Steady States of a Nonequilibrium Lattice Gas

We present a Monte Carlo study of a lattice gas driven out of equilibrium by a local hopping bias. Sites can be empty or occupied by one of two types of particles, which are distinguished by their response to the hopping bias. All particles interact via excluded volume and a nearest-neighbor attractive force. The main result is a phase diagram with three phases: a homogeneous phase, and two distinct ordered phases. Continuous boundaries separate the homogeneous phase from the ordered phases, and a first-order line separates the two ordered phases. The three lines merge in a nonequilibrium bicritical point.Comment: 14 pages, 24 figure

Anomalous nucleation far from equilibrium

We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a $2 \times L$ lattice. We propose a scenario which resolves a stark discrepancy between earlier simulation data, suggesting the existence of an ordered phase, and an analytic conjecture according to which the system should revert to a disordered state in the thermodynamic limit. By analyzing the finite size effects in detail, we argue that the presence of a single, seemingly macroscopic, cluster is an intermediate stage of a complex nucleation process: In smaller systems, this cluster is destabilized while larger systems allow the formation of multiple clusters. Both limits lead to exponential cluster size distributions which are, however, controlled by very different length scales.Comment: 5 pages, 3 figures, one colum

Novel Quenched Disorder Fixed Point in a Two-Temperature Lattice Gas

We investigate the effects of quenched randomness on the universal properties of a two-temperature lattice gas. The disorder modifies the dynamical transition rates of the system in an anisotropic fashion, giving rise to a new fixed point. We determine the associated scaling form of the structure factor, quoting critical exponents to two-loop order in an expansion around the upper critical dimension d$_c=7$. The close relationship with another quenched disorder fixed point, discovered recently in this model, is discussed.Comment: 11 pages, no figures, RevTe

Controlling surface morphologies by time-delayed feedback

We propose a new method to control the roughness of a growing surface, via a time-delayed feedback scheme. As an illustration, we apply this method to the Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25,0.33], for a significant length of time. The method is quite general and can be applied to a wide range of growth phenomena. A possible experimental realization is suggested.Comment: 4 pages, 3 figure

Nonequilibrium quantum phase transition in itinerant electron systems

We study the effect of the voltage bias on the ferromagnetic phase transition in a one-dimensional itinerant electron system. The applied voltage drives the system into a nonequilibrium steady state with a non-zero electric current. The bias changes the universality class of the second order ferromagnetic transition. While the equilibrium transition belongs to the universality class of the uniaxial ferroelectric, we find the mean-field behavior near the nonequilibrium critical point.Comment: Final version as accepted to Phys. Rev. Let

Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process

As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a 1-dimensional open lattice, and its power spectrum. Using both Monte Carlo simulations and analytic methods, we explore its behavior in different characteristic regimes. In the maximal current phase and on the coexistence line (between high/low density phases), the power spectrum displays algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the high/low density phases, we find pronounced \emph{oscillations}, which damp into power laws. This behavior can be understood in terms of driven biased diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure

Reversibility, heat dissipation and the importance of the thermal environment in stochastic models of nonequilibrium steady states

We examine stochastic processes that are used to model nonequilibrium processes (e.g, pulling RNA or dragging colloids) and so deliberately violate detailed balance. We argue that by combining an information-theoretic measure of irreversibility with nonequilibrium work theorems, the thermal physics implied by abstract dynamics can be determined. This measure is bounded above by thermodynamic entropy production and so may quantify how well a stochastic dynamics models reality. We also use our findings to critique various modeling approaches and notions arising in steady-state thermodynamics.Comment: 8 pages, 2 figures, easy-to-read, single-column, large-print RevTeX4 format; version with modified abstract and additional discussion, references to appear in Phys Rev Let

Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models

The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of corre- lation functions are closed, are considered. A transfer matrix method is used to find the static solution. It is seen that this transfer matrix can be obtained in a closed form, if the reaction rates satisfy certain conditions. We call such models superautonomous. Possible static phase transitions of such models are investigated. At the end, as an example of superau- tonomous models, a nonuniform voter model is introduced, and solved explicitly.Comment: 14 page

Effects of differential mobility on biased diffusion of two species

Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility, and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species.Comment: 15 pages, 4 figure

Convection cells induced by spontaneous symmetry breaking

Ubiquitous in nature, convection cells are a clear signature of systems out-of-equilibrium. Typically, they are driven by external forces, like gravity (in combination with temperature gradients) or shear. In this article, we show the existence of such cells in possibly the simplest system, one that involves only a temperature gradient. In particular, we consider an Ising lattice gas on a square lattice, in contact with two thermal reservoirs, one at infinite temperature and another at $T$. When this system settles into a non-equilibrium stationary state, many interesting phenomena exist. One of these is the emergence of convection cells, driven by spontaneous symmetry breaking when $T$ is set below the critical temperature.Comment: published version, 2 figures, 5 page