Non-equilibrium Quantities Research Articles

Dynamical scaling in Ising and vector spin glasses

We have studied numerically the dynamics of spin glasses with Ising and XY symmetry (gauge glass) in space dimensions 2, 3, and 4. The nonequilibrium spin-glass susceptibility and the nonequilibrium energy per spin of samples of large size L_b are measured as a function of anneal time t_w after a quench to temperatures T. The two observables are compared to the equilibrium spin-glass susceptibility and the equilibrium energy, respectively, measured as functions of temperature T and system size L for a range of system sizes. For any time and temperature a nonequilibrium time-dependent length scale L*(t_w,T) can be defined by comparing equilibrium and nonequilibrium quantities. Our analysis shows that for all systems studied, an "effective dynamical critical exponent" parametrization L*(t_w,T) = A(T) t^(1/z(T)) fits the data well at each temperature within the whole temperature range studied, which extends from well above the critical temperature to near T = 0 for dimension 2, or to well below the critical temperature for the other space dimensions studied. In addition, the data suggest that the dynamical critical exponent z varies smoothly when crossing the transition temperature.

Theoretical approaches to charged surfaces

We summarize some of our recent theoretical and numerical work on the behaviour andstructure of charged surfaces. Due to the coupling of effects on vastly different lengthscales, a complete treatment of charged surfaces is out of reach with present computerpower. On the other hand, some progress can and has been made by concentrating on onespecific aspect at a time with a suitably chosen numerical method. We discuss four suchcalculations, each using a different computational scheme, that yield various levels ofdescription of charged surfaces. (i) Coarse grained Monte Carlo simulations of idealizedsurfaces incorporate large-length-scale fluctuation and correlation effects in thecounterion cloud at a charged surface. (ii) Brownian dynamics simulations ofmore realistic, structured surfaces give modified counterion distributions andalso allow one to estimate dynamic and non-equilibrium quantities such as themobility of counterions at charged surfaces. (iii) All-atomistic molecular dynamicssimulations of water at surfaces correctly reproduce water structuring effects atsurfaces such as hydration and hydrophobic dewetting. (iv) On the nanoscopic level,quantum mechanical ab initio calculations give the effective interactions betweenoppositely charged groups in vacuum and in solution. The real theoretical challenge isto correctly piece together results obtained on all these different length scales.

Transport through quasi-degenerate states in coupled quantum dots

By means of a general method for treating mesoscopic systems with strong internal correlations, transport properties through a set of quasi-degenerate transitions in the interacting region, or active element (AE), are considered. It is shown that the behaviour of the AE drastically changes as the couplings to the contacts are varied from the strong to the weak coupling limit. These changes strongly influence the transport properties of the system, from a single increase of the current to a staircase form with unequally large steps. In the present study, kinematic interactions, non-equilibrium populations numbers and dependence on the bias voltage has been included in the treatment of the local properties of the AE. Analytical results for the equilibrium situation are presented as well as a derivation of the corresponding non-equilibrium quantities. Results from self-consistent numerical calculations of the considered case are presented.

Nonequilibrium statistical thermodynamics: Nonequilibrium grand ensemble method for sheared dilute gases

The nonequilibrium grand ensemble method previously reported is rigorously implemented for a nonequilibrium dilute gas mixture sheared in plane Couette flow geometry and analytic results are presented for the nonequilibrium thermodynamic quantities of the sheared gas. The calortropy is shown to contain all the constitutive information of the system. The notions of temperature and pressure for the nonequilibrium gas are examined on the basis of the calortropy calculated from the nonequilibrium grand partition function. The shear rate dependence of the nonlinear shear and first normal stress coefficients is calculated numerically and also by means of an iterative method. The first iterative solutions are found to give a qualitatively correct behavior for all Peclet numbers.

The Glass Transition Within the Thermodynamics of Irreversible Processes

Abstract The glass transition caused by a finite cooling rate is a continuous non-linear dissipative process whose description requires a clear distinction between equilibrium and non-equilibrium quantities. The so-called Davies or Prigogine-Defay relations (in form of an equation as well as in form of an inequality) are not relevant in such a process. The determining quantities of the glass transition are -from a macroscopic phenomenological point of view -the fluidity of the melt and the partial free enthalpy of the microscopic vacancies in the melt. All of the characteristics of the dynamics of the glass transition are essentially due to these two quantities.

Calculations of turbulent flames using a PSR microstructural library

An alternative to the laminar flamelet model is developed for intensely turbulent flame calculations. The turbulent structure of the flame is assumed to be in the distributed-reaction-zone regime. A library or lookup table of thermochemical quantities (species, temperature, and density) is constructed a priori by performing PSR calculations over a range of mixture fractions and a range of residence times corresponding to the expected range in the mixing scales. The PDF of residence times is related to the PDF of the scalar dissipation rate. The model is implemented in a two-dimensional axisymmetric k-e-g code, assuming a beta function PDF for the mixture fraction and a log-normal PDF for the scalar dissipation rate. Calculations are compared with Raman data from three turbulent bluff-body-stabilized flames (1) a non-premixed CO/H2/N2-air flame, (2) a non-premixed CH4/H2-air flame, and (3) a premixed CH4-air flame, with very encouraging results. The shapes of the profiles are similar, and the quantitative agreement is generally within 200 K or better on mean temperature and within a factor of 2 or better even on highly nonequilibrium quantities such as CO in the core of a CH4-air flame.

On a scaling law for the nonequilibrium relaxation of spin glasses

A scaling relation between remanent magnetization and excess energy of spin-glasses is tested numerically. Based on a simple domain picture of non-equilibrium states of spin-glasses a power law can be derived, which relates the excess energy to the remanent magnetization Delta E varies as Mx. The exponent x is related to the interface exponent y, which determines whether a spin-glass phase exists for T=0 or not. Therefore equilibrium properties can be determined by measurement of non-equilibrium quantities, x is calculated numerically for different temperatures T and the spatial dimensions d=2 and d=3. The numerical results are consistent with the suggested scaling relation.

Field thermodynamic potentials and geometric thermodynamics with heat transfer and fluid flow.

In order to treat the effects of local nonequilibrium in fluids the thermodynamic metric, previously used for measuring dissipation, is extended from a space of extensive state variables into a space of the field variables involving nonequilibrium quantities such as heat flux. The metric is investigated in the context of the field description of transport and flow phenomena off but close to equilibrium. Thermodynamic potentials and corresponding tensors are constructed on the basis of the extended Gibbs equation involving heat and macroscopic velocity terms. An extension of the theory is suggested to the problem of multicomponent heat and mass diffusion.

Diffusion in polyelectrolyte solutions

Molecular migration in nonhomogeneous flows of a polyelectrolyte solution is considered. The solution is modelled as a binary mixture whose electrically-charged constituents are regarded as compressible fluids. Upon deriving a set of thermodynamic restrictions for the mixture, non-equilibrium quantities are examined in detail. As a result, two schemes are elaborated for the description of cross streamline migration, induced by the second gradient of the velocity, where also occur coupling effects. In the first scheme the migration effect is described through a stress term which involves a coupling with the conformation of the macromolecule; in the second scheme it is described through a term in the diffusion velocity where coupling occurs with the velocity gradient. In both cases the thermodynamic approach leads to a systematic framework with a minimal number of constitutive coefficients, which is an essential aspect for any comparison with experimental data.

Statistical foundation of nonequilibrium contact quantities bridging phenomenological and statistical nonequilibrium-thermodynamics

Intensive variables of discrete nonequilibrium systems are defined by inequalities which are derivable quantumstatistically for contacts between discrete equilibrium and nonequilibrium systems. These contacts are described by a generalized grand-canonical nonequilibrium density operator of maximal entropy by which heat-, mass-, and power-exchange through the contact can be evaluated. A straightforward calculation yields inequalities whose interpretation enables definitions of intensive nonequilibrium quantities for discrete systems.

Spin-glass transition in a magnetic field

Abstract Studies of the spin-glass phase transition in the presence of magnetic fields are reviewed. Most of the theoretical results on the existence of such a transition and its properties are derived from the mean-field theory of spin glasses, which describes infinite-range systems. In this limit, there exists a line T c(H) which separates the region (T > T c(H)) of a unique equilibrium paramagnetic state and the region (T > T c(H)) where ergodicity is broken and the system is frozen in one of many equilibrium spin-glass states. The singularities in both equilibrium and non-equilibrium quantities at the finite-field transition are described. In vector spin glasses this transition is associated with the freezing of transverse degrees of freedom. However, weak random anisotropy may induce a cross-over to Ising behaviour if it is sufficiently strong compared to the magnetic field. In two-dimensional systems with short-range forces, and perhaps in three-dimensional systems as well, the spin-glass transition...