Entropy / CONCEPT
Maximum Entropy on a Finite Alphabet
Finite Shannon entropy in nats is at most the natural logarithm of the alphabet cardinality.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES9
PROOF DEPTH2
DOCUMENT LINKS1
Finite Shannon entropy is at most log-cardinality
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- Collision Entropy versus Shannon Entropytruth-dependency · Closed
- Collision-Entropy Uncertaintytruth-dependency · Closed
- Conditional Entropy and Its Chain Ruletruth-dependency · Closed
- Finite Readout Alphabet Entropy Capacitytruth-dependency · Closed
- Green-Class Window Entropytruth-dependency · Closed
- Mutual Information as an Entropy Balancetruth-dependency · Closed
- Shannon Entropy Is Invariant Under Injective Relabelingtruth-dependency · Closed
- Symmetry of Finite Mutual Informationtruth-dependency · Closed
- The Entropy-Divergence Consistency Identitytruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Channel Monotonicity of Finite Classical KL Divergencestructural-affinity · Closed
- Collision Entropy versus Shannon Entropystructural-affinity · Closed
- Collision-Entropy Uncertaintystructural-affinity · Closed
- Conditional Entropy and Its Chain Rulestructural-affinity · Closed
- Differential Entropy Change of Variablesstructural-affinity · Closed
- Finite Readout Alphabet Entropy Capacitystructural-affinity · Closed
- Green-Class Window Entropystructural-affinity · Closed
- Marginal Monotonicity of Finite Classical KL Divergencestructural-affinity · Closed
- Mutual Information as an Entropy Balancestructural-affinity · Closed
- Nonnegativity of the Classical Data-Processing Defectstructural-affinity · Closed
- Shannon Entropy Is Invariant Under Injective Relabelingstructural-affinity · Closed
- Strict Positivity of Finite Classical KL Divergencestructural-affinity · Closed
- Symmetry of Finite Mutual Informationstructural-affinity · Closed
- The Classical Petz Equality Conditionstructural-affinity · Closed
- The Data-Processing Defect on General Supportstructural-affinity · Closed
- The Entropy-Divergence Consistency Identitystructural-affinity · Closed
- The Grandmother Theoremstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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