On the weak-noise limit of Fokker-Planck models

R. Graham, T. Tél

Research output: Contribution to journalArticle

126 Citations (Scopus)


The weak-noise limit of Fokker-Planck models leads to a set of nonlinear Hamiltonian canonical equations. We show that the existence of a nonequilibrium potential in the weak-noise limit requires the existence of whiskered tori in the Hamiltonian system and, therefore, the complete integrability of the latter. A specific model is considered, where the Hamiltonian system in the weak-noise limit is not integrable. Two different perturbative solutions are constructed: the first solution describes analytically the breakdown of the whiskered tori due to the appearance of wild séparatrices; the second solution allows the analytic construction of an approximate nonequilibrium potential and an asymptotic expression for the probability density in the steady state.

Original languageEnglish
Pages (from-to)729-748
Number of pages20
JournalJournal of Statistical Physics
Issue number5-6
Publication statusPublished - Jun 1 1984


  • Fokker-Planck processes
  • dynamical systems
  • integrability of Hamiltonian systems
  • nonequilibrium potentials
  • weak-noise limit
  • whiskered tori

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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