Entropy Moduli and BKM Coercivity for Rank-Deficient Non-Commutative Markov Semigroups

• URL: http://arxiv.org/abs/2604.16616v1
• Date: Fri, 17 Apr 2026 18:13:15 GMT
• Title: Entropy Moduli and BKM Coercivity for Rank-Deficient Non-Commutative Markov Semigroups
• Abstract summary: entropy-based certification of convergence can exhibit a slowdown near the boundary regime, with a rate of order e-alpha t/sqrt(alpha t)<n>We show that, under explicit local conditions, entropy-based certification of convergence can exhibit a slowdown near the boundary regime, with a rate of order e-alpha t/sqrt(alpha t)<n>The mechanism is identified as a coherence-population effect and disappears for incoherent initial states, where classical Pinsker-type bounds are recovered.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study entropy-based certification for non-commutative Markov semigroups with rank-deficient stationary states. We introduce a boundary-activation functional that quantifies deviation from the support of the stationary state and prove a logarithmic lower bound on relative entropy in terms of this quantity, based on a BKM coercivity argument and an exact block-decomposition identity. Combining this estimate with dynamical bounds for Davies semigroups under a modified logarithmic Sobolev inequality, we show that, under explicit local conditions, entropy-based certification of convergence can exhibit a slowdown near the boundary regime, with a rate of order e^{-alpha t}/sqrt(alpha t). The mechanism is identified as a coherence-population effect and disappears for incoherent initial states, where classical Pinsker-type bounds are recovered.

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