We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the context of the equivalence of ensembles, providing a general characterization of the condensation transition for homogeneous and inhomogeneous systems in the thermodynamic limit. This leads to strengthened results on weak convergence for subcritical systems, and establishes the equivalence of ensembles for spatially inhomogeneous systems under very general conditions, extending previous results which focused on attractive and finite systems. We use relative entropy techniques which provide simple proofs, making use of general versions of local limit theorems for independent random variables. This paper is dedicated to Herbert Spohn in honour of his 65th birthday.

We consider the non-equilibrium dynamics of the East model, a linear chain of 0-1 spins evolving under a simple Glauber dynamics in the presence of a kinetic constraint which forbids flips of those spins whose left neighbor is 1. We focus on the glassy effects caused by the kinetic constraint as q ↓ 0, where q is the equilibrium density of the 0's. In the physical literature this limit is equivalent to the zero temperature limit. We first prove that, for any given L = O(1/q), the divergence as q ↓ 0 of three basic η Φ 2,11 (η) Φ 2,9 (η) Φ 3,7 (η) Φ 4,4 (η)

We study the dynamics of condensation of the inclusion process on a one-dimensional periodic lattice in the thermodynamic limit, generalising recent results on finite lattices for symmetric dynamics. Our main focus is on totally asymmetric dynamics which have not been studied before, and which we also compare to exact solutions for symmetric systems. We identify all relevant dynamical regimes and corresponding time scales as a function of the system size, including a coarsening regime where clusters move on the lattice and exchange particles, leading to a growing average cluster size. Suitable observables exhibit a power law scaling in this regime before they saturate to stationarity following an exponential decay depending on the system size. Our results are based on heuristic derivations and exact computations for symmetric systems, and are supported by detailed simulation data. arXiv:1311.4814v2 [cond-mat.stat-mech]

We study zero-range processes which are known to exhibit a condensation transition, where above a critical density a non-zero fraction of all particles accumulates on a single lattice site. This phenomenon has been a subject of recent research interest and is well understood in the thermodynamic limit. The system shows large finite size effects, and we observe a switching between metastable fluid and condensed phases close to the critical point, in contrast to the continuous limiting behaviour of relevant observables. We describe the leading order finite size effects and establish a discontinuity near criticality in a rigorous scaling limit. We also characterise the metastable phases using a current matching argument and an extension of the fluid phase to supercritical densities. This constitutes an interesting example where the thermodynamic limit fails to capture essential parts of the dynamics, which are particularly relevant in applications with moderate system sizes such as traffic flow or granular clustering.