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

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

Brownian-Vacancy Mediated Disordering Dynamics

The disordering of an initially phase segregated system of finite size, induced by the presence of highly mobile vacancies, is shown to exhibit dynamic scaling in its late stages. A set of characteristic exponents is introduced and computed analytically, in excellent agreement with Monte Carlo data. In particular, the characteristic time scale, controlling the crossover between increasing disorder and saturation, is found to depend on the exponent scaling the number of vacancies in the sample.Comment: 6 pages, typeset using Euro-LaTex, 6 figures, compresse

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

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

Long Range Correlations in the Disordered Phase of a Simple Three State Lattice Gas

We investigate the dynamics of a three-state stochastic lattice gas, consisting of holes and two oppositely "charged" species of particles, under the influence of an "electric" field, at zero total charge. Interacting only through an excluded volume constraint, particles can hop to nearest neighbour empty sites. With increasing density and drive, the system orders into a charge-segregated state. Using a combination of Langevin equations and Monte Carlo simulations, we study the steady-state structure factors in the disordered phase where homogeneous configurations are stable against small harmonic perturbations. They show a discontinuity singularity at the origin which in real space leads to an intricate crossover between power laws of different kinds.Comment: 7 RevTeX pages, 1 postscript figure include

Dynamic instability transitions in 1D driven diffusive flow with nonlocal hopping

One-dimensional directed driven stochastic flow with competing nonlocal and local hopping events has an instability threshold from a populated phase into an empty-road (ER) phase. We implement this in the context of the asymmetric exclusion process. The nonlocal skids promote strong clustering in the stationary populated phase. Such clusters drive the dynamic phase transition and determine its scaling properties. We numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current and first order in the regime where the bulk is in control. The first order transition originates from a turn-about of the cluster drift velocity. At the critical line, the current remains analytic, the road density vanishes linearly, and fluctuations scale as uncorrelated noise. A self-consistent cluster dynamics analysis explains why these scaling properties remain that simple.Comment: 11 pages, 14 figures (25 eps files); revised as the publised versio

Will jams get worse when slow cars move over?

Motivated by an analogy with traffic, we simulate two species of particles (`vehicles'), moving stochastically in opposite directions on a two-lane ring road. Each species prefers one lane over the other, controlled by a parameter $0 \leq b \leq 1$ such that $b=0$ corresponds to random lane choice and $b=1$ to perfect `laning'. We find that the system displays one large cluster (`jam') whose size increases with $b$, contrary to intuition. Even more remarkably, the lane `charge' (a measure for the number of particles in their preferred lane) exhibits a region of negative response: even though vehicles experience a stronger preference for the `right' lane, more of them find themselves in the `wrong' one! For $b$ very close to 1, a sharp transition restores a homogeneous state. Various characteristics of the system are computed analytically, in good agreement with simulation data.Comment: 7 pages, 3 figures; to appear in Europhysics Letters (2005