Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0501338

Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models

M. R. Evans·T. Hanney
View original source ↗Read source document ↗Export metadata ↓

Abstract

We review recent progress on the zero-range process, a model of interacting particles which hop between the sites of a lattice with rates that depend on the occupancy of the departure site. We discuss several applications which have stimulated interest in the model such as shaken granular gases and network dynamics, also we discuss how the model may be used as a coarse-grained description of driven phase-separating systems. A useful property of the zero-range process is that the steady state has a factorised form. We show how this form enables one to analyse in detail condensation transitions, wherein a finite fraction of particles accumulate at a single site. We review condensation transitions in homogeneous and heterogeneous systems and also summarise recent progress in understanding the dynamics of condensation. We then turn to several generalisations which also, under certain specified conditions, share the property of a factorised steady state. These include several species of particles; hop rates which depend on both the departure and the destination sites; continuous masses; parallel discrete-time updating; non-conservation of particles and sites.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. R. Evans, T. Hanney. 2005-07-18. Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models. https://doi.org/10.1088/0305-4470%2F38%2F19%2Fr01

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Altered temporal scaling of semantic similarity fluctuations in psychosis

Scale-free temporal organization, in which fluctuations show similar statistical structures across timescales, is a feature of many complex systems considered to support optimal functioning. Alterations of such scaling have been reported in several pathologies, but whether comparable alterations characterize the temporal organization of language remains largely unexplored. We address this question in the domain of psychosis, where language anomalies are pervasively documented. Specifically, we apply detrended fluctuation analysis (DFA) to quantify temporal scaling in Qwen3-derived continuous cosine similarity time series, capturing trajectories through semantic space computed from transcripts of picture descriptions across three independent datasets. DFA scaling exponents α were extracted to characterize the strength of long-range temporal correlations. Across all datasets, patients exhibited significantly elevated α relative to controls, indicating increased temporal persistence in semantic fluctuations. This analysis opens a window into the multi-timescale organization of meaning as it unfolds in discourse and reveals a signature of altered temporal scaling. This alteration parallels known departures from critical scaling in brain dynamics in psychosis, suggesting the exploration of possible links between these two.

cond-mat.stat-mech↗
arXiv2026

Modified Family-Vicsek Scaling and Probability Distributions for Brownian Castle Interfaces

The Brownian Castle is a new interface growth model that is a variation on the well-known ballistic deposition model that results in an entirely new universality class. We present numerical verification that the interface width for BC interfaces displays modified Family-Vicsek scaling properties up to finite size corrections. Specifically, we find a growth exponent of $β=0.470 \pm 0.012$ and a roughness exponent of $α=1.01 \pm 0.018$. The scaling is modified at short times with a size scaling exponent that described the early time dependence of interface width on length. The probability distribution of heights for the BC interface shows significant deviations from simple Gaussian behavior and the probability distribution of height changes shows a Cauchy-Lorentz form consistent with expectations for a process involving relatively large jumps.

cond-mat.stat-mech↗
arXiv2026

Ensemble theory of thermodiffusion

Heat flow sustained by a temperature difference generates a gradient of matter as observed, for example, in atomistic simulations of hard-core gases. We use path-ensemble theory to represent the coupled thermal and diffusive transport by dynamics on a graph. Calibrated from a single equilibrium simulation, this model accurately predicts nonequilibrium mass distribution in a hard-core gas across a wide range of applied temperature gradients. It also enables estimation of transport properties, such as the Soret coefficient, using analytical expressions.

cond-mat.stat-mech↗