Markov Categories and Entropy — Paolo Perrone (2022). arXiv:2212.11719 (v2, PDF); IEEE Transactions of Information Theory 70(3), 2024.
Combines Markov categories with divergences and metrics on hom-sets, defining mutual information as distance from independence and entropy as distance from determinism, recovering Shannon and Rényi entropies and data-processing inequalities.
Sources: the paper, arXiv:2212.11719v2, checked against the arXiv listing. Index: Papers.
Key definitions and results
- Enriched Markov categories; entropy as distance from determinism