trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

Mutual Information as an Entropy Balance

Finite mutual information in nats decomposes into marginal and joint Shannon entropies, yielding entropy subadditivity.

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DIRECT PREREQUISITES2
DIRECT CONSEQUENCES7
PROOF DEPTH3
DOCUMENT LINKS1
THEOREM

Mutual information is the entropy balance

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Maximum Entropy on a Finite AlphabetMaximum Entropy on a FiniteAlphabetNonnegativity of Finite Classical Mutual InformationNonnegativity of FiniteClassical Mutual InformationMutual Information as an Entropy BalanceMutual Information as anEntropy BalanceHidden Arithmetic WeightHidden Arithmetic WeightMacroscopic Predictive Efficiency IncreaseMacroscopic PredictiveEfficiency IncreaseConditioning Reduces EntropyConditioning Reduces EntropyExpected Posterior Entropy ReductionExpected Posterior EntropyReductionStrong Subadditivity and Conditional ProductsStrong Subadditivity andConditional ProductsEstimator-Error Lower Bounds from Finite Fano InequalitiesEstimator-Error Lower Boundsfrom Finite Fano InequalitiesPure-state ECQC fails in dimension fivePure-state ECQC fails indimension five
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Lean sourceResearch workspace
Status
Closed
Depth
3
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/MutualInformationEntropy
Repository path
D5/S3/Entropy/MutualInformationEntropy.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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