Entropy production in nonequilibrium systems at stationary states

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.     

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

A new approach to the properties of a harmonic crystal in a stationary nonequilibrium state

An exact analytical solution has been obtained for the covariance matrix resulting from a stochastic interaction of a linear chain ofN coupled harmonic oscillators with different heat reservoirs via its endparticles. For the special case, that the friction forces on the endparticles, which result from the system-heatbath-interaction, are equal, we obtain the same results as Lebowitz et al. by applying an entirely different mathematical technique as these authors have used. For the realistic coupling, where friction and diffusion coefficient differ for different heatbaths and are only connected via the Einstein relation we obtain additional contributions to the correlation matrices between the momenta and between the displacements.On leave from the School of Nuclear Engineering, The University of New South Wales, Sydney, Australia     

Laser-induced nonthermal mechanical stresses and optical damage in a transparent dielectric

Optical damage of pure transparent dielectrics in laser fields is considered. An elasticity theory problem concerning mechanical stresses that appear in the crystal lattice subjected to arbitrary spherically symmetric forces with a specified density is stated. A mathematically rigorous general solution to this problem is found, and arising boundary conditions are studied. A model of volume forces due to the action of hot nonequilibrium electrons on the lattice is described. In general, the early approximate results [1] are confirmed. The mechanism behind radiation-induced mechanical fracture of dielectrics proposed in this work is found to be adequate. Ways for the further study of this nonthermal inertia-free mechanism of optical damage, which has a purely mechanical nature, are discussed.     

Heat transport in quantum spin chains

We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with the reservoirs: a model of stochastic heat baths and the quantum trajectories solution of the quantum master equation. The stochastic heat bath procedure operates on the pure wave function of the isolated system, so that it is locally and periodically collapsed to a quantum state consistent with a boundary nonequilibrium state. In contrast, the quantum trajectories procedure evaluates ensemble averages in terms of the reduced density matrix operator of the system. We apply these procedures to different models of quantum spin chains and numerically show their applicability to study the heat flow.     

Specific heat as a general statistical measure

A general statistical measure for probability distributions is connected with specific heat, which therefore can find an analogy in non-equilibrium phase transitions. The statistical measure is discussed for illustrating examples. A similar measure is given for quantum mechanical density matrices.     

Structural phase transitions in isotropic magnetic elastomers

Magnetic elastomers represent a new type of materials that are “soft” matrices with “hard” magnetic granules embedded in them. The elastic forces of the matrix and the magnetic forces acting between granules are comparable in magnitude even under small deformations. As a result, these materials acquire a number of new properties; in particular, their mechanical and/or magnetic characteristics can depend strongly on the polymer matrix filling with magnetic particles and can change under the action of an external magnetic field, pressure, and temperature. To describe the properties of elastomers, we use a model in which the interaction of magnetic granules randomly arranged in space with one another is described in the dipole approximation by the distribution function of dipole fields, while their interaction with the matrix is described phenomenologically. A multitude of deformation, magnetic-field, and temperature effects that are described in this paper and are quite accessible to experimental observation arise within this model.     

Classical and quantum kinetic equations with exact conservation laws

Stationary and dynamic properties of reduced density matrices can be determined from formal or approximate closures of an infinite hierarchy of equations. The local macroscopic conservation laws place weak but important constraints on the reduced density matrices which should be respected by any closure. For pairwise additive forces conditions on the closure of the one- and two-particle equations are obtained that preserve the exact functional dependence of the conserved densities and their fluxes on the reduced density matrices. To illustrate the nature of these conditions, a closure approximation suitable for a quantum gas is given, yielding an extension of the time-dependent Hartree-Fock equations for the dynamics of a nuclear fluid to include collisions.     

Spin-boson thermal rectifier

Rectification of heat transfer in nanodevices can be realized by combining the system inherent anharmonicity with structural asymmetry. We analyze this phenomenon within the simplest anharmonic system-a spin-boson nanojunction model. We consider two variants of the model that yield, for the first time, analytical solutions: a linear separable model in which the heat reservoirs contribute additively, and a nonseparable model suitable for a stronger system-bath interaction. Both models show asymmetric (rectifying) heat conduction when the couplings to the heat reservoirs are different.     

Vibration of large turbo-rotors in fluid-film bearings on an elastic foundation

In the first sections of this paper the flexible rotating shaft of a turbo-rotor is treated by finite element analysis. Internal and external damping, gyroscopic forces, fluid-film forces, aerodynamic cross-coupling from steam flow and magnetic pull are taken into account. Although some hundred degrees of freedom have to be introduced to describe a realistic turbo-rotor, computational effort can be enormously reduced by making use of the banded structure of the system matrices.In the second part foundation dynamics are introduced into the rotor equations via a receptance formulation. The receptance matrices of the foundation or supporting systems can be obtained either from shaker tests or from the mode analysis of the foundation without shaft. Numerical examples are given.     

Heat Transport in Harmonic Lattices

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the non-equilibrium Green’s function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to self-consistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the high-temperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen.     

A generic model for the ionic contribution to the equation of state

Abstract

We describe an extended standard model that yields the thermodynamics of the ionic contribution for general materials, from the low temperature solid region, through melting, to the ideal gas limit. We use the Debye model for the solid. Melting is determined by the Lindemann formula with standard rules of thumb used to determine density and energy discontinuities. The model interpolates through the liquid regime to the ideal gas assuming that the specific heat drops monotonically from about 3R at melting, to 9R/4 at five times melting, and continuing to 3R/2 at high temperatures. The area under the specific heat curve is constrained in the model to reproduce the correct high temperature entropy. Thus, for a compound the extra contribution from the entropy of mixing forces into the model, in a crude way, the extra specific heat due to dissociation.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

Spatial fluctuations of the chemical potential in case of nearly coherent transport along an ordered chain

The Landauer-Büttiker approach is used to describe electron transport along a chain of scatterers which allow elastic as well as inelastic processes. The inelastic scattering takes place via side branches coupling the chain to electron reservoirs which serve as a heat bath. For small inelastic coupling of the scatterers to the heat bath strong interference effects lead to spatial fluctuations of the charge density. The corresponding oscillations of the chemical potential are discussed in view of phase-sensitive experiments measuring the four-probe resistance.     

Spectral changes in homogeneous media; a quasi-optical approach

In the past decade spectral changes depending on the spatial coherence of the source have been described by a cross-spectral density method. It is shown that for Gaussian-Schell model sources a quasi-optical approach is valid which uses Gaussian beams and ABCD matrices to describe the optical system.     

Theoretical study of the decaying convective turbulence in a shear-buoyancy PBL

The derivation of a theoretical model for the decaying convective turbulence in a shear-buoyancy planetary boundary layer is considered. The model is based on the dynamical equation for the energy density spectrum in which the buoyancy, mechanical and inertial transfer terms are retained. The parameterization for the buoyancy and mechanical terms is provided by the flux Richardson number. Regarding the inertial term an approach employing Heisenberg’s spectral transfer theory is used to describe the turbulence friction, caused by small eddies, responsible for the energy dissipation of the large eddies. Therefore, a novelty in this study is to utilize the Adomian decomposition method to solve directly without linearization the energy density spectrum equation, with this the nonlinear nature of the problem is preserved. Therefore, the errors found are only due to the parameterization used. Comparison of the theoretical model is performed against large-eddy simulation data for a decaying convective turbulence in a shear-buoyancy planetary boundary layer. The results show that the existence of a mechanical turbulent driving mechanism reduces in an accentuated way the energy density spectrum and turbulent kinetic energy decay generated by the decaying convective production in a shear-buoyancy planetary boundary layer.     

A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics

We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both bosonic or fermionic reservoirs we develop a quantum field-theoretical diagrammatic formulation in Liouville space by expanding systematically in the reservoir-system coupling and integrating out the reservoir degrees of freedom. As a result we obtain a kinetic equation for the reduced density matrix of the quantum system. Based on this formalism, we present a formally exact perturbative renormalization group (RG) method from which the kernel of this kinetic equation can be calculated. It is demonstrated how the nonequilibrium stationary state (induced by several reservoirs kept at different chemical potentials or temperatures), arbitrary observables such as the transport current, and the time evolution into the stationary state can be calculated. Most importantly, we show how RG equations for the relaxation and dephasing rates can be derived and how they cut off generically the RG flow of the vertices. The method is based on a previously derived real-time RG technique [1-4] but formulated here in Laplace space and generalized to arbitrary reservoir-system couplings. Furthermore, for fermionic reservoirs with flat density of states, we make use of a recently introduced cutoff scheme on the imaginary frequency axis [5] which has several technical advantages. Besides the formal set-up of the RG equations for generic problems of dissipative quantum mechanics, we demonstrate the method by applying it to the nonequilibrium isotropic Kondo model. We present a systematic way to solve the RG equations analytically in the weak-coupling limit and provide an outlook of the applicability to the strong-coupling case.     

薄油层SAGD开发蒸汽腔发育和生产指标预测

通过分析现场生产数据和数值模拟结果,将薄层稠油油藏蒸汽辅助重力驱油(SAGD)生产中蒸汽腔发育分为横向扩展和向下运移两个过程,并进行简化处理预测SAGD生产指标.联合质量守恒方程、能量守恒方程和周围地层散热模型得到一个描述蒸汽腔发育的综合表达式,该方程属于典型的第二类Volterra积分函数.通过拉普拉斯变换对Volterra积分函数进行半解析求解,最终得到不同时刻蒸汽腔发育状态.为验证模型的正确性,将模型的计算结果与CMG Stars的计算结果对比,整体误差小于5%.新模型可以方便简单地预测SAGD生产中蒸汽腔发育过程和生产动态指标,从而确定SAGD生产的极限油藏参数和合理的注采参数.