Showing papers on "Non-equilibrium thermodynamics published in 2000"
TL;DR: In this paper, the Kawasaki nonlinear response relation, the transient fluctuation theorem, and the Jarzynski nonequilibrium work relation are all expressions that describe the behavior of a system that has been driven from equilibrium by an external perturbation.
Abstract: The Kawasaki nonlinear response relation, the transient fluctuation theorem, and the Jarzynski nonequilibrium work relation are all expressions that describe the behavior of a system that has been driven from equilibrium by an external perturbation In contrast to linear response theory, these expressions are exact no matter the strength of the perturbation, or how far the system has been driven away from equilibrium In this paper, I show that these three relations (and several other closely related results) can all be considered special cases of a single theorem This expression is explicitly derived for discrete time and space Markovian dynamics, with the additional assumptions that the unperturbed dynamics preserve the appropriate equilibrium ensemble, and that the energy of the system remains finite
933 citations
Book•
01 Mar 2000
TL;DR: In this article, the authors present an answer to Even-Numbered Numerical Problems Index (AOPI) for even-numbered numerical problems in thermodynamics and their applications.
Abstract: Introduction The Gas Laws Kinetic Theory of Gases The First Law of Thermodynamics The Second Law of Thermodynamics Gibbs and Helmholtz Energies and Their Applications Nonelectrolyte Solutions Electrolyte Solutions Chemical Equilibrium Electrochemistry Acids and Bases Chemical Kinetics Enzyme Kinetics Quantum Mechanics The Chemical Bond Intermolecular Forces Spectroscopy Molecular Symmetry and Optical Activity Photochemistry and Photobiology The Solid State The Liquid State Macromolecules Statistical Thermodynamics Appendices Glossary Answers to Even-Numbered Numerical Problems Index
205 citations
TL;DR: The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta as mentioned in this paper, which leads to modifications of some of thermodynamic relations.
Abstract: The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This leads to modifications of some of thermodynamic relations for nonextensive systems. Here, taking the first law of thermodynamics and the Legendre transform structure as the basic premises, it is found that Clausius definition of the thermodynamic entropy has to be appropriately modified, and accordingly the thermodynamic relations proposed by Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are also to be rectified. It is shown that the definition of specific heat and the equation of state remain form invariant. As an application, the classical gas model is reexamined and, in marked contrast with the previous result obtained by Abe [Phys. Lett. A 263 (1999) 424: Erratum A 267 (2000) 456] using the unphysical temperature and the unphysical pressure, the specific heat and the equation of state are found to be similar to those in ordinary extensive thermodynamics.
182 citations
TL;DR: This work presents a definition of entropy production rate for classes of deterministic and stochastic dynamics, motivated by recent work on the Gallavotti–Cohen (local) fluctuation theorem.
Abstract: We present a definition of entropy production rate for classes of deterministic and stochastic dynamics. The point of departure is a Gibbsian representation of the steady state path space measure for which “the density” is determined with respect to the time-reversed process. The Gibbs formalism is used as a unifying algorithm capable of incorporating basic properties of entropy production in nonequilibrium systems. Our definition is motivated by recent work on the Gallavotti–Cohen (local) fluctuation theorem and it is illustrated via a number of examples.
158 citations
TL;DR: In this article, the authors derived a theoretical model for thermal diffusion coefficients in ideal and non-ideal multicomponent mixtures, based on the thermodynamics of irreversible processes and the molecular kinetic approach incorporating explicit effects of nonequilibrium properties, such as the net heat of transport and molecular diffusion coefficients, and of equilibrium properties of the mixture, which are determined by the Peng-Robinson equation of state.
Abstract: Unlike molecular diffusion, neither measured thermal diffusion coefficients nor the theoretical framework exist for the estimation of thermal diffusion coefficients in nonideal multicomponent mixtures. This work derives a theoretical model for thermal diffusion coefficients in ideal and nonideal multicomponent mixtures, based on the thermodynamics of irreversible processes and the molecular kinetic approach incorporating explicit effects of nonequilibrium properties, such as the net heat of transport and molecular diffusion coefficients, and of equilibrium properties of the mixture, which are determined by the Peng-Robinson equation of state. An interesting feature of this model is that in nonideal multicomponent mixtures thermal diffusion coefficients depend on molecular diffusion coefficients, while in binary mixtures they do not. The model successfully describes thermal diffusion factors of binary mixtures for which experimental data are available, even those in extreme nonideal conditions and close to the critical point. Since experimental data on thermal diffusion factors in multicomponent hydrocarbon mixtures are not available, testing the model's accuracy was not possible. The model, however, successfully predicted spatial variation of composition in a ternary mixture of nC{sub 24}/nC{sub 16}/nC{sub 12}, providing an indirect verification. The six-component mixture of C{sub 1}/C{sub 3}/nC{sub 5}/nC{sub 10}/nC{sub 16}/C{sub 2} shows significant dependency of thermal diffusionmore » factors on the distance to the critical point. It also demonstrates for the first time that there is no need to adopt a sign convention for thermal diffusion coefficients in binary and higher mixtures. The thermodynamic stability analysis shows that when the thermal diffusion coefficient is positive, the component should go to the cold region in a binary mixture.« less
130 citations
TL;DR: This work focuses on the multidroplet regime of the two-dimensional kinetic Ising model, where the metastable phase decays through nucleation and growth of many droplets of the stable phase, and investigates the universal aspects of this dynamic phase transition at various temperatures and field amplitudes via large-scale Monte Carlo simulations.
Abstract: We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multidroplet regime, where the metastable phase decays through nucleation and growth of many droplets of the stable phase. At a critical frequency, the system undergoes a genuine nonequilibrium phase transition, in which the symmetry-broken phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. We investigate the universal aspects of this dynamic phase transition at various temperatures and field amplitudes via large-scale Monte Carlo simulations, employing finite-size scaling techniques adopted from equilibrium critical phenomena. The critical exponents, the fixed-point value of the fourth-order cumulant, and the critical order-parameter distribution all are consistent with the universality class of the two-dimensional equilibrium Ising model. We also study the cross-over from the multidroplet regime to the strong-field regime, where the transition disappears.
124 citations
TL;DR: In this paper, the dynamics of unstable particles within the real-time formulation of nonequilibrium field theory initiated in a previous paper are described. And the validity conditions for the resulting quantum four-phase-space kinetic theory are discussed under the perspective to treat particles with broad damping widths.
113 citations
01 Dec 2000
TL;DR: Evidence is presented for the hypothesis of local equilibrium for a liquid-vapor interface in a one-component fluid, using molecular dynamics simulations and it is shown that the equation of state for the interface applies also when there is heat and mass transport through the interface.
Abstract: Coupled transport phenomena across a gas/liquid interface, relevant for distillation, were studied by nonequilibrium molecular dynamics simulations. The simulations were set in the context of bulk irreversible thermodynamics. It was then shown that mole fraction profiles in the liquid phase and the gas phase of ideal isotope mixtures are linear. For nonideal mixtures, Fick's law cannot be applied in the interface region, because the activity coefficients change dramatically across the interface. Fourier's law has a constant heat conductivity for both types of liquid mixtures but not for gas mixtures. The coupling between heat and mass transfer becomes negligible for distillation in the special case of ideal mixtures with constant molal overflow. In all other cases, the heat of transfer contributes significantly to the heat flux and causes deviations from Fourier's law in the gas phase. This all means that coupled flux equations are needed to describe distillation and that the properties of the surface are...
108 citations
Book•
01 Mar 2000
TL;DR: In this article, the authors present a comprehensive overview of physics, chemistry, physics, and physics in terms of the properties of Gases and their properties as a set of properties.
Abstract: I. CLASSICAL THERMODYNAMICS. 1. Properties of Gases. 2. The First Law of Thermodynamics. 3. Thermochemistry. 4. The Second Law of Thermodynamics. 5. Chemical Equilibrium. 6. Phase Equilibrium. 7. The Thermodynamics of Solids. 8. Thermodynamics of Nonelectrolytic Solutions. 9. Thermodynamics of Electrolytic Solutions. II. QUANTUM MECHANICS AND BONDING. 10. The Mathematics of Chance. 11. Introduction to Quantum Mechanics. 12. Translational, Rotational and Vibrational Energies of Molecular Systems. 13. The Electronic Structure of Atoms. 14. Molecular Structure and Bonding. III. SPECTROSCOPY. 15. Rotational, Vibrational, and Electronic Spectra. 16. Magnetic and Diffraction Spectroscopy. IV. STATISTICAL MECHANICS. 17. Molecular Energy Distributions-Kinetic Theory of Gases. 18. Statistical Thermodynamics. V. KINETICS AND DYNAMICS. 19. Phenomenological Kinetics. 20. Theoretical Kinetics and Reaction Dynamics. Epilogue. Bibliography. Appendices. Index.
98 citations
TL;DR: Equilibrium properties such as Gibbs distributions and detailed balance are recovered at intermediate, coarse-grained scales, which suggests that the macroscopic behavior of some far-from-equilibrium systems might be understood in terms of equilibrium statistical mechanics.
Abstract: Far-from-equilibrium, spatially extended chaotic systems have generally eluded analytical solution, leading researchers to consider theories based on a statistical rather than a detailed knowledge of the microscopic length scales. Building on the recent discovery of a separation of length scales between macroscopic behavior and microscopic chaos, a simple far-from-equilibrium spatially extended chaotic system has been studied computationally at intermediate, coarse-grained scales. Equilibrium properties such as Gibbs distributions and detailed balance are recovered at these scales, which suggests that the macroscopic behavior of some far-from-equilibrium systems might be understood in terms of equilibrium statistical mechanics.
Book•
01 Jan 2000
TL;DR: In this paper, the authors present a discussion of the first and second laws of thermodynamics and their application in the field of physics, including the notion of entropy change for a liquid or a solid.
Abstract: (NOTE: Each chapter concludes with Problems.) 1. The Nature of Thermodynamics. What Is Thermodynamics? Definitions. The Kilomile. Limits of the Continuum. More Definitions. Units. Temperature and the Zeroth Law of Thermodynamics. Temperature Scales. 2. Equations of State. Introduction. Equation of State of an Ideal Gas. Van der Waals' Equation for a Real Gas. P-v-T Surfaces for Real Substances. Expansivity and Compressibility. An Application. 3. The First Law of Thermodynamics. Configuration Work. Dissipative Work. Adiabatic Work and Internal Energy. Heat. Units of Heat. The Mechanical Equivalent of Heat. Summary of the First Law. Some Calculations of Work. 4. Applications of the First Law. Heat Capacity. Mayer's Equation. Enthalpy and hats of Transformation. Relationships Involving Enthalpy. Comparison of u and h. Work Done in an Adiabatic Process. 5. Consequences of the First Law. The Gay-Lussac-Joule Experiment. The Joule-Thomson Experiment. Heat Engines and the Carnot Cycle. 6. The Second Law of Thermodynamics. Introduction. The Mathematical Concept of Entropy. Irreversible Processes. Carnot's Theorem. The Clausius Inequality and the Second Law. Entropy and Available Energy. Absolute Temperature. Combined First and Second Laws. 7. Applications of the Second Law. Entropy Changes in Reversible Processes. Temperature-Entropy Diagrams. Entropy Change of the Surroundings for a Reversible Process. Entropy Change for an Ideal Gas. The Tds Equations. Entropy Change in Irreversible Processes. Free Expansion of an Ideal Gas. Entropy Change for a Liquid or Solid. 8. Thermodynamic Potentials. Introduction. The Legendre Transformation. Definition of the Thermodynamic Potentials. The Maxwell Relations. The Helmholtz Function. The Gibbs Function. Application of the Gibbs Function to Phase Transitions. An Application of the Maxwell Relations. Conditions of Stable Equilibrium. 9. The Chemical Potential and Open Systems. The Chemical Potential. Phase Equilibrium. The Gibbs Phase Rule. Chemical Recessions. Mixing Processes. 10. The Third Law of Thermodynamics. Statements of the Third Law. Methods of Cooling. Equivalence of the Statements. Consequences of the Third Law. 11. The Kinetic Theory of Gases. Basic Assumptions. Molecular Flux. Gas Pressure and the Ideal Gas Law. Equipartition of Energy. Specific Heat Capacity of an Ideal Gas. Distribution of Molecular Speeds. Mean Free Path and Collision Frequency. Effusion. Transport Processes. 12. Statistical Thermodynamics. Introduction. Coin-Tossing Experiment. Assembly of Distinguishable Particles. Thermodynamic Probability and Entropy. Quantum States and Energy Levels. Density of Quantum States. 13. Classical and Quantum Statistics. Bloltzmann Statistics. The Method of Lagrange Multipliers. The Boltzmann Distribution. The Fermi-Dirac Distribution. The Bose-Einstein Distribution. Dilute Gases and the Maxwell-Boltzmann Distribution. The Connection between Classical and Statistical Thermodynamics. Comparison of the Distributions. Alternative Statistical Models. 14. The Classical Statistical Treatment of an Ideal Gas. Thermodynamic Properties from the Partition Function. Partition Function for a Gas. Properties of a Monatomic Ideal Gas. Applicability of the Maxwell-Boltzmann Distribution. Distribution of Molecular Speeds. Equipartition of Energy. Entropy Change of Mixing Revisited. Maxwell's Demon. 15. The Heat Capacity of a Diatomic Gas. Introduction. The Quantified Linear Oscillator. Vibrational Modes of Diatomic Molecules. Rotational Modes of Diatomic Molecules. Electronic Excitation. The Total Heat Capacity. 16. The Heat Capacity of a Solid. Introduction. Einstein's Theory of the Heat Capacity of a Solid. Debye's Theory of the Heat Capacity of a Solid. 17. The Thermodynamics of Magnetism. Introduction. Paramagnetism. Properties of a Spin-1/2 Paramagnet. Adiabatic Demagnetization. NegativeTemperature. Ferromagnetism. 18. Bose-Einstein Gases. Blackbody Radiation. Properties of a Photon Gas. Bose-Einstein Condensation. Properties of a Boson Gas. Application to Liquid Helium. 19. Fermi-Dirac Gases. The Fermi Energy. The Calculation of ...m(T). Free Electrons in a Metal. Properties of a Fermion Gas. Application to White Dwarf Stars. 20. Information Theory. Introduction. Uncertainty and Information. Unit of Information. Maximum Entropy. The Connection to Statistical Thermodynamics. Information Theory and the Laws of Thermodynamics. Maxwell's Demon Exorcised. Appendix A. Review of Partial Differentiation. Partial Derivatives. Exact and Inexact Differentials. Appendix B. Stirling's Approximation. Appendix C. Alternative Approach to Finding the Boltzmann Distribution. Appendix D. Various Integrals. Bibliography. Answers to Selected Problems. Index.
TL;DR: In this article, nonequilibrium properties of a one-dimensional lattice Hamiltonian with quartic interactions in strong thermal gradients were studied and a quantitative description of T(x) including boundary jumps were developed.
TL;DR: An analytic relation between temperature, and generation time, is exploited to show that the directionality principle for evolutionary entropy is a non-equilibrium extension of the principle of a uni-directional increase of thermodynamic entropy.
TL;DR: In this article, the divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials.
Abstract: The divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials. Two different numerical approaches based on nonequilibrium and equilibrium simulations provide consistent indications in favour of a logarithmic divergence in “ergodic”, i.e., highly chaotic, dynamical regimes. Analytical estimates obtained in the framework of linear-response theory confirm this finding, while tracing back the physical origin of this anomalous transport to the slow diffusion of the energy of hydrodynamic modes. Finally, numerical evidence of superanomalous transport is given in the weakly chaotic regime, typically observed below a threshold value of the energy density.
TL;DR: Details of the exact dynamical solution of two simple models introduced recently: uncoupled harmonic oscillators subject to parallel Monte Carlo dynamics, and independent spherical spins in a random field with such dynamics are presented.
Abstract: A picture for thermodynamics of the glassy state was introduced recently by us [Phys. Rev. Lett. 79, 1317 (1997); 80, 5580 (1998)]. It starts by assuming that one extra parameter, the effective temperature, is needed to describe the glassy state. This approach connects responses of macroscopic observables to a field change with their temporal fluctuations, and with the fluctuation-dissipation relation, in a generalized, nonequilibrium way. Similar universal relations do not hold between energy fluctuations and the specific heat. In the present paper, the underlying arguments are discussed in greater length. The main part of the paper involves details of the exact dynamical solution of two simple models introduced recently: uncoupled harmonic oscillators subject to parallel Monte Carlo dynamics, and independent spherical spins in a random field with such dynamics. At low temperature, the relaxation time of both models diverges as an Arrhenius law, which causes glassy behavior in typical situations. In the glassy regime, we are able to verify the above-mentioned relations for the thermodynamics of the glassy state. In the course of the analysis, it is argued that stretched exponential behavior is not a fundamental property of the glassy state, though it may be useful for fitting in a limited parameter regime.
TL;DR: In this article, a nonequilibrium approach to the dynamics and statistics of the condensate of an ideal N-atom Bose gas cooling via interaction with a thermal reservoir using the canonical ensemble is developed.
Abstract: A nonequilibrium approach to the dynamics and statistics of the condensate of an ideal N-atom Bose gas cooling via interaction with a thermal reservoir using the canonical ensemble is developed. We derive simple analytical expressions for the canonical partition function and equilibrium distribution of the number of atoms in the ground state of a trap under different approximations, and compare them with exact numerical results. The N-particle constraint associated with the canonical ensemble is usually a burden. In the words of Kittel, ‘‘in the investigation of the Bose-Einstei n...l aws it is very inconvenient to impose the restriction that the number of particles in the subsystem shall be held constant.’’ But in the present approach, based on the analogy between a second-order phase transition and laser threshold behavior, the N-particle constraint makes the problem easier. We emphasize that the present work provides another example of a case in which equilibrium ~detailed balance! solutions to nonequilibrium equations of motion provide a useful supplementary approach to conventional statistical mechanics. We also discuss some dynamical and mesoscopic aspects of Bose-Einstein condensation. The conclusion is that the present analytical ~but approximate! results, based on a nonequilibrium approach, are in excellent agreement with exact ~but numerical! results. The present analysis has much in common with the quantum theory of the laser.
TL;DR: The theory of entropy production in nonequilibrium, Hamiltonian systems, previously described for steady states using partitions of phase space, is extended to time dependent systems relaxing to equilibrium, and the central results are the entropy production is governed by an underlying, exponentially decaying fractal structure in phase space.
Abstract: The theory of entropy production in nonequilibrium, Hamiltonian systems, previously described for steady states using partitions of phase space, is here extended to time dependent systems relaxing to equilibrium. We illustrate the main ideas using a simple multibaker model with some nonequilibrium initial state, and we study its progress toward equilibrium. For this model, the central results are: (1) the entropy production is governed by an underlying, exponentially decaying fractal structure in phase space; (2) the rate of entropy production is largely independent of the scale of resolution used in constructing the partitions; and (3) the rate of entropy production so obtained is in agreement with the predictions of nonequilibrium thermodynamics.
TL;DR: In this paper, the Green's Function Method (GFM) is applied to analyze multi-dimensional transport from persistent solute sources typical of nonaqueous phase liquids (NAPLs).
Abstract: Equilibrium and bicontinuum nonequilibrium formulations of the advection–dispersion equation (ADE) have been widely used to describe subsurface solute transport. The Green's Function Method (GFM) is particularly attractive to solve the ADE because of its flexibility to deal with arbitrary initial and boundary conditions, and its relative simplicity to formulate solutions for multi‐dimensional problems. The Green's functions that are presented can be used for a wide range of problems involving equilibrium and nonequilibrium transport in semi‐infinite and infinite media. The GFM is applied to analytically model multi‐dimensional transport from persistent solute sources typical of nonaqueous phase liquids (NAPLs). Specific solutions are derived for transport from a rectangular source (parallel to the flow direction) of persistent contamination using first‐, second‐, or third‐type boundary or source input conditions. Away from the source, the first‐ and third‐type condition cannot be expected to represent the exact surface condition. The second‐type condition has the disadvantage that the diffusive flux from the source needs to be specified a priori. Near the source, the third‐type condition appears most suitable to model NAPL dissolution into the medium. The solute flux from the pool, and hence the concentration in the medium, depends strongly on the mass transfer coefficient. For all conditions, the concentration profiles indicate that nonequilibrium conditions tend to reduce the maximum solute concentration and the total amount of solute that enters the porous medium from the source. On the other hand, during nonequilibrium transport the solute may spread over a larger area of the medium compared to equilibrium transport.
TL;DR: Simulations support predictions providing new insight into the long-time nonlinear fate of the wave due to Landau damping in plasmas, and a critical initial wave intensity is found.
Abstract: Gibbs statistical mechanics is derived for the Hamiltonian system coupling a wave to $N$ particles self-consistently. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data with warm particles, a critical initial wave intensity is found: above it, thermodynamics predicts a finite wave amplitude in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$; below it, the equilibrium amplitude vanishes. Simulations support these predictions providing new insight into the long-time nonlinear fate of the wave due to Landau damping in plasmas.
TL;DR: In this article, a number of approaches have been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in non-equilibrium stationary states, via the theory of dynamical systems.
Abstract: Recently, a number of approaches have been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in non-equilibrium stationary states, via the theory of dynamical systems. In this way a direct connection between dynamics and irreversible thermodynamics has been claimed to have been found. However, the main quantity used in these studies is a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its present form, to characterize non-equilibrium states. Various simplified models have also been devised to give explicit examples of how the coarse-grained approach may succeed in giving a full description of the irreversible thermodynamics. We analyse some of these models and point out a number of difficulties which, in our opinion, need to be overcome in order to establish a physically relevant connection between these models and irreversible thermodynamics.
TL;DR: In this article, a kinetic theory providing bases for an analytical treatment of nonlinear quantum transport is described, based on a nonequilibrium statistical ensemble formalism, which constitutes a soundly approach for the study of dissipative manybody systems driven arbitrarily away from equilibrium.
Abstract: It is described a kinetic theory providing bases for an analytical treatment of nonlinear quantum transport. It is founded on a nonequilibrium statistical ensemble formalism, which constitutes a soundly approach for the study of dissipative many-body systems driven arbitrarily away from equilibrium. This theory is applied to the study of transport of charge in n- and p- type doped polar semiconductors. Evolution of the carriers’ quasitemperature and mobility as well as of the relaxation times for energy and momentum are derived. Some comparison with experimental data is done.
TL;DR: A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed, resulting in a comprehensive theory for the Brownian dynamics and statistical thermodynamics of single macromolescules.
Abstract: A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement are stochastic; the former is represented by a master equation for a set of discrete states, and the latter is described by a continuous Smoluchowski equation. Combining these two equations into one, a comprehensive theory for the Brownian dynamics and statistical thermodynamics of single macromolecules arises. This approach is shown to have wide applications. It is applied to protein-ligand dissociation under external force, unfolding of polyglobular proteins under extension, movement along linear tracks of motor proteins against load, and enzyme catalysis by single fluctuating proteins. As a generalization of the classic polymer theory, the dynamic equation is capable of characterizing a single macromolecule in aqueous solution, in probabilistic terms, (1) its thermodynamic equilibrium with fluctuations, (2) transient relaxation kinetics, and most importantly and novel (3) nonequilibrium steady-state with heat dissipation. A reversibility condition which guarantees an equilibrium solution and its thermodynamic stability is established, an H-theorem like inequality for irreversibility is obtained, and a rule for thermodynamic consistency in chemically pumped nonequilibrium steady-state is given.
Book•
28 Feb 2000
TL;DR: In this article, the authors define the postulates of equilibrium thermodynamics and steady state thermodynamics as follows: equilibrium thermodynamic potentials, Massieu functions, and pivotal functions.
Abstract: Preface. Equilibrium Thermodynamics. Definitions. The postulates of equilibrium thermodynamics. The fundamental equation. Thermodynamic equilibrium. Thermodynamic processes. Reversible sources and reservoirs. Work and heat. Thermodynamic potentials. Massieu functions. Second order partial derivatives. Ideal systems. The ideal gas. The monatomic ideal gas. The ideal mixture. The multicomponent ideal gas. The ideal solution. The ideal rubber. Stability. Phase transitions. Chemical reactions. Reaction equilibrium. Steady-state Thermodynamics. Chemical reactions as irreversible processes. The postulates of steady-state thermodynamics. Coupled linear steady states. Entropy production in the steady state. The pivotal functions. Matter and heat flow. The quantities of transport. Uses of the heat of transport. Minimum entropy production. Appendices. Exact and inexact differentials. Jacobians. The Legendre transformation. The fundamental equation of the ideal gas. The equation of state of the ideal rubber. Positive definiteness of a quadratic form. Heat conduction at the system boundaries. References. List of symbols. Author and subject index.
TL;DR: In this paper, the effect of phase-lags in temperature and in heat flux on the nonequilibrium entropy production was investigated under the dual-phase-lag heat conduction model.
Abstract: The nonequilibrium entropy production under the effect of the dual-phase-lag heat conduction model is investigated. The entropy production cannot be described using the classical form of the equilibrium entropy production where using this form leads to a violation for the thermodynamics second law. The effect of the phase-lags in temperature and in heat flux on the nonequilibrium entropy production is investigated. Also, the difference between the equilibrium and the nonequilibrium temperatures under the effect of the dual-phase-lag heat conduction model is studied
TL;DR: In this paper, the authors present a mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process.
Abstract: We present a novel mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process We apply our method to the periodic Lorentz gas, where a point particle moves diffusively through an ensemble of hard disks arranged on a triangular lattice First, collision rules are defined for this system in thermal equilibrium They determine the velocity of the moving particle such that the system is deterministic, time-reversible, and microcanonical These collision rules can systematically be adapted to the case where one associates arbitrarily many degrees of freedom to the disk, which here acts as a boundary Subsequently, the system is investigated in nonequilibrium situations by applying an external field We show that in the limit where the disk is endowed by infinitely many degrees of freedom it acts as a thermal reservoir yielding a well-defined nonequilibrium steady state The characteristic properties of this state, as obtained from computer simulations, are finally compared to those of the so-called Gaussian thermostated driven Lorentz gas
TL;DR: In this paper, a comparative analysis of the descriptions of fluctuations in statistical mechanics (the Gibbs approach) and in statistical thermodynamics (the Einstein approach) is given, and solutions are obtained for the Gibbs and Einstein problems that arise in pressure fluctuation calculations for a spatially limited equilibrium (or slightly nonequilibrium) macroscopic system.
Abstract: A comparative analysis of the descriptions of fluctuations in statistical mechanics (the Gibbs approach) and in statistical thermodynamics (the Einstein approach) is given. On this basis solutions are obtained for the Gibbs and Einstein problems that arise in pressure fluctuation calculations for a spatially limited equilibrium (or slightly nonequilibrium) macroscopic system. A modern formulation of the Gibbs approach which allows one to calculate equilibrium pressure fluctuations without making any additional assumptions is presented; to this end the generalized Bogolyubov – Zubarev and Hellmann – Feynman theorems are proved for the classical and quantum descriptions of a macrosystem. A statistical version of the Einstein approach is developed which shows a fundamental difference in pressure fluctuation results obtained within the context of two approaches. Both the 'genetic' relation between the Gibbs and Einstein approaches and the conceptual distinction between their physical grounds are demonstrated. To illustrate the results, which are valid for any thermodynamic system, an ideal nondegenerate gas of microparticles is considered, both classically and quantum mechanically. Based on the results obtained, the correspondence between the micro- and macroscopic descriptions is considered and the prospects of statistical thermodynamics are discussed.
TL;DR: In this paper, a generalized hydrodynamic theory is derived in the long-wave limit of a kinetic equation, which does not rest on the requirement of a local equilibrium, and it is shown that nonequilibrium effects qualitatively change the collective dynamics in comparison with the predictions of the heuristic Bloch's hydrodynamics.
Abstract: Generalized hydrodynamic theory, which does not rest on the requirement of a local equilibrium, is derived in the long-wave limit of a kinetic equation. The theory bridges the whole frequency range between the quasistatic (Navier-Stokes) hydrodynamics and the high-frequency (Vlasov) collisionless limit. In addition to pressure and velocity the theory includes new macroscopic tensor variables. In a linear approximation these variables describe an effective shear stress of a liquid and the generalized hydrodynamics recovers the Maxwellian theory of highly viscous fluids---the media behaving as solids on a short time scale, but as viscous fluids on long-time intervals. It is shown that the generalized hydrodynamics can be applied to the Landau theory of Fermi liquid. Illustrative results for collective modes in confined systems are given, which show that nonequilibrium effects qualitatively change the collective dynamics in comparison with the predictions of the heuristic Bloch's hydrodynamics. Earlier improvements of the Bloch theory are critically reconsidered.
TL;DR: In this article, the Kramers theory of activated processes is generalized for nonequilibrium open one-dimensional systems, where both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and characterized by arbitrary decaying correlation functions are considered.
Abstract: The Kramers theory of activated processes is generalized for nonequilibrium open one-dimensional systems. We consider both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. We stress the role of a nonequilibrium stationary state distribution for this open system which is reminiscent of an equilibrium Boltzmann distribution in calculation of rate. The generalized rate expression we derive here reduces to the specific limiting cases pertaining to the closed and open systems for thermal and nonthermal steady state activation processes.