Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures

We have employed a simple Galerkin-approximation scheme to calculate nonequilibrium temperature and concentration fluctuations in a binary fluid subjected to a temperature gradient with realistic boundary conditions. When a fluid mixture is driven outside thermal equilibrium, there are two instability mechanisms, namely a Rayleigh (stationary) and a Hopf (oscillatory) instability, causing long-ranged fluctuations. The competition of these two mechanisms causes the structure factor associated with the temperature fluctuations to exhibit two maxima as a function of the wave number q of the fluctuations, in particular, close to the convective instability. In the presence of thermally conducting but impermeable walls the intensity of the temperature fluctuations vanishes as q goes to zero, while the intensity of the concentration fluctuations remains finite in the limit of vanishing q. Finally, we propose a simpler small-Lewis-number approximation scheme, which is useful to represent nonequilibrium concentration fluctuations for mixtures with positive separation ratio, even close to (but below) the convective instability.     

Long-range order and dynamic structure factor of a nematic under a thermal gradient

We use a fluctuating hydrodynamic approach to calculate the orientation fluctuations correlation functions of a thermotropic nematic liquid crystal in a nonequilibrium state induced by a stationary heat flux. Since in this nonequilibrium stationary state the hydrodynamic fluctuations evolve on three widely separated times scales, we use a time-scale perturbation procedure in order to partially diagonalize the hydrodynamic matrix. The wave number and frequency dependence of these orientation correlation functions is evaluated and their explicit functional form on position is also calculated analytically in and out of equilibrium. We show that for both states these correlations are long-ranged. This result shows that indeed, even in equilibrium there is long-range orientational order in the nematic, consistently with the well known properties of these systems.We also calculate the dynamic structure of the fluid in both states for a geometry consistent with light scattering experiments. We find that as with isotropic simple fluids, the external temperature gradient introduces an asymmetry in the spectrum shifting its maximum by an amount proportional to the magnitude of the gradient. This effect may be of the order of 7 per cent. Also, the width at half height may decrease by a factor of about 10 per cent. Since to our knowledge there are no experimental results available in the literature to compare with, the predictions of our model calculation remains to be assessed.     

Order and fluctuations in nonequilibrium molecular dynamics simulations of two-dimensional fluids

Finite systems of hard disks placed in a temperature gradient and in an external constant field have been studied, simulating a fluid heated from below. We used the methods of nonequilibrium molecular dynamics. The goal was to observe the onset of convection in the fluid. Systems of more than 5000 particles have been considered and the choice of parameters has been made in order to have a Rayleigh number larger than the critical one calculated from the hydrodynamic equations. The appearance of rolls and the large fluctuations in the velocity field are the main features of these simulations.     

Fokker-Planck equation approach to fluctuations about nonequilibrium steady states

We examine the properties of steady states in systems which interact at the boundary with a nonequilibrium environment. The examination is based on a nonlinear Fokker-Planck equation, the structure of which is determined by the fact that it also governs the time evolution of the equilibrium fluctuations of the system. The nonlinearities in the Fokker-Planck equation may have two origins: thermodynamic nonlinearities which arise if the thermodynamic potential is not a bilinear function of the state variables, and nonlinear mode coupling which arises if the transport coefficients depend on the state. While these nonlinearities have only a small effect on the equilibrium fluctuations of a system away from critical points, they are shown to be important for the determination of fluctuations about nonequilibrium steady states. In particular the state dependence of the transport coefficients may lead to deviations from local equilibrium and to a breakdown of detail balance. An explicit formula for the time correlations of fluctuations about the nonequilibrium steady state is obtained. The formula leads to long-range correlations in fluids in the presence of a temperature gradient. The result is compared with earlier approaches to the same problem. Finally, we study the linear response to external forces and obtain a generalization of the fluctuation-dissipation formula relating the response functions with the nonequilibrium correlation functions.     

Phase transitions and relaxation characteristics of Quantum Magnets and Quantum Glasses

An overview is presented of the phase changes as well as certain relaxation characteristics of model quantum magnets, magnetic glasses and proton glasses. Although the systems considered are quite varied, they are connected by the common themes of tunneling, transverse Ising model, long-ranged interactions and above all, the occurrence of quantum phase transitions. Because the interactions are long-ranged, mean-field theory is eminently suitable for analyzing both the equilibrium and nonequilibrium properties. Wherever pertinent, detailed comparisons with experimental data have been presented.     

Stochastic resonance and scale invariance in nonequilibrium metastable states

Using computer simulations, we study metastability in a two-dimensional Ising ferromagnet relaxing toward a nonequilibrium steady state. The interplay between thermal and nonequilibrium fluctuations induces resonant and scale-invariant phenomena not observed in equilibrium. In particular, we measure noise-enhanced stability of the metastable state in a nonequilibrium environment. The limit of metastability, or pseudospinodal separating the metastable regime from the unstable one, exhibits reentrant behavior as a function of temperature for strong nonequilibrium conditions. Furthermore, when subject to both open boundaries and nonequilibrium fluctuations, the metastable system decays via well-defined avalanches. These exhibit power-law size and lifetime distributions, resembling the scale-free avalanche dynamics observed in real magnets and other complex systems. We expect some of these results to be verifiable in actual (impure) specimens.     

Lyapunov Instability for a Hard-Disk Fluid in Equilibrium and Nonequilibrium Thermostated by Deterministic Scattering

We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and under shear. The Lyapunov exponents are calculated using a recently developed formalism for systems with elastic hard collisions. The system is thermalized by deterministic and time-reversible scattering at the boundary, whereas the bulk dynamics remains Hamiltonian. This thermostating mechanism allows for energy fluctuations around a mean value which is reflected by only two vanishing Lyapunov exponents in equilibrium and nonequilibrium. In nonequilibrium steady states the phase-space volume is contracted on average, leading to a negative sum of the Lyapunov exponents. Since the system is driven inhomogeneously we do not expect the conjugate pairing rule to hold, which is indeed shown to be the case. Finally, the Kaplan–Yorke dimension and the Kolmogorov–Sinai entropy are calculated from the Lyapunov spectra.     

Crossover between complete wetting and critical adsorption

The effects of bulk critical fluctuations on the adsorption of a fluid on a planar attractive substrate are studied as a function of the temperature and chemical potential in the presence of long-ranged forces. The latter are explicitly included in a phenomenological free energy functional constructed to give non-classical critical exponents. The crossover between the complete wetting and the critical adsorption regime is studied along different paths in thermodynamic space and a comparison is made with the results of recent experiments.     

Flicker Noise in a Locally Nonequilibrium Medium

A model implying that particles of a medium are subjected to external forces with a flicker noise spectrum has been proposed to describe fluctuations in locally nonequilibrium physical media. The Langevin equation with additional integral terms describing the action of the locally nonequilibrium medium has been derived. The spectral density of fluctuations of an electric current flowing in the locally nonequilibrium medium has been calculated. It has been found that this density in the low-frequency spectral range is flicker noise.     

Nonequilibrium work fluctuations in a driven Ising model

Monte Carlo simulations of a sheared Ising model are used to study nonequilibrium fluctuations of mechanical work. The validity of the transient (starting from equilibrium) and the steady state fluctuation relations is verified. A fluctuation relation has been also shown to hold for the mechanical work done on the system, during the transition between two nonequilibrium steady states corresponding to different drivings.     

Fluctuations of internal energy flow in a vibrated granular gas

The nonequilibrium fluctuations of power flux in a fluidized granular media have been recently measured in an experiment [Phys. Rev. Lett. 92, 164301 (2004)], which was announced to be a verification of the fluctuation relation (FR) by Gallavotti and Cohen. An effective temperature was also identified and proposed to be a useful probe for such nonequilibrium systems. We explain these results in terms of a two-temperature Poisson process. Within this model, supported by independent molecular dynamics simulations, power flux fluctuations do not satisfy the FR and the nature of the effective temperature is clarified. In the pursuit of a hypothetical global quantity fulfilling the FR, this points to the need of considering candidates other than the power flux.     

Phase transitions in a driven lattice gas in two planes

We report on a Monte Carlo study of ordering in a nonequilibrium system. The system is a lattice gas that comprises two equal, parallel square lattices with stochastic particle-conserving irreversible dynamics. The particles are driven along a principal direction under the competition of the heat bath and a large, constant external electric field. There is attraction only between particles on nearest-neighbor sites within the same lattice. Particles may jump from one plane to the other; therefore, density fluctuations have an extra mechanism to decay and build up. It helps to obtain the steady-state accurately. Spatial correlations decay with distance according to a power law at high enough temperature, as for the ordinary two-dimensional case. We find two kinds of nonequilibrium phase transitions. The first one has a critical point for half occupation of the lattice, and seems to be related to the anisotropic phase transition reported before for the plane. This transition becomes discontinuous for low enough density. The difference of density between the planes changes discontinuously for any density at a lower temperature. This seems to correspond to a phase transition that does not have a counterpart in equilibrium nor in the two-dimensional nonequilibrium case.     

Spin fluctuations of nonequilibrium electrons and excitons in semiconductors

Effects that are related to deviations from thermodynamic equilibrium have a special place in modern physics. Among these, nonequilibrium phenomena in quantum systems attract the highest interest. The experimental technique of spin-noise spectroscopy has became quite widespread, which makes it possible to observe spin fluctuations of charge carriers in semiconductors under both equilibrium and nonequilibrium conditions. This calls for the development of a theory of spin fluctuations of electrons and electron–hole complexes for nonequilibrium conditions. In this paper, we consider a range of physical situations where a deviation from equilibrium becomes pronounced in the spin noise. A general method for the calculation of electron and exciton spin fluctuations in a nonequilibrium state is proposed. A short review of the theoretical and experimental results in this area is given.     

Water polarization under thermal gradients

We investigate the response of bulk liquid water to a temperature gradient using nonequilibrium molecular dynamics simulations. It is shown that the thermal gradient polarizes water in the direction of the gradient, leading to a non-negligible electrostatic field whose origin lies in the water reorientation under nonequilibrium conditions. The dependence of the magnitude of the electrostatic field with the temperature gradient is in agreement with nonequilibrium thermodynamics theory. We conclude that temperature gradients of the order of 10(8) K/m could result in fairly large polarizations approximately 10(6) V/m.     

Measurement of effective temperatures in an aging colloidal glass

We study the thermal fluctuations of an optically confined probe particle, suspended in an aging colloidal suspension, as the suspension transforms from a viscous liquid into an elastic glass. The micron-sized bead forms a harmonic oscillator. By monitoring the equal-time fluctuations of the tracer, at two different laser powers we determine the temperature of the oscillator, T(o). In the ergodic liquid the temperatures of the oscillator and its environment are equal, while in contrast, in a nonequilibrium glassy phase we find that T(o) substantially exceeds the bath temperature.     

The theory of shot noise in the space-charge-limited diffusive conduction regime

As is well known, fluctuations from a stable stationary nonequilibrium state are described by the linearized inhomogeneous Boltzmann-Langevin equation. The stationary state itself can be described by the nonlinear Boltzmann equation. The ways of its linearization sometimes seem to be not unique. We argue that there is actually a unique way to obtain a linear equation for the fluctuations. As an example, we consider an analytical theory of nonequilibrium shot noise in a diffusive conductor under the space-charge-limited regime. Our approach is compared to that in [11]. We find some difference between the present theory and the approach in [11] and discuss a possible origin of the difference. We believe that it is related to the fundamentals of the theory of fluctuation phenomena in a nonequilibrium electron gas.     

Density fluctuations in the presence of spinodal instabilities

Density fluctuations resulting from spinodal decomposition in a nonequilibrium first-order chiral phase transition are explored. We show that such instabilities generate divergent fluctuations of conserved charges along the isothermal spinodal lines appearing in the coexistence region. Thus, divergent density fluctuations could be a signal not only for the critical end point but also for the first-order phase transition expected in strongly interacting matter. We also compute the mean-field critical exponent at the spinodal lines. Our analysis is performed in the mean-field approximation to the Nambu-Jona-Lasinio model formulated at finite temperature and density. However, our main conclusions are expected to be generic and model independent.     

Universal behavior of nonequilibrium fluctuations in free diffusion processes

We show that giant nonequilibrium fluctuations are present during the free diffusive remixing occurring in ordinary liquid mixtures and in macromolecular solutions. The static structure factor of the fluctuations is measured by using a quantitative shadowgraph technique. We show that structure factors at different times and from different samples can be rescaled onto a single master curve without any adjustable parameter, thus giving strong evidence that nonequilibrium fluctuations are a universal feature of free diffusion processes.     

Kinetic mechanism of the electroplastic effect in metals

A new mechanism of electroplastic deformation is proposed, which is based on nonequilibrium fluctuations of dislocation vibrations due to the interaction between dislocations and hot electrons. It is shown that, when an electric current flows through a metal, the average energy of dislocation vibrations differs from that corresponding to the lattice temperature. As a result, the frequency of fluctuation-induced jumps of dislocations over obstacles increases.