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arXiv · 2608.23482

Sharp Complete Modified Log-Sobolev Inequalities on Classical and Quantum Tori

Long Zhao
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Abstract

We prove that the heat semigroup on the circle has optimal complete modified logarithmic Sobolev constant \(1\). The proof is based on a matrix-valued Wirtinger inequality and yields the stronger Bogoliubov--Kubo--Mori Fisher information contraction with rate \(e^{-2t}\). As a consequence, the complete tensorization and transference principle yields the same sharp constant for the heat semigroups on classical and quantum tori.

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Long Zhao. 2026-08-24. Sharp Complete Modified Log-Sobolev Inequalities on Classical and Quantum Tori. https://arxiv.org/abs/2608.23482

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