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Local estimates for entropy densities in coupled map lattices

Olbrich1, Hegger, Kantz

  • 1Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, D 01187 Dresden, Germany.

Physical Review Letters
|October 4, 2000
PubMed
Summary

We developed a new method to estimate entropy density in complex systems using local data. This approach helps understand the system

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Information theory

Background:

  • Coupled map lattices (CML) are complex systems exhibiting rich dynamics.
  • Estimating entropy density in such systems is crucial for understanding their behavior.
  • Traditional methods often require global information, which is not always accessible.

Purpose of the Study:

  • To present a novel method for deriving an upper bound for entropy density in CML.
  • To enable entropy estimation from local observations only.
  • To identify the local character of the underlying equations of motion.

Main Methods:

  • Utilizing a combined time delay and spatial embedding technique.
  • Applying this embedding to reconstruct the system's dynamics from local data.
  • Employing the correlation integral for approximate entropy density estimation.

Main Results:

  • Successfully derived an upper bound for entropy density.
  • Demonstrated the feasibility of estimating entropy from local observations.
  • The embedding technique effectively captures the local dynamics.

Conclusions:

  • The proposed method provides a practical approach to quantify the complexity of CML.
  • Local observations are sufficient for estimating key thermodynamic properties like entropy density.
  • This work advances the understanding of information processing in spatially extended systems.

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