Dynamical-system models of transport: Chaos characteristics, the macroscopic limit, and irreversibility

Jürgen Vollmer, Tamás Tél, Wolfgang Breymann

Research output: Contribution to journalArticle

3 Citations (Scopus)


The escape-rate formalism and the thermostating algorithm describe relaxation towards a decaying state with absorbing boundaries and a steady state of periodic systems, respectively. It has been shown that the key features of the transport properties of both approaches, if modeled by low-dimensional dynamical systems, can conveniently be described in the framework of multibaker maps. In the present paper we discuss in detail the steps required to reach a meaningful macroscopic limit. The limit involves a sequence of coarser and coarser descriptions (projections) until one reaches the level of irreversible macroscopic advection-diffusion equations. The influence of boundary conditions is studied in detail. Only a few of the chaos characteristics possess a meaningful macroscopic limit, but none of these is sufficient to determine the entropy production in a general non-equilibrium state.

Original languageEnglish
Pages (from-to)108-127
Number of pages20
JournalPhysica D: Nonlinear Phenomena
Issue number1-4
Publication statusPublished - Jan 1 2004


  • Chaos
  • Macroscopic limit
  • Multibaker maps
  • Transport equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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