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

Document Type

Article

Publication Date

10-1-2019

Abstract

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.

Identifier

85074020747 (Scopus)

Publication Title

Entropy

External Full Text Location

https://doi.org/10.3390/e21100938

e-ISSN

10994300

Issue

10

Volume

21

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