Discontinuous condensation transition and nonequivalence of ensembles in a zero-range process

Abstract

We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of a condensation transition. In contrast to previous results, the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases. This leads to a richer phase diagram, including nonequivalence of ensembles in certain phase regions. The paper is motivated by results from granular clustering, where these features have been observed experimentally.

arXiv comment39 pages, 7 figures; Journal version contains errors in (18) to (22) which have been corrected

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Cited by in corpus (22)

• Thermodynamics and dynamics of systems with long-range interactions
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Condensation in the inclusion process and related models
• Diffusions conditioned on occupation measures
• Condensation in stochastic particle systems with stationary product measures
• Finite size effects and metastability in zero-range condensation
• Condensation transition in joint large deviations of linear statistics
• Dynamical large deviations of linear diffusions
• Instability of condensation in the zero-range process with random interaction
• Long-range correlations and ensemble inequivalence in a generalized ABC model
• Blockage induced condensation controlled by a local reaction
• Phase diagram of the ABC model with nonconserving processes
• Structure of the condensed phase in the inclusion process
• Two-point correlation function of an exclusion process with hole-dependent rates
• Ensemble inequivalence : Landau theory and the ABC model
• A dynamical transition and metastability in a size-dependent zero-range process
• Trapping in bottlenecks: interplay between microscopic dynamics and large scale effects
• Emergent motion of condensates in mass-transport models
• Condensation in randomly perturbed zero-range processes
• Stationary currents in particle systems with constrained hopping rates
• Emergence of particle clusters in a one-dimensional model: connection to condensation processes
• Condensation in zero-range processes with a fast rate