Entropy Moduli and Support-Sensitive BKM Coercivity for Rank-Deficient Non-Commutative Markov Semigroups
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918485696708608 |
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| author | Nasreddine, Hassan |
| author_facet | Nasreddine, Hassan |
| contents | We study entropy--coherence relations near rank-deficient support boundaries in finite-dimensional quantum systems. For block-diagonal reference states, we establish support-sensitive coercivity estimates showing that the entropy cost of cross-boundary coherence acquires a logarithmic enhancement as the population scale approaches the support boundary.
Combined with finite-time entropy bounds, these estimates yield conditional entropy--activation bounds with a logarithmic correction factor of order \(e^{-αt}(1+αt)^{-1/2}\) in coherence-dominant regimes. The analysis proceeds through pinching reductions and effective \(2\times2\) Bogoliubov--Kubo--Mori (BKM) estimates adapted to the coherence--population structure.
We further apply the framework to Davies semigroups under additional secular decoupling and population-rate assumptions. The resulting statements provide conditional certification bounds near rank-deficient stationary states, rather than general mixing-time or convergence-rate estimates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_16616 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entropy Moduli and Support-Sensitive BKM Coercivity for Rank-Deficient Non-Commutative Markov Semigroups Nasreddine, Hassan Quantum Physics 47D07 (Primary), 46L55, 94A17 (Secondary) We study entropy--coherence relations near rank-deficient support boundaries in finite-dimensional quantum systems. For block-diagonal reference states, we establish support-sensitive coercivity estimates showing that the entropy cost of cross-boundary coherence acquires a logarithmic enhancement as the population scale approaches the support boundary. Combined with finite-time entropy bounds, these estimates yield conditional entropy--activation bounds with a logarithmic correction factor of order \(e^{-αt}(1+αt)^{-1/2}\) in coherence-dominant regimes. The analysis proceeds through pinching reductions and effective \(2\times2\) Bogoliubov--Kubo--Mori (BKM) estimates adapted to the coherence--population structure. We further apply the framework to Davies semigroups under additional secular decoupling and population-rate assumptions. The resulting statements provide conditional certification bounds near rank-deficient stationary states, rather than general mixing-time or convergence-rate estimates. |
| title | Entropy Moduli and Support-Sensitive BKM Coercivity for Rank-Deficient Non-Commutative Markov Semigroups |
| topic | Quantum Physics 47D07 (Primary), 46L55, 94A17 (Secondary) |
| url | https://arxiv.org/abs/2604.16616 |