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Journal of Statistical Physics

, Volume 123, Issue 5, pp 1059–1069 | Cite as

Exact Dimensional Reduction of Linear Dynamics: Application to Confined Diffusion

  • Pavol KalinayEmail author
  • Jerome K. Percus
Article

Abstract

In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the “classical” Fick-Jacobs approximate reduction to an exact subdynamics.

Keywords

diffusion Fick-Jacobs equation dimensional reduction mapping 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Institute of Physics, Slovak Academy of SciencesBratislavaSlovak Republic
  3. 3.Department of PhysicsNew York UniversityNew YorkUSA

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