Showing papers on "Non-equilibrium thermodynamics published in 1995"
TL;DR: This presents the first test of the Ruelle principle on a many particle system far from equilibrium, and a specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid.
Abstract: Ruelle`s principle for turbulence leading to what is usually called the Sinai-Ruelle-Bowen (SRB) distribution is applied to the statistical mechanics of many particle systems in nonequilibrium stationary states. A specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid. This presents the first test of the principle on a many particle system far from equilibrium. A possible application to fluid mechanics is also discussed.
1,587 citations
TL;DR: In this paper, a chaotic hypothesis for reversible dissipative many-particle systems in nonequilibrium stationary states in general is proposed, which leads to the identification of a unique distribution μ describing the asymptotic properties of the system for initial data randomly chosen with respect to a uniform distribution on phase space.
Abstract: We propose, as a generalization of an idea of Ruelle's to describe turbulent fluid flow, a chaotic hypothesis for reversible dissipative many-particle systems in nonequilibrium stationary states in general. This implies an extension of the zeroth law of thermodynamics to nonequilibrium states and it leads to the identification of a unique distribution μ describing the asymptotic properties of the time evolution of the system for initial data randomly chosen with respect to a uniform distribution on phase space. For conservative systems in thermal equilibrium the chaotic hypothesis implies the ergodic hypothesis. We outline a procedure to obtain the distribution μ: it leads to a new unifying point of view for the phase space behavior of dissipative and conservative systems. The chaotic hypothesis is confirmed in a nontrivial, parameter-free, way by a recent computer experiment on the entropy production fluctuations in a shearing fluid far from equilibrium. Similar applications to other models are proposed, in particular to a model for the Kolmogorov-Obuchov theory for turbulent flow.
910 citations
TL;DR: The mean square displacement as a function of time is calculated and the Einstein relation of diffusivity and temperature for random walks of the Levy-Right type is generalized.
Abstract: It is pointed out that the generalized statistical mechanics introduced by Tsallis [J. Stat. Phys. 52, 479 (1988)] provides a natural frame for developing a thermodynamical formalism of anomalous diffusion. Within such a frame, we calculate the mean square displacement as a function of time and generalize the Einstein relation of diffusivity and temperature for random walks of the L\'evy-flight type.
201 citations
TL;DR: In this paper, it was shown by numerical calculations that in extended thermodynamics of 13, 14, 20, and 21 moments a continuous shock structure exists up to a critical Mach number.
Abstract: It is shown by numerical calculations that in extended thermodynamics of 13, 14, 20, and 21 moments a continuous shock structure exists up to a critical Mach number. The critical Mach number increases by increasing the number of moments; the value runs from 1.65 for 13 moments up to 1.887 for 21 moments.
142 citations
TL;DR: In this article, the coupled heat and mass transport in a binary isotope mixture of particles interacting with a Lennard-Jones/spline potential has been studied, and four different criteria are used to analyze the concept of local equilibrium in the nonequilibrium system.
Abstract: Nonequilibrium molecular dynamics is used to compute the coupled heat and mass transport in a binary isotope mixture of particles interacting with a Lennard-Jones/spline potential. Two different stationary states are studied, one with a fixed internal energy flux and zero mass flux, and the other with a fixed diffusive mass flux and zero temperature gradient. Computations are made for one overall temperature,T=2, and three overall number densities,n=0.1, 0.2, and 0.4. (All numerical values are given in reduced, Lennard-Jones units unless otherwise stated.) Temperature gradients are up to ∇T=0.09 and weight-fraction gradients up to ∇w1=0.007. The flux-force relationships are found to be linear over the entire range. All four transport coefficients (theL-matrix) are determined and the Onsager reciprocal relationship for the off-diagonal coefficients is verified. Four different criteria are used to analyze the concept of local equilibrium in the nonequilibrium system. The local temperature fluctuation is found to be δT≈0.03T and of the same order as the maximum temperature difference across the control volume, except near the cold boundary. A comparison of the local potential energy, enthalpy, and pressure with the corresponding equilibrium values at the same temperature, density, and composition also verifies that local equilibrium is established, except near the boundaries of the system. The velocity contribution to the BoltzmannH-function agrees with its Maxwellian (equilibrium) value within 1%, except near the boundaries, where the deviation is up to 4%. Our results do not support the Eyring-type transport theory involving jumps across energy barriers; we find that its estimates for the heat and mass fluxes are wrong by at least one order of magnitude.
106 citations
TL;DR: In this paper, a multiconfigurational self-consistent reaction field (MCSCF) was proposed for solvent effects on a solute molecular system that is not in equilibrium with the outer solvent.
Abstract: We present multiconfigurational self‐consistent reaction field theory and implementation for solvent effects on a solute molecular system that is not in equilibrium with the outer solvent. The approach incorporates two different polarization vectors for studying the influence of the solvent. The solute, an atom, a molecule or a supermolecule, is assumed to be surrounded by a linear, homogeneous medium described by two polarization vector fields, the optical polarization vector and the inertial polarization vector fields. The optical polarization vector is always in equilibrium with the actual electronic structure whereas the inertial polarization vector is not necessarily in equilibrium with the actual electronic structure. The electronic structure of the compound is described by a correlated electronic wave function—a multiconfigurational self‐consistent field (MCSCF) wave function. This wave function is fully optimized with respect to all variational parameters in the presence of the surrounding polariz...
102 citations
TL;DR: A Maxwell's demon type information engine that extracts work from a bath is constructed from a microscopic Hamiltonian for the whole system including a subsystem, a thermal bath, and a nonequilibrium bath of phonons or photons that represents an information source or sink.
Abstract: A Maxwell's demon type information engine'' that extracts work from a bath is constructed from a microscopic Hamiltonian for the whole system including a subsystem, a thermal bath, and a nonequilibrium bath of phonons or photons that represents an information source or sink. The kinetics of the engine is calculated self-consistently from the state of the nonequilibrium bath, and the relation of this kinetics to the underlying microscopic thermodynamics is established.
77 citations
TL;DR: A local-nonequilibrium model for rapid solidification of highly undercooled melts is proposed in this paper, which predicts an abrupt change of the effective diffusion coefficient, the partition coefficient, and hence the solidification mechanism when the interface velocity is equal to the diffusive speed.
70 citations
TL;DR: In this article, the authors developed a formalism to model configurational thermodynamics in ionic systems with multiple anion and cation species, where cations and anions can be partitioned into two interacting sublattices that do not exchange species, and the dimensionality of configuration space is significantly reduced.
Abstract: We develop a formalism to model configurational thermodynamics in ionic systems with multiple anion and cation species. Because cations and anions can be partitioned into two interacting sublattices that do not exchange species, the dimensionality of configuration space is significantly reduced. The result is a model applicable to many important problems in ionic systems. Here we show that the effect of an order-disorder transition in one sublattice on the other depends on how the symmetry is changed through the transition, as well as on the strength of the interactions.
65 citations
TL;DR: It is shown that for general mean field models driven at low rates fluctuations in the internal energy field are characterized by Boltzmann statistics, and results indicate thatmean field models can be effectively treated as equilibrium systems.
Abstract: Nonequilibrium threshold systems such as slider blocks are now used to model a variety of dynamical systems, including earthquake faults, driven neural networks, and sliding charge density waves. We show that for general mean field models driven at low rates fluctuations in the internal energy field are characterized by Boltzmann statistics. Numerical simulations confirm this prediction. Our results indicate that mean field models can be effectively treated as equilibrium systems.
64 citations
TL;DR: In this paper, it was shown that kinetic anisotropy stabilizes dendritic growth in electrochemical deposition of copper, and that in its absence the growth tips are unstable to splitting.
Abstract: It is shown that kinetic anisotropy stabilizes dendritic growth in electrochemical deposition of copper, and that in its absence the growth tips are unstable to splitting. The degree of anisotropy in the interfacial dynamics, which may be controlled through the chemistry of the electrolyte solution, was determined by the measurement of open-circuit potentials of single-crystal electrodes under nonequilibrium conditions. The experiments provide direct evidence that microscopic interfacial anisotropy in depositional growth stabilizes the dendritic morphology.
TL;DR: In this article, the authors studied the long-time effect of relaxation when the initial data is a perturbation of an equilibrium constant state, and showed that the effect is equivalent to a viscous effect, or in other words, the Chapman-Enskog expansion is valid.
Abstract: The hyperbolic conservation laws with relaxation appear in many physical systems such as nonequilibrium gas dynamics, flood flow with friction, viscoelasticity, magnetohydrodynamics, etc. This article studies the long-time effect of relaxation when the initial data is a perturbation of an equilibrium constant state. It is shown that in this case the long-time effect of relaxation is equivalent to a viscous effect, or in other words, the Chapman-Enskog expansion is valid. It is also shown that the corresponding solution tends to a diffusion wave time asymptotically. This diffusion wave carries an invariant mass. The convergence rate to this diffusion wave in theLp-sense for 1≦p≦∞ is also obtained and this rate is optimal.
TL;DR: In this article, a mechano-statistical formalism for the description of nonequilibrium classical Hamiltonian many-body systems is presented, based on a variational principle that recovers known approaches as particular cases.
Abstract: We consider a mechano-statistical formalism for the description of nonequilibrium classical Hamiltonian many-body systems. It is described how such formalism, the so called nonequilibrium statistical operator method at the classical mechanical level is obtained through the use of a variational principle that recovers known approaches as particular cases. The method is shown to be encompassed in the context of Jaynes' Predictive Statistical Mechanics. On the basis of this formalism it is shown how to obtain a nonlinear generalized transport theory of large scope. This theory is applied to derive the equations of evolution for the single- and two-particle distribution functions to obtain generalized transport equations including relaxation effects to all orders in the interaction strength, valid, in principle, for arbitrary nonequilibrium dissipative states. The classical Boltzmann equation and Boltzmann's H-theorem are recovered within restrictive approximations. Finally we discuss the connection with phenomenological irreversible thermodynamics, for which the method provides microscopic foundations in what is termed Informational Statistical Thermodynamics. The questions of entropy production and a generalized H-theorem are considered and conceptual aspects of the method are discussed.
TL;DR: This work treats the general problem of transferring a system from a given initial state to a given final state in a given finite time such that the produced entropy or the loss of availability is minimized.
Abstract: We treat the general problem of transferring a system from a given initial state to a given final state in a given finite time such that the produced entropy or the loss of availability is minimized. We give exact equations for the optimal process for the general case of a system with several state variables. For linear processes, e.g., in the limit of slow processes or if the Onsager coefficients do not depend on the fluxes, we find a constant entropy production rate or constant loss rate of availability. An alternative kinetic process length is introduced. The entropy production rate is the square of the speed based on this length and clock time. This length adequately treats variations of the system time scale matrix along the path. For the nonlinear case, the entropy production rate or loss rate of availability is generally not constant for an optimal process.
TL;DR: The calculus of variations can be applied in thermodynamics obtaining both local and global analysis for the thermodynamical systems as mentioned in this paper, where Gyarmati's principle is demonstrated to be the mathematical fundamental of the theorem of maximum for the entropy of open systems.
Abstract: The calculus of variations can be applied in thermodynamics obtaining both local and global analysis for the thermodynamical systems. Gyarmati’s principle is demonstrated to be the mathematical fundamental of the theorem of maximum for the entropy of the open systems. This last theorem is demonstrated for a general thermodynamical transformation, and also when chemical reactions can occur.
TL;DR: This work presents a detailed dynamical study of the transitions in the bifurcation sequence in both the elementary cell and the fundamental domain of a Lorentz gas system.
Abstract: We study the conductivity of a Lorentz gas system, composed of a regular array of fixed scatterers and a point‐like moving particle, as a function of the strength of an applied external field. In order to obtain a nonequilibrium stationary state, the speed of the point particle is fixed by the action of a Gaussian thermostat. For small fields the system is ergodic and the diffusion coefficient is well defined. We show that in this range the Periodic Orbit Expansion can be successfully applied to compute the values of the thermodynamic variables. At larger values of the field we observe a variety of possible dynamics, including the breakdown of ergodic behavior, and later the existence of a single stable trajectory for the largest fields. We also study the behavior of the system as a function of the orientation of the array of scatterers with respect to the external field. Finally, we present a detailed dynamical study of the transitions in the bifurcation sequence in both the elementary cell and the funda...
Abstract: A two-temperature model is developed for the description of thermal and chemical nonequilibrium viscous hypersonic flows including ionization. A preferential dissociation model and nonpreferential removal of vibrational and electronic energy are assumed. For weakly ionized flows, an ambipolar diffusion coefficient is introduced to describe ion diffusion. The numerical technique relies on a finite-volume approach based on a second-order accurate Total-Variation-Diminishing formulation that allows for thermal and chemical nonequilibrium effects as well as for ionization. The model has been applied to compute ionizing hypersonic flows over a wedge and a RAM-C geometry. Applications have shown that, for weakly ionized flows, ionization is essentially decoupled from the other field properties. Moreover, the computations show the importance of considering kinetic and diffusive mechanisms fully coupled in order to properly understand the flow features.
TL;DR: In this article, the authors developed the thermodynamics of the phase reaction between nonhydrostatically stressed grains and an intervening water layer by using the concept of the disjoining pressure to account for surface forces acting in the grain-to-grain contact zone.
Abstract: Existing work on mineral solubility in fluid-infiltrated and stressed rock has remained limited in that it has neglected surface forces. These forces are appreciable only when the fluid exists as a thin film, as in the grain-to-grain contact zone and in microcracks. Indeed, when the film thickness is of the order of 10−9 m or so, the strength of the forces can be comparable to overburden stress at several kilometers depth. In this contribution we develop the thermodynamics of the phase reaction between nonhydrostatically stressed grains and an intervening water layer by using the concept of the disjoining pressure to account for surface forces acting in the grain-to-grain contact zone. Using a thermodynamic extremum principle, we find an extended version of Gibbs's classical condition for the equilibrium of a stressed solid in contact with its solution phase. We then employ nonequilibrium thermodynamics to formulate kinetic equations describing phase boundary migration and intergranular mass transfer. It is demonstrated that surface forces weaken the efficacy with which diffusion removes dissolved material from the grain-to-grain contact zone and enhance the tendency of intergranular pressure solution to flatten initially rough surfaces.
TL;DR: In this article, the dynamic surface tension of aqueous Triton X solutions (X-45, X100, X-100, x-114 and X-165) were measured by using a maximum bubble pressure technique in a broad concentration and temperature interval.
Abstract: The dynamic surface tensions of aqueous Triton X solutions (X-45, X-100, X-114, X-165, X-305, and X-405) were measured by using a maximum bubble pressure technique in a broad concentration and temperature interval. Using a special measuring cell for the MPT1/LAUDA, studies in the time interval from 100 μs up to 50 s were achieved. The results at very short adsorption times simulate a faster surface tension decrease than expected from a common diffusion-controlled mechanism. The deviation from that theory increases with temperature and the length of the ethylene oxide chains. The experimental results are in agreement with a theoretical model taking into consideration different orientations of the EO chain in diluted and compressed adsorption layers and the temperature effect on the interfacial water structure.
TL;DR: In this paper, a unified treatment of elementary surface phenomena based on the formalism of thermodynamics is presented and compared to more familiar treatments based on Newtonian mechanics, where emphasis is put on the surface free energy concept rather than on surface tension, not only because the former is more fundamental but also because the latter may mislead if pushed too far.
Abstract: A unified treatment of elementary surface phenomena based on the formalism of thermodynamics is presented and compared to more familiar treatments based on the formalism of Newtonian mechanics. Emphasis is put on the surface free energy concept rather than on surface tension, not only because the former is more fundamental, but also because the latter may mislead if pushed too far. The examples discussed (Young–Laplace and Young–Dupre equations, and capillary rise) can be easily described with the help of the Helmholtz function, and clearly show some of the advantages of the thermodynamic approach. In particular, several misleading results appearing in elementary treatments can be avoided by using this approach. It is concluded that: (i) thermodynamics and physical chemistry courses should favor the formalism of thermodynamics rather than mechanics when dealing with surface phenomena; and (ii) when the mechanical approach is still preferred, some weak points in the standard derivations (e.g., the existenc...
TL;DR: In this paper, a nonequilibrium model for the dynamic simulation of distillation columns is described, which includes the direct calculation of the rates of mass and energy transfer and is better able to model the actual physical processes occurring on a real distillation tray than is the conventional equilibrium stage model.
Abstract: A nonequilibrium model for the dynamic simulation of distillation columns is described. The nonequilibrium model includes the direct calculation of the rates of mass and energy transfer and is better able to model the actual physical processes occurring on a real distillation tray than is the conventional equilibrium stage model. Example calculations show that heat-transfer limitations and the vapor holdup above the froth cannot be neglected at elevated pressures. Back-computed Murphree tray efficiencies are not constant over time, which implies that the equilibrium model should not be used for dynamic simulations.
TL;DR: In this paper, a simulation of stress relaxation in a model polymer melt is performed with a nonequilibrium molecular dynamics algorithm, where the chains are freely jointed with N=30, 100, and 200 bonds and with both intra-and inter-chain excluded volume interactions.
Abstract: The computer simulation of stress relaxation in a model polymer melt is performed with a nonequilibrium molecular dynamics algorithm. The chains are freely jointed with N=30, 100, and 200 bonds and with both intra‐ and interchain excluded volume interactions. For N=200, the model exhibits incipient plateau behavior as evidenced by an inflection point in the stress relaxation history. Comparison is made between the stress history as computed on the atomic level by the virial stress formula and on the molecular level using the entropic spring formulation. The two histories are in agreement only for the case of N=200, with entanglement length Ne=40, and only for the time period following the inflection point.
TL;DR: In this article, the authors review the molecular origins of nonequilibrium (irreversible) interactions of surfaces that give rise to adhesion hysteresis, contact angle hysteressesis, friction, and other thin-film properties.
Abstract: The use of thermodynamic functions such as surface energy (y) or the reversible work of adhesion (W) implicitly assumes that two surfaces are interacting under conditions of thermodynamic equilibrium. Likewise, the concept of the adhesion force or pressure between two surfaces, molecules, or colloidal particles also suggests the existence of well-defined time-independent values for these quantities. Yet most interactions involving molecules, surfaces, and complex fluid systems are irreversible, involving the transfer of energy from one system to another; that is, they involve “energy dissipation”. We review the molecular origins nonequilibrium (irreversible) interactions of surfaces that give rise to adhesion hysteresis, contact angle hysteresis, friction, and other thin-film properties, and discuss the important role of “time” in such processes which can have a significant effect on what we measure. We also consider the possible central role of nonequilibrium interactions in biological systems, where nature often makes use of the finite time of molecular processes for regulating the interactions of proteins, membranes, and cells.
TL;DR: In this paper, a chaotic hypothesis for reversible dissipative many particle systems in nonequilibrium stationary states in general is proposed, which leads to the identification of a unique distribution describing the asymptotic properties of the time evolution of the system for initial data randomly chosen with respect to a uniform distribution on phase space.
Abstract: We propose as a generalization of an idea of Ruelle to describe turbulent fluid flow a chaotic hypothesis for reversible dissipative many particle systems in nonequilibrium stationary states in general. This implies an extension of the zeroth law of thermodynamics to non equilibrium states and it leads to the identification of a unique distribution $\m$ describing the asymptotic properties of the time evolution of the system for initial data randomly chosen with respect to a uniform distribution on phase space. For conservative systems in thermal equilibrium the chaotic hypothesis implies the ergodic hypothesis. We outline a procedure to obtain the distribution $\m$: it leads to a new unifying point of view for the phase space behavior of dissipative and conservative systems. The chaotic hypothesis is confirmed in a non trivial, parameter--free, way by a recent computer experiment on the entropy production fluctuations in a shearing fluid far from equilibrium. Similar applications to other models are proposed, in particular to a model for the Kolmogorov--Obuchov theory for turbulent flow.
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15 Dec 1995
TL;DR: In this article, the authors present a survey of the literature on gases, liquids, and crystals in terms of their relationship with radiation and thermodynamics, including the following categories: 1. Gases. 2. Crystals.
Abstract: Preface. 1. Gases. 2. Radiation. 3. Crystals. 4. Liquids. 5. Thermodynamics. Bibliography. Index.
TL;DR: It is shown that the Pfaffian form descends from the Clausius inequality, which is regarded as equivalent to the second law of thermodynamics.
Abstract: A form of uncompensated heat is presented which gives rise to a Pfaffian differential form for a non- equilibrium extension of equilibrium entropy when the thermodynamic space is broadened to include fluxes of various orders. It is thereby shown that the Pfaffian form descends from the Clausius inequality, which is regarded as equivalent to the second law of thermodynamics.
TL;DR: In this article, the authors compared the characteristics of planar Couette, planar elongation, uniaxial stretching, and biaaxial stretching flows in simple fluids at different strain rates.
Abstract: Nonequilibrium molecular dynamics simulations have been performed in order to compare the characteristics of planar Couette, planar elongation, uniaxial stretching, and biaxial stretching flows in simple fluids at different strain rates. After deriving the periodic boundary conditions for general flow fields and introducing some methodological improvements for elongation flow calculations we simulated the combination of shear and shear‐free flows as well. We found that even at high strain rates where simple fluids exhibit strong non‐Newtonian behavior (shear‐thinning) it is a reasonable approximation to consider the two planar flows to be rotationally equivalent. This is because in planar Couette flow the in‐plane normal stress difference of simple fluids is approximately zero even far from equilibrium. Similarly to planar Couette flow, the trace of the pressure tensor and the internal energy vary approximately as function of the 3/2 power of the strain rate in shear free flows. However, the individual diagonal elements of elongation flow pressure tensors deviate considerably from this approximation. In the extension direction the pressure seems to have a minimum in terms of the strain rate in every shear‐free flow. We have discussed the implications of these results.
TL;DR: In this paper, a physically based formulation relating the chemical state of nonequilibrium combustion in turbulent flows to the mixing state of a conserved scalar is presented, motivated by results from detailed imaging studies of scalar mixing.