Dimension Reduction for Systems with Slow Relaxation: In Memory of Leo P. Kadanoff

Shankar C. Venkataramani, Raman C. Venkataramani, Juan M. Restrepo

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize ‘optimal’ model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.

Original languageEnglish (US)
Pages (from-to)892-933
Number of pages42
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - May 1 2017


  • Aging
  • Dimension reduction
  • Glassy systems
  • Mori–Zwanzig projection
  • Multi-scale
  • Oil spills
  • Sloppy models
  • Slow relaxation
  • Weathering

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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