Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 123, Issue 5, Pages 1059-1069Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10955-006-9081-3
Keywords
diffusion; Fick-Jacobs equation; dimensional reduction; mapping
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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.
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