Functional inequalities for Boolean entropy

Guillaume Cébron; Kewei Pan

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arXiv · 2602.23527

Functional inequalities for Boolean entropy

Guillaume Cébron·Kewei Pan

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Abstract

Building on the recently introduced notion of Boolean entropy, we define the corresponding Boolean Fisher information via a de Bruijn identity. We study the monotonicity of this Fisher information in the Boolean Central Limit Theorem and establish several functional inequalities involving these quantities, including a logarithmic Sobolev inequality. We also develop Non-microstate counterparts and prove the associated functional inequalities. In addition, we introduce a notion of Stein discrepancy in the Boolean setting, which leads to new Berry--Esseen type bounds in the Boolean central limit theorem.

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Guillaume Cébron, Kewei Pan. 2026-02-26. Functional inequalities for Boolean entropy. https://arxiv.org/abs/2602.23527

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