Topological forms of information

Journal Article · Tue Jan 13 00:00:00 EST 2015 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4905981· OSTI ID:22390864

Baudot, Pierre ^[1]; Bennequin, Daniel ^[2]

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1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig (Germany)
2. Universite Paris Diderot-Paris 7, UFR de Mathematiques, Equipe Geometrie et Dynamique, Batiment Sophie Germain, 5 rue Thomas Mann, 75205 Paris Cedex 13 (France)

We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: 1) classical probabilities and random variables; 2) quantum probabilities and observable operators; 3) dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes. We discuss briefly its application to complex data, in particular to the structures of information flows in biological systems. This short note summarizes results obtained during the last years by the authors. The proofs are not included, but the definitions and theorems are stated with precision.

• OSTI ID: 22390864
• Journal Information: AIP Conference Proceedings, Vol. 1641, Issue 1; Conference: MAXENT 2014: Conference on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Clos Luce, Amboise (France), 21-26 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ENTROPY
INFORMATION
PROBABILITY
QUANTUM MECHANICS
QUANTUM OPERATORS
RANDOMNESS
TOPOLOGY