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This study uniquely characterizes mutual information using novel axioms, including a Markov triangle concept for communication channels. This provides a coordinate-free mathematical framework for information theory.

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Area of Science:

  • Information Theory
  • Probability Theory
  • Mathematical Physics

Background:

  • Shannon entropy is foundational for quantifying information.
  • Existing characterizations of information measures often rely on specific mathematical formulations.
  • Understanding the fundamental properties of mutual information is crucial for various fields.

Purpose of the Study:

  • To provide a unique axiomatic characterization of mutual information.
  • To introduce a novel axiom based on the concept of a Markov triangle.
  • To develop coordinate-free proofs for information-theoretic concepts.

Main Methods:

  • Axiomatic characterization of mutual information.
  • Introduction of a new axiom involving Markov triangles.
  • Coordinate-free mathematical derivations, avoiding logarithms.

Main Results:

  • Mutual information is uniquely characterized by a set of axioms.
  • A new axiom, based on Markov triangles, is introduced, with no analog for Shannon entropy.
  • Proofs are presented in a coordinate-free manner, simplifying calculations.

Conclusions:

  • The proposed axiomatic system offers a novel perspective on mutual information.
  • The Markov triangle concept provides a new way to understand channel composition and conditional entropy.
  • The coordinate-free approach facilitates a deeper, more general understanding of information measures.