Entropy / CONCEPT
Conditioning Reduces Entropy
For a finite normalized joint, conditioning on the first coordinate cannot increase the entropy of the second, in nats.
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DIRECT PREREQUISITES2
DIRECT CONSEQUENCES1
PROOF DEPTH4
DOCUMENT LINKS1
Conditioning cannot increase entropy
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Conditional Entropy and Its Chain Rulestructural-affinity · Closed
- Expected Posterior Entropy Reductionstructural-affinity · Closed
- Future-Word Information Chainstructural-affinity · Closed
- Mutual Information as an Entropy Balancestructural-affinity · Closed
- Mutual Information Vanishes on Product Lawsstructural-affinity · Closed
- Nonnegativity of Finite Entropystructural-affinity · Closed
- Strong Subadditivity and Conditional Productsstructural-affinity · Closed
- Symmetry of Finite Mutual Informationstructural-affinity · Closed
- The Finite Mixture Entropy Bracketstructural-affinity · Closed
Documents & exposition
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