The linear Fokker-Planck equation for the Ornstein-Uhlenbeck process as an (almost) nonlinear kinetic equation for an isolated N-particle system

Michael Kiessling, Carlo Lancellotti

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation.

Original languageEnglish (US)
Pages (from-to)525-546
Number of pages22
JournalJournal of Statistical Physics
Volume123
Issue number3
DOIs
StatePublished - May 2006

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Diffusion equation on a high-dimensional sphere
  • Fokker-Planck equation
  • Kac program
  • Kinetic theory
  • Propagation of chaos

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