On the Mean Residence Time in Stochastic Lattice-Gas Models

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 i...

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Bibliographic Details
Published in:Journal of statistical physics 2019-01, Vol.174 (1), p.120-134
Main Authors: Zamparo, Marco, Dall’Asta, Luca, Gamba, Andrea
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Fish
Flow (Dynamics)
Ising model
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-018-2175-x