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Journal of Statistical Physics

, Volume 174, Issue 1, pp 120–134 | Cite as

On the Mean Residence Time in Stochastic Lattice-Gas Models

  • Marco ZamparoEmail author
  • Luca Dall’Asta
  • Andrea Gamba
Article

Abstract

A heuristic law widely used in fluid dynamics for steady flows states that the amount of a fluid in a control volume is the product of the fluid influx and the mean time that the particles of the fluid spend in the volume, or mean residence time. We rigorously prove that if the mean residence time is introduced in terms of sample-path averages, then stochastic lattice-gas models with general injection, diffusion, and extraction dynamics verify this law. Only mild assumptions are needed in order to make the particles distinguishable so that their residence time can be unambiguously defined. We use our general result to obtain explicit expressions of the mean residence time for the Ising model on a ring with Glauber + Kawasaki dynamics and for the totally asymmetric simple exclusion process with open boundaries.

Keywords

Residence time Interacting particle systems Sample-path averages Strong law of large numbers 

Mathematics Subject Classification

60F15 60J27 60K35 82C20 82C22 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Scienza Applicata e TecnologiaPolitecnico di TorinoTurinItaly
  2. 2.Italian Institute for Genomic MedicineTurinItaly
  3. 3.Collegio Carlo AlbertoUniversità degli Studi di TorinoTurinItaly
  4. 4.Istituto Nazionale di Fisica NucleareTurinItaly

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