Factorised Steady States in Mass Transport Models

Abstract

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and random sequential dynamics and includes models such as the Zero-range process and Asymmetric random average process as special cases. We derive a necessary and sufficient condition for the steady state to factorise, which takes a rather simple form.

6 pages

Cited by in corpus (69)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Stochastic fluctuations in metabolic pathways
• The Nature of the Condensate in Mass Transport Models
• Canonical Analysis of Condensation in Factorised Steady State
• On integrability of zero-range chipping models with factorized steady state
• Interaction driven real-space condensation
• Complete Condensation in a Zero Range Process on Scale-Free Networks
• Condensation and Extreme Value Statistics
• Asymmetric exclusion processes with shuffled dynamics
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Definition and relevance of nonequilibrium intensive thermodynamic parameters
• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Factorised Steady States in Mass Transport Models on an Arbitrary Graph
• Intensive thermodynamic parameters in nonequilibrium systems
• Stationary and dynamical properties of a zero range process on scale-free networks
• Condensation for a fixed number of independent random variables
• A minimal model for congestion phenomena on complex networks
• Condensation transition in joint large deviations of linear statistics
• Construction of the factorized steady state distribution in models of mass transport
• Shocks in the asymmetric exclusion process with internal degree of freedom
• The $q$-Hahn asymmetric exclusion process
• Dependence of the fluctuation-dissipation temperature on the choice of observable
• Condensation transitions in a model for a directed network with weighted links
• Mass condensation in one dimension with pair-factorized steady states
• Occupation Probabilities and Fluctuations in the Asymmetric Simple Inclusion Process
• Emergence of jams in the generalized totally asymmetric simple exclusion process
• Product Measure Steady States of Generalized Zero Range Processes
• Exact gap statistics for the random average process on a ring with a tracer
• Gammalike mass distributions and mass fluctuations in conserved-mass transport processes
• Pair-factorized steady states on arbitrary graphs
• Condensation Transition in Polydisperse Hard Rods
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Finite-size localization scenarios in condensation transitions
• The kinetic exclusion process: a tale of two fields
• Explosive condensation in symmetric mass transport models
• Macroscopic fluctuations of a driven tracer in the symmetric exclusion process
• An exactly solvable dissipative transport model
• Tracy-Widom limit of q-Hahn TASEP
• Monotonicity and Condensation in Homogeneous Stochastic Particle Systems
• Additivity property and emergence of power laws in nonequilibrium steady states
• A mass transport model with a simple non-factorized steady-state distribution
• Matrix product formula for $U_q(A_2^{(1)})$-zero range process
• Mass-Transport Models with Fragmentation and Aggregation
• Conserved mass models with stickiness and chipping
• Bose-Einstein Condensation of a Gaussian Random Field in the Thermodynamic Limit
• Long range correlations in stochastic transport with energy and momentum conservation
• Out of equilibrium stationary states, percolation, and sub-critical instabilities in a fully non conservative system
• Influence of flux balance on the generalized chemical potential in mass transport models
• A short proof of a symmetry identity for the $(q,\mu ,\nu )$-deformed Binomial distribution
• Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature
• Arrival Times in a Zero-Range Process with Injection and Decay
• Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach
• Nonequilibrium grand-canonical ensemble built from a physical particle reservoir
• Integrable Structure of Multispecies Zero Range Process
• Condensation in models with factorized and pair-factorized stationary states
• Matrix Product representation of the stationary state of the open Zero Range Process
• Maintenance of order in a moving strong condensate
• Long-range correlations in a simple stochastic model of coupled transport
• Zero-range process with long-range interactions at a T-junction
• Dynamic fluctuations of current and mass in nonequilibrium mass transport processes
• Mass fluctuations in Random Average Transfer Process in open set-up
• Factorised steady states for multi-species mass transfer models
• Non-additive large deviations function for the particle densities of driven systems in contact
• A simple non-equilibrium, statistical-physics toy model of thin-film growth
• The steady state of the boundary-driven multiparticle asymmetric diffusion model
• Generic power laws in higher-dimensional lattice models with multidirectional hopping