrium process. I will describe the theoretical foundations of these relations, connections with irreversibility and the second law of thermodynamics, and potential experimental and computational applications.

Introduction to Modern Thermodynamics

Abstract: Preface. Part I: The Formalism of Modern Thermodynamics. 1. Basic Concepts and the Laws of Gases. 2. The First Law of Thermodynamics. 3. The Second Law of Thermodynamics and the Arrow of Time. 4. Entropy in the Realm of Chemical Reactions. 5. Extremum Principles and General Thermodynamic Relations. Part II: Applications: Equilibrium and Nonequilibrium Systems. 6. Basic Thermodynamics of Gases, Liquids and Solids. 7. Thermodynamics of Phase Change. 8. Thermodynamics of Solutions. 9. Thermodynamics of Chemical Transformations. 10. Fields and Internal Degrees of Freedom. 11. Introduction to Nonequilibrium Systems. Part III: Additional Topics. 12. Thermodynamics of Radiation. 13. Biological Systems. 14. Thermodynamics of Small Systems. 15. Classical Stability Theory. 16. Critical Phenomena and Configurationally Heat Capacity. 17. Elements of Statistical Thermodynamics. List of Variables. Standard Thermodynamic Properties. Physical Constants and Data. Name Index. Subject Index.

Shear-transformation-zone theory of plastic deformation near the glass transition

Abstract: The shear-transformation-zone (STZ) theory of plastic deformation in glass-forming materials is reformulated in light of recent progress in understanding the roles played by the effective disorder temperature and entropy flow in nonequilibrium situations. A distinction between fast and slow internal-state variables reduces the theory to just two coupled equations of motion, one describing the plastic response to applied stresses and the other the dynamics of the effective temperature. The analysis leading to these equations contains, as a by-product, a fundamental reinterpretation of the dynamic yield stress in amorphous materials. In order to put all these concepts together in a realistic context, I conclude with a reexamination of the experimentally observed rheological behavior of a bulk metallic glass. That reexamination serves as a test of the STZ dynamics, confirming that system parameters obtained from steady-state properties such as the viscosity can be used to predict transient behaviors.

Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. IV: Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics

Abstract: This is the fourth paper, the last one, on solution to the problem of absence of detailed balance in nonequilibrium processes. It is an approach based on another known universal dynamics: The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology; The statistical mechanics and thermodynamics, while enormously successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding; Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.

Microscopic diagonal entropy and its connection to basic thermodynamic relations

Abstract: We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as $S_d=-\sum_n \rho_{nn}\ln \rho_{nn}$ with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy $S_n=-{\rm Tr}\, \rho\ln\rho$. However, in contrast to $S_n$, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed through the energy distribution function and thus it is measurable, at least in principle. Under very generic assumptions of the locality of the Hamiltonian and non-integrability the d-entropy becomes a unique function of the average energy in large systems and automatically satisfies the fundamental thermodynamic relation. This relation reduces to the first law of thermodynamics for quasi-static processes. The d-entropy is also automatically conserved for adiabatic processes. We illustrate our results with explicit examples and show that $S_d$ behaves consistently with expectations from thermodynamics.

Entropy and the Time Evolution of Macroscopic Systems

Abstract: 1. Introduction 2. Some Clarification from Another Direction 3. The Probability Connection 4. Equilibrium Statistical Mechanics and Thermodynamics 5. The Presumed Extensivity of Entropy 6. Nonequilibrium States 7. Steady-State Processes 8. Sources and Time-Dependent Proceses 9. Thermal Driving 10. Application to Fluid Dynamics 11. Irreversibility, Relaxation, and the Approach to Equilibrium 12. Entropy Production and Dissipation Rates A. Perturbation Theory B. Dissipative Currents and Galilean Invariance C. Analytic Continuation of Covariance Functions

Conserving approximations in time-dependent quantum transport: Initial correlations and memory effects

Abstract: We study time-dependent quantum transport in a correlated model system by means of time-propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green function. We consider an initially contacted equilibrium system of a correlated central region coupled to tight-binding leads. Subsequently a time-dependent bias is switched on after which we follow in detail the time-evolution of the system. Important features of the Kadanoff-Baym approach are 1) the possibility of studying the ultrafast dynamics of transients and other time-dependent regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. We find that initial correlation and memory terms due to many-body interactions have a large effect on the transient currents. Furthermore the value of the steady state current is found to be strongly dependent on the approximation used to treat the electronic interactions.

Water polarization under thermal gradients.

Abstract: One may wonder whether such coupling effects between molecular orientation and temperature gradients may be observed in other systems. In this Letter, we discuss that effect for the most important solvent in biology and materials science, water. Water reorientation under a thermal gradient has not been discussed before to the best of our knowledge. We show that thermal gradients achievable in experiments can induce water reorientation and as a consequence large polarization fields. We start our discussion with the nonequilibrium thermodynamics background of this particular thermoelectric effect. Let us consider an isotropic polarizable medium subjected to a heat flux. According to nonequilibrium thermodynamics, the entropy production is given by [1,8]

Lattice Boltzmann simulations of soft matter systems

Abstract: This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.

Steady-state thermodynamics for heat conduction: microscopic derivation.

Abstract: Starting from microscopic mechanics, we derive thermodynamic relations for heat conducting nonequilibrium steady states. The extended Clausius relation enables one to experimentally determine nonequilibrium entropy to the second order in the heat current. The associated Shannon-like microscopic expression of the entropy is suggestive. When the heat current is fixed, the extended Gibbs relation provides a unified treatment of thermodynamic forces in the linear nonequilibrium regime.

Electron relaxation in metals: Theory and exact analytical solutions

Abstract: The nonequilibrium dynamics of electrons is of a great experimental and theoretical value, providing important microscopic parameters of the Coulomb and electron-phonon interactions in metals and other cold plasmas. Because of the mathematical complexity of collision integrals, theories of electron relaxation often rely on the assumption that electrons are in a ``quasiequilibrium'' (QE) with a time-dependent temperature, or on the numerical integration of the time-dependent Boltzmann equation. We transform the integral Boltzmann equation to a partial differential Schr\"odinger-type equation with imaginary time in a one-dimensional ``coordinate'' space reciprocal to energy which allows for exact analytical solutions in both cases of electron-electron and electron-phonon relaxations. The exact relaxation rates are compared with the QE relaxation rates at high and low temperatures.

Nonequilibrium Dynamics of Scalar Fields in a Thermal Bath

Abstract: We study the approach to equilibrium for a scalar field which is coupled to a large thermal bath. Our analysis of the initial value problem is based on Kadanoff-Baym equations which are shown to be equivalent to a stochastic Langevin equation. The interaction with the thermal bath generates a temperature-dependent spectral density, either through decay and inverse decay processes or via Landau damping. In equilibrium, energy density and pressure are determined by the Bose-Einstein distribution function evaluated at a complex quasi-particle pole. The time evolution of the statistical propagator is compared with solutions of the Boltzmann equations for particles as well as quasi-particles. The dependence on initial conditions and the range of validity of the Boltzmann approximation are determined.

Electron transport driven by nonequilibrium magnetic textures

Abstract: Spin-polarized electron transport driven by inhomogeneous magnetic dynamics is discussed in the limit of a large exchange coupling. Electron spins rigidly following the time-dependent magnetic profile experience spin-dependent fictitious electric and magnetic fields. We show that the electric field acquires important corrections due to spin dephasing, when one relaxes the spin-projection approximation. Furthermore, spin-flip scattering between the spin bands needs to be taken into account in order to calculate voltages and spin accumulations induced by the magnetic dynamics. A phenomenological approach based on the Onsager reciprocity principle is developed, which allows us to capture the effect of spin dephasing and make a connection to the well studied problem of current-driven magnetic dynamics. A number of results that recently appeared in the literature are related and generalized.

Thermal Casimir versus Casimir-Polder forces: equilibrium and nonequilibrium forces.

Abstract: We critically discuss whether and under what conditions Lifshitz theory may be used to describe thermal Casimir-Polder forces on atoms or molecules. An exact treatment of the atom-field coupling reveals that for a ground-state atom (molecule), terms associated with virtual-photon absorption lead to a deviation from the traditional Lifshitz result; they are identified as a signature of nonequilibrium dynamics. Even the equilibrium force on a thermalized atom (molecule) may be overestimated when using the ground-state polarizability instead of its thermal counterpart.

Thermodynamics and Fluctuations far from Equilibrium

Abstract: We review a coherent mesoscopic presentation of thermodynamics and fluctuations far from and near equilibrium, applicable to chemical reactions, energy transfer and transport processes, and electrochemical systems. Both uniform and spatially dependent systems are considered. The focus is on processes leading to and in non-equilibrium stationary states; on systems with multiple stationary states; and on issues of relative stability of such states. We establish thermodynamic state functions, dependent on the irreversible processes, with simple physical interpretations that yield the work available from these processes and the fluctuations. A variety of experiments are cited that substantiate the theory. The following topics are included: one-variable systems, linear and nonlinear; connection of thermodynamic theory with stochastic theory; multivariable systems; relative stability of different phases; coupled transport processes; experimental determination of thermodynamic and stochastic potentials; dissipation in irreversible processes and nonexistence of extremum theorems; efficiency of oscillatory reactions, including biochemical systems; and fluctuation-dissipation relations.

Thermodynamic and Transport Properties of Two-Temperature Nitrogen-Oxygen Plasma

Abstract: Thermodynamic and transport properties are computed for a 17 species model of nitrogen-oxygen plasma under different degrees of thermal non-equilibrium, pressures and volume ratios of component gases. In the computation electron temperatures range from 300 to 45,000 K, mole fractions range from 0.8 to 0.2, pressures range from 0.1 atmosphere to 5 atmospheres, and thermal nonequilibrium parameters (Te/Th) range from 1 to 20. It is assumed that all the electrons follow a temperature Te and the rest of the species in the plasma follow a temperature Th. Compositions are calculated using the two temperature Saha equation derived by van de Sanden et al. Updated energy level data from National Institute of Standards and Technology (NIST) and recently compiled collision integrals by Capitelli et al., have been used to obtain thermodynamic and transport properties. In the local thermodynamic equilibrium (LTE) regime, the results are compared with published data and an overall good agreement is observed.