Information and Its Relation to Complexity

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Keywords:

  • information: syntactic - semantic - pragmatic & order - complexity - disorder (an introduction)
  • Shannon information, an axiomatic approach
  • unbiased guess and Jaynes principle
  • Kullback measure and transinformation
  • static vs. dynamic information: block and conditional entropies
  • source entropy and Kolmogorov-Sinai entropy (symbolic dynamics)
  • effective measure complexity (EMC) and alternative complexity measures
  • the chaos edge and complexity
  • Rényi information and the thermodynamic formalism, Tsallis information
  • the estimation problem in practical applications: rank ordered distributions
  • parameter estimation: Cramer-Rao bound and Fisher information

References:

  1. T. M. Cover and J. A. Thomas: Elements of Information Theory, (Wiley-Interscience, New York, 1991).
  2. R. Badii and A. Politi: Complexity: Hierarchical Structures and Scaling in Physics, (Cambridge UP, Cambridge, 1997).
  3. C. Beck and F. Schlögl: Thermodynamics of Chaotic Systems: An Introduction, (Cambridge UP, Cambridge, 1993).
  4. W. Ebeling, J. Freund, and F. Schweitzer: Komplexe Strukturen: Entropie und Information, (B. G. Teubner, Stuttgart/Leipzig, 1998).
  5. W. H. Zurek (ed.): Complexity, Entropy and the Physics of Information, (Addison-Wesley, Redwood City, 1990).

           
Revised 4.14.04