Entropy / CONCEPT
Symmetry of Finite Mutual Information
Finite joint Shannon entropy and mutual information in nats are invariant under coordinate swap without distributional hypotheses.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES6
PROOF DEPTH3
DOCUMENT LINKS1
Joint entropy is invariant under coordinate swap
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- Coarse-Graining Cannot Add Informationtruth-dependency · Closed
- Fano Error Bounds after Finite Channelstruth-dependency · Closed
- Fusion State Entropytruth-dependency · Closed
- Mutual-Information Chain Ruletruth-dependency · Closed
- The Finite Mixture Entropy Brackettruth-dependency · Closed
- Translation Loss under Postprocessingtruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Coarse-Graining Cannot Add Informationstructural-affinity · Closed
- Collision Entropy versus Shannon Entropystructural-affinity · Closed
- Collision-Entropy Uncertaintystructural-affinity · Closed
- Conditional Mutual Informationstructural-affinity · Closed
- Conditioning Reduces Entropystructural-affinity · Closed
- Fano Error Bounds after Finite Channelsstructural-affinity · Closed
- Fusion State Entropystructural-affinity · Closed
- Maximum Entropy on a Finite Alphabetstructural-affinity · Closed
- Mutual Information as an Entropy Balancestructural-affinity · Closed
- Mutual Information Vanishes on Product Lawsstructural-affinity · Closed
- Mutual-Information Chain Rulestructural-affinity · Closed
- Nonnegativity of Finite Classical Mutual Informationstructural-affinity · Closed
- Strong Subadditivity and Conditional Productsstructural-affinity · Closed
- The Feedback Divergence Identitystructural-affinity · Closed
- The Finite Mixture Entropy Bracketstructural-affinity · Closed
- Translation Loss under Postprocessingstructural-affinity · Closed
- Vanishing Mutual Information Characterizes Independencestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance