trureturingGitHub MATHEMATICAL ATLAS

Entropy / CONCEPT

The Finite Mixture Entropy Bracket

Finite mixture entropy lies between weighted component entropy and that entropy plus the weight entropy; the upper equality case for pairwise disjoint supports is not covered in this stratum.

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DIRECT PREREQUISITES4
DIRECT CONSEQUENCES4
PROOF DEPTH5
DOCUMENT LINKS1
THEOREM

The first mixture-joint marginal is the weight law

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Conditioning Reduces EntropyConditioning Reduces EntropyNonnegativity of Finite EntropyNonnegativity of Finite EntropyVanishing Mutual Information Characterizes IndependenceVanishing Mutual InformationCharacterizes IndependenceSymmetry of Finite Mutual InformationSymmetry of Finite MutualInformationThe Finite Mixture Entropy BracketThe Finite Mixture EntropyBracketThe entropic Glibichuk–Konyagin conjectureThe entropic Glibichuk–KonyaginconjectureClassical Markov monogamy for every permutationClassical Markov monogamy forevery permutationEquality in the Upper Mixture-Entropy BoundEquality in the Upper Mixture-Entropy BoundA finite counterexample to improved thermal recall convergenceA finite counterexample toimproved thermal recallconvergence
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Lean sourceResearch workspace
Status
Closed
Depth
5
Layer
D5/S3
Domain
Entropy
Node ID
D5/S3/Entropy/Mixing/MixtureEntropyBracket
Repository path
D5/S3/Entropy/Mixing/MixtureEntropyBracket.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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