Void formation in diffusive lattice gases

P. L. Krapivsky*, Baruch Meerson, Pavel V. Sasorov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

What is the probability that a macroscopic void will spontaneously arise, at a specified time T, in an initially homogeneous gas? We address this question for diffusive lattice gases, and also determine the most probable density history leading to the void formation. We employ the macroscopic fluctuation theory by Bertini et al and consider both annealed and quenched averaging procedures (the initial condition is allowed to fluctuate in the annealed setting). We show that in the annealed case the void formation probability is given by the equilibrium Boltzmann-Gibbs formula, so the probability is independent of T (and also of the void shape, as only the volume matters). In the quenched case, which is intrinsically non-equilibrium, we evaluate the void formation probability analytically for non-interacting random walkers and probe it numerically for the simple symmetric exclusion process. For voids that are small compared with the diffusion length √ T, the equilibrium result for the void formation probability is recovered. We also re-derive our main results for non-interacting random walkers from an exact microscopic analysis.

Original languageAmerican English
Article numberP12014
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2012
Issue number12
DOIs
StatePublished - Dec 2012

Keywords

  • diffusion
  • exact results
  • large deviations in non-equilibrium systems
  • stochastic particle dynamics (theory)

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