Phase transitions and universality in nonequilibrium steady states of stochastic Ising models

We present results of direct computer simulations and of Monte Carlo renormalization group (MCRG) studies of the nonequilibrium steady states of a spin system with competing dynamics and of the voter model. The MCRG method, previously used only for equilibrium systems, appears to give useful information also for these nonequilibrium systems. The critical exponents are found to be of Ising type for the competing dynamics model at its second-order phase transitions, and of mean-field type for the voter model (consistent with known results for the latter).     

Convoluted Gauss-Levy distributions and exploding Coulomb clusters

We study the kinetics and the distributions of nonequilibrium systems including Gaussian and Levy-type stochastic forces. We develop the assumption that deviations from the Maxwell distribution which are often observed in nonequilibrium systems may be described by convoluted Gauss-Levy distributions. We derive these distributions by solving Langevin and Fokker-Planck equations for the velocities including two noise sources, centrally distributed over Levy and Gauss functions. As an application, we estimate the evolution of the velocity distributions of exploding Coulomb clusters analytically and by simulations. We show the development of a shoulder in the distribution which is typical for convoluted Gauss-Levy distributions.     

Thermodynamically guided nonequilibrium Monte Carlo method for generating realistic shear flows in polymeric systems

A thermodynamically guided atomistic Monte Carlo methodology is presented for simulating systems beyond equilibrium by expanding the statistical ensemble to include a tensorial variable accounting for the overall structure of the system subjected to flow. For a given shear rate, the corresponding tensorial conjugate field is determined iteratively through independent nonequilibrium molecular dynamics simulations. Test simulations for the effect of flow on the conformation of a C50H102 polyethylene liquid show that the two methods (expanded Monte Carlo and nonequilibrium molecular dynamics) provide identical results.     

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.     

Numerical evidence for critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model

We give numerical evidence that the two-dimensional nonequilibrium zero-temperature random field Ising model exhibits critical behavior. Our findings are based on the results of scaling analysis and collapsing of data, obtained in extensive simulations of systems with sizes sufficiently large to clearly display the critical behavior.     

Introduction to colloidal dispersions in external fields

Progress in the research area of colloidal dispersions in external fields within the last years is reviewed. Colloidal dispersions play a pivotal role as model systems for phase transitions in classical statistical mechanics. In recent years the leading role of colloids to realize model systems has become evident not only for equilibrium situations but also far away from equilibrium. By using external fields (such as shear flow, electric, magnetic or laseroptical fields as well as confinement), a colloidal suspension can be brought into nonequilibrium in a controlled way. Various kinds of equilibrium and nonequilibrium phenomena explored by colloidal dispersions are described providing also a guide and summary to this special issue. Particular emphasis is put on the comparison of real-space experiments, computer simulations and statistical theories.     

Heterogeneous aging in spin glasses

We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations of short-range spin glasses. Local fluctuations and responses are shown to be connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. Scaling relationships are uncovered for the slow evolution of heterogeneities at all time scales.     

Correlation effects in the diffusion and electrical conductivity of an interacting lattice gas

A simple and effective self-consistent scheme is proposed for the determination of the average potentials which allows thermodynamic functions and other characteristics of lattice systems in equilibrium to be calculated with high accuracy and short computing time. This scheme has been used for analysis of the expressions for the coefficients of diffusion and electrical conductivity obtained on the basis of the modern statistical theory of nonequilibrium processes. Results of the simulations are correlated with the data of Monte Carlo simulations obtained using parallel vector algorithms on a Cray TZE computer of the Max Plank Society (Germany).     

Nonequilibrium interface equations: An application to thermocapillary motion in binary systems

Interface equations are derived for both binary diffusive and binary fluid systems subjected to nonequilibrium conditions, starting from coarse-grained (mesoscopic) models. The equations are used to describe thermocapillary motion of a droplet in both purely diffusive and fluid cases, and the results are compared with numerical simulations. A mesoscopic chemical potential shift owing to the temperature gradient, and associated mesoscopic corrections involved in droplet motion, are elucidated.     

Driven alloys in the athermal limit

Static molecular simulations of binary alloys under extrinsic forcing show that complex ordered or segregated structures may evolve even in the absence of thermally activated diffusion. This result is in opposition to the standard theoretical framework for so-called "driven alloys," which assumes that extrinsic driving is an ideally randomizing process, and therefore predicts only random atomic configurations in the athermal limit. We propose a qualitative modification to the theory that introduces a new control parameter and use additional Monte Carlo simulations to demonstrate the physical plausibility of this modification. New research directions in nonequilibrium dynamic systems are also suggested by this analysis.     

Inequivalence of dynamical ensembles in a generalized driven diffusive lattice gas

We generalize the driven diffusive lattice gas model by using a combination of Kawasaki and Glauber dynamics. We find via Monte Carlo simulations and perturbation studies that the simplest possible generalization of the equivalence of the canonical and grand-canonical ensembles, which holds in equilibrium, does not apply for this class of nonequilibrium systems.     

Fluctuation Relations for Dissipative Systems in Constant External Magnetic Field: Theory and Molecular Dynamics Simulations

We illustrate how, contrary to common belief, transient Fluctuation Relations (FRs) for systems in constant external magnetic field hold without the inversion of the field. Building on previous work providing generalized time-reversal symmetries for systems in parallel external magnetic and electric fields, we observe that the standard proof of these important nonequilibrium properties can be fully reinstated in the presence of net dissipation. This generalizes recent results for the FRs in orthogonal fields—an interesting but less commonly investigated geometry—and enables direct comparison with existing literature. We also present for the first time a numerical demonstration of the validity of the transient FRs with nonzero magnetic field via nonequilibrium molecular dynamics simulations of a realistic model of liquid NaCl.     

Dynamic importance sampling for the escape problem in nonequilibrium systems: observation of shifts in optimal paths

The activation problem is investigated in two-dimensional nonequilibrium systems. A numerical approach based on dynamic importance sampling (DIMS) is introduced. DIMS accelerates the simulations and allows the investigation to access noise intensities that were previously forbidden. The escape path is observed to be shifted compared to a heteroclinic trajectory calculated in the limit of zero-noise intensity. A theory to account for such shifts is presented and shown to agree with the simulations for a wide range of noise intensities.     

Equilibrium and nonequilibrium thermomechanics for an effective pair potential used in smooth particle applied mechanics

The smooth-particle weighting functions used in numerical solutions of the thermomechanical continuum equations can be interpreted as weak pair potentials from the standpoint of statistical physics. We examine both equilibrium and nonequilibrium thermomechanical properties of many-body systems using a typical smooth particle potential, Lucy's, and discuss the implications for macroscopic continuum simulations.     

Superlattice patterns in vertically oscillated rayleigh-Benard convection

We report the first observations of superlattices in thermal convection. The superlattices are selected by a four-mode resonance mechanism that is qualitatively different from the three-mode resonance responsible for complex-ordered patterns observed previously in other nonequilibrium systems. Numerical simulations quantitatively describe both the pattern structure and the stability boundaries of superlattices observed in laboratory experiments. In the presence of the inversion symmetry, superlattices are found numerically to bifurcate supercritically directly from conduction or from a striped base state.     

Simulating nonequilibrium quantum fields with stochastic quantization techniques

We present lattice simulations of nonequilibrium quantum fields in Minkowskian space-time. Starting from a nonthermal initial state, the real-time quantum ensemble in (3 + 1) dimensions is constructed by a stochastic process in an additional (5th) "Langevin-time." For the example of a self-interacting scalar field, we show how to resolve apparent unstable Langevin dynamics and compare our quantum results with those obtained in classical field theory. Such a direct simulation method is crucial for our understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in strongly coupled quantum many-body systems.     

Generic Two-Phase Coexistence and Nonequilibrium Criticality in a Lattice Version of Schlögl’s Second Model for Autocatalysis

A two-dimensional atomistic realization of Schlögl’s second model for autocatalysis is implemented and studied on a square lattice as a prototypical nonequilibrium model with first-order transition. The model has no explicit symmetry and its phase transition can be viewed as the nonequilibrium counterpart of liquid-vapor phase separations. We show some familiar concepts from study of equilibrium systems need to be modified. Most importantly, phase coexistence can be a generic feature of the model, occurring over a finite region of the parameter space. The first-order transition becomes continuous as a temperature-like variable increases. The associated critical behavior is studied through Monte Carlo simulations and shown to be in the two-dimensional Ising universality class. However, some common expectations regarding finite-size corrections and fractal properties of geometric clusters for equilibrium systems seems to be inapplicable.     

Scaling and universality of critical fluctuations in granular gases

The total energy fluctuations of a low-density granular gas in the homogeneous cooling state near the threshold of the clustering instability are studied by means of molecular dynamics simulations. The relative dispersion of the fluctuations is shown to exhibit a power-law divergent behavior. Moreover, the probability distribution of the fluctuations presents data collapse as the system approaches the instability, for different values of the inelasticity. The function describing the collapse turns out to be the symmetric of the one found in several molecular equilibrium and nonequilibrium systems.     

Thermodynamics of Currents in Nonequilibrium Diffusive Systems: Theory and Simulation

Understanding the physics of nonequilibrium systems remains as one of the major challenges of modern theoretical physics. We believe nowadays that this problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing nonequilibrium behavior, their statistics, associated structures and microscopic origin. This fundamental line of research has been severely hampered by the overwhelming complexity of this problem. However, during the last years two new powerful and general methods have appeared to investigate fluctuating behavior that are changing radically our understanding of nonequilibrium physics: a powerful macroscopic fluctuation theory (MFT) and a set of advanced computational techniques to measure rare events. In this work we study the statistics of current fluctuations in nonequilibrium diffusive systems, using macroscopic fluctuation theory as theoretical framework, and advanced Monte Carlo simulations of several stochastic lattice gases as a laboratory to test the emerging picture. Our quest will bring us from (1) the confirmation of an additivity conjecture in one and two dimensions, which considerably simplifies the MFT complex variational problem to compute the thermodynamics of currents, to (2) the discovery of novel isometric fluctuation relations, which opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations, and to (3) the observation of coherent structures in fluctuations, which appear via dynamic phase transitions involving a spontaneous symmetry breaking event at the fluctuating level. The clear-cut observation, measurement and characterization of these unexpected phenomena, well described by MFT, strongly support this theoretical scheme as the natural theory to understand the thermodynamics of currents in nonequilibrium diffusive media, opening new avenues of research in nonequilibrium physics.