Microscopic models of hydrodynamic behavior

Joel L. Lebowitz, Errico Presutti, Herbert Spohn

Research output: Contribution to journalArticle

90 Scopus citations


We review recent developments in the rigorous derivation of hydrodynamic-type macroscopic equations from simple microscopic models: continuous time stochastic cellular automata. The deterministic evolution of hydrodynamic variables emerges as the "law of large numbers," which holds with probability one in the limit in which the ratio of the microscopic to the macroscopic spatial and temporal scales go to zero. We also study fluctuations in the microscopic system about the solution of the macroscopic equations. These can lead, in cases where the latter exhibit instabilities, to complete divergence in behavior between the two at long macroscopic times. Examples include Burgers' equation with shocks and diffusion-reaction equations with traveling fronts.

Original languageEnglish (US)
Pages (from-to)841-862
Number of pages22
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Jun 1 1988

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Stochastic particle systems
  • fluctuation theory
  • hydrodynamic limit

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