Reconsideration of Information-Theoretic Principles-Perspective from the Dual Probability Distribution.

Yoshikazu Ohtaki, Tomomi Nakamura, Hiroshi-H Hasegawa, Tatsuaki Wada

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Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

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1citing papers in PubMed

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1 citing paper in PubMed.

Beyond Entropy: Organization as the Preservation of Structural Identity.Entropy (Basel, Switzerland) · 2026
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5 · Who and what money

Authors and funding

4 authors.

Yoshikazu OhtakiDepartment of Mathematics and Informatics, Ibaraki University, Mito 310-8512, Japan.ORCID 0009-0004-3072-6096

Tomomi NakamuraDepartment of Mathematics and Informatics, Ibaraki University, Mito 310-8512, Japan.ORCID 0000-0001-8639-7341

Hiroshi-H HasegawaDepartment of Mathematics and Informatics, Ibaraki University, Mito 310-8512, Japan.

Tatsuaki WadaRegion of Electrical and Electronic Systems Engineering, Ibaraki University, Hitachi 316-8511, Japan.ORCID 0000-0002-7954-0549

Funding

Japan Society for the Promotion of Science Grants-in-aid for Scientific Research (KAKENHI) grant numbers 22K03431

6 · The paper itself

Abstract

We reconsider information-theoretic principles, such as the maximum entropy principle/minimum Massieu potential principle, from the perspective of the dual probability distribution. This is introduced through Sanov's Lemma for the multinomial distribution. The dual correspondence becomes asymptotically manifest. The Massieu potential is rewritten as the Kullback-Leibler divergence between the dual probability distribution and the dual reference distribution. Similarly, the dual potential is rewritten as the cumulant generating function with respect to the dual reference distribution. This perspective gives us new insight into information-theoretic principles. As the dual probability distribution naturally arises in data sampling, we anticipate that this new perspective will play a significant role in data analysis.

Indexed as

divergenceinformation geometrylarge deviation principleLegendre transformationMassieu potentialmaximum entropy principleminimum Massieu potential principlePythagorean theoremRobbins’ boundSanov’s Lemma

Identifiers

PMID42352191

DOI10.3390/e28060681

PMCPMC13297851

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