Rigorous Derivation of Reaction-Diffusion Equations with Fluctuations

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

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97 Scopus citations


We study interacting particle (spin) systems on a lattice under the combined influence of Glauber (spin flip) and simple exchange (Kawasaki) dynamics. We prove that when the conserving exchanges occur on a microscopically fast scale the macroscopic density (magnetization) 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)1947-1949
Number of pages3
JournalPhysical review letters
Issue number19
StatePublished - 1985

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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