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 CONSEQUENCES20
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
- Binomial and kappa states do not exhaust truncated entropy minimizerstruth-dependency · Closed
- Collision Entropy versus Shannon Entropytruth-dependency · Closed
- Collision-Entropy Uncertaintytruth-dependency · Closed
- Conditional Entropy and Its Chain Ruletruth-dependency · Closed
- Entropytruth-dependency · Closed
- Finite Deletion-Channel Entropy Orderingtruth-dependency · Closed
- Finite Readout Alphabet Entropy Capacitytruth-dependency · Closed
- Green-Class Window Entropytruth-dependency · Closed
- Increasing DomiRank entropy on connected nonregular graphstruth-dependency · Closed
- Mutual Information as an Entropy Balancetruth-dependency · Closed
- Orthogonal Records and Pointer Informationtruth-dependency · Closed
- Schur--Horn Shannon Entropy Monotonicitytruth-dependency · Closed
- Selective LOCC can increase the Moreau-Yosida entanglement of formationtruth-dependency · Closed
- Shannon Entropy Is Invariant Under Injective Relabelingtruth-dependency · Closed
- SinghviMaxInputEntropytruth-dependency · Closed
- Spectral Readout Entropy Equalitytruth-dependency · Closed
- Symmetry of Finite Mutual Informationtruth-dependency · Closed
- The Entropy-Divergence Consistency Identitytruth-dependency · Closed
- The X-state conditional entropy f_1 need not be weakly unimodaltruth-dependency · Closed
- TwoDeletionChannelEntropytruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Binomial and kappa states do not exhaust truncated entropy minimizersstructural-affinity · Closed
- 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
- Entropystructural-affinity · Closed
- Finite Readout Alphabet Entropy Capacitystructural-affinity · Closed
- Increasing DomiRank entropy on connected nonregular graphsstructural-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
- Schur--Horn Shannon Entropy Monotonicitystructural-affinity · Closed
- Shannon Entropy Is Invariant Under Injective Relabelingstructural-affinity · Closed
- SinghviMaxInputEntropystructural-affinity · Closed
- Spectral Readout Entropy Equalitystructural-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 Entropy-Divergence Consistency Identitystructural-affinity · Closed
- The Grandmother Theoremstructural-affinity · Closed
- The X-state conditional entropy f_1 need not be weakly unimodalstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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