Factorised Steady States in Mass Transport Models on an Arbitrary Graph

Abstract

We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from a site-dependent distribution, is transported between the nodes at each time step. The dynamics conserves the total mass and the system eventually reaches a steady state. This general model includes as special cases various previously studied models such as the Zero-range process and the Asymmetric random average process. We derive a general condition on the stochastic mass transport rules, valid for arbitrary graph and for both parallel and random sequential dynamics, that is sufficient to guarantee that the steady state is factorisable. We demonstrate how this condition can be achieved in several examples. We show that our generalized result contains as a special case the recent results derived by Greenblatt and Lebowitz for $d$-dimensional hypercubic lattices with random sequential dynamics.

17 pages 1 figure

References in corpus (17)

• Statistical Physics of Vehicular Traffic and Some Related Systems
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• A Model for Force Fluctuations in Bead Packs
• Phase Transitions in one-dimensional nonequilibrium systems
• Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
• Criterion for phase separation in one-dimensional driven systems
• Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation
• The Nature of the Condensate in Mass Transport Models
• Factorised Steady States in Mass Transport Models
• Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation and Fragmentation
• Complete Condensation in a Zero Range Process on Scale-Free Networks
• Asymmetric particle systems on R
• Exact Tagged Particle Correlations in the Random Average Process
• Analytic study of clustering in shaken granular material using zero-range processes
• Construction of the factorized steady state distribution in models of mass transport
• A simple sandpile model of active-absorbing state transitions
• Product Measure Steady States of Generalized Zero Range Processes

Cited by in corpus (32)

• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Interaction driven real-space condensation
• Condensation in the inclusion process and related models
• Condensation and Extreme Value Statistics
• Intensive thermodynamic parameters in nonequilibrium systems
• Condensation in stochastic particle systems with stationary product measures
• Tuning the shape of the condensate in spontaneous symmetry breaking
• Condensation in zero-range processes on inhomogeneous networks
• Mass condensation in one dimension with pair-factorized steady states
• Pair-factorized steady states on arbitrary graphs
• The kinetic exclusion process: a tale of two fields
• Power laws in zero-range processes on random networks
• Multivariate Juggling Probabilities
• A mass transport model with a simple non-factorized steady-state distribution
• Local structure of current fluctuations in diffusive systems beyond one dimension
• Conserved mass models with stickiness and chipping
• Statistical mechanics of complex networks
• Current fluctuations in boundary driven diffusive systems in different dimensions: a numerical study
• Rényi Entropy of Zeta-Urns
• Influence of flux balance on the generalized chemical potential in mass transport models
• Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach
• On Random Allocation Models in the Thermodynamic Limit
• Current loops and fluctuations in the zero-range process on a diamond lattice
• Nonequilibrium grand-canonical ensemble built from a physical particle reservoir
• Condensation in models with factorized and pair-factorized stationary states
• Zero-range process with long-range interactions at a T-junction
• Factorised steady states for multi-species mass transfer models
• Partition function zeros of zeta-urns
• Mass-Transport Models with Multiple-Chipping Processes
• Finite-size effects in dynamics of zero-range processes
• Yang-Lee zeros for real-space condensation
• Non-additive large deviations function for the particle densities of driven systems in contact