Reaction-diffusion equations for interacting particle systems

A. De Masi, P. A. Ferrari, J. L. Lebowitz

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142 Scopus citations


We study interacting spin (particle) systems on a lattice under the combined influence of spin flip (Glauber) and simple exchange (Kawasaki) dynamics. We prove that when the particle-conserving exchanges (stirrings) occur on a fast time scale of order e{open}-2 the macroscopic density, defined on spatial scale e{open}-1, evolves according to an autonomous nonlinear diffusion-reaction equation. Microscopic fluctuations about the deterministic macroscopic evolution are found explicitly. They grow, with time, to become infinite when the deterministic solution is unstable.

Original languageEnglish (US)
Pages (from-to)589-644
Number of pages56
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Aug 1986

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Glauber dynamics
  • Stirring process
  • branching processes
  • generalized Orenstein-Uhlenbeck processes
  • hydrodynamic limit


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