A dynamical systems-based Hierarchy for Shannon, metric and topological entropy

Raymond Addabbo, Denis Blackmore

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A rigorous dynamical systems-based hierarchy is established for the definitions of entropy of Shannon (information), Kolmogorov-Sinai (metric) and Adler, Konheim & McAndrew (topological). In particular, metric entropy, with the imposition of some additional properties, is proven to be a special case of topological entropy and Shannon entropy is shown to be a particular form of metric entropy. This is the first of two papers aimed at establishing a dynamically grounded hierarchy comprising Clausius, Boltzmann, Gibbs, Shannon, metric and topological entropy in which each element is ideally a special case of its successor or some kind of limit thereof.

Original languageEnglish (US)
Article number938
Issue number10
StatePublished - Oct 1 2019

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Electrical and Electronic Engineering
  • General Physics and Astronomy
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)


  • Bernoulli scheme
  • Shannon entropy: metric entropy
  • Topological entropy


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