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PreprintarXiv licencearXiv

Tight entropy contraction beyond detailed balance

  • Li Gao
  • Jingyu Guo
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Abstract

We establish quantitative entropy contraction bounds for finite-dimensional quantum channels beyond detailed balance. For channels compatible with a faithful conditional expectation, we show that GNS (Gelfand--Naimark--Segal) norm contraction yields relative entropy contraction with only a logarithmic loss in the dimensional constant. For quantum Markov semigroups with a faithful asymptotic conditional expectation, this gives a lower bound on the complete modified logarithmic Sobolev constant in terms of the GNS spectral gap. The bounds allow initial entanglement with an external environment and are independent of its system size. Applications to alternating reservoir pulses and continuously coupled energy ladders give bounds with optimal size dependence.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026tight,
  title = {{Tight entropy contraction beyond detailed balance}},
  author = {Li Gao and Jingyu Guo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24953},
  eprint = {2609.24953},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24953},
}
RIS
TY  - UNPB
TI  - Tight entropy contraction beyond detailed balance
AU  - Li Gao
AU  - Jingyu Guo
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24953
UR  - https://arxiv.org/abs/2609.24953
AB  - We establish quantitative entropy contraction bounds for finite-dimensional quantum channels beyond detailed balance. For channels compatible with a faithful conditional expectation, we show that GNS (Gelfand--Naimark--Segal) norm contraction yields relative entropy contraction with only a logarithmic loss in the dimensional constant. For quantum Markov semigroups with a faithful asymptotic conditional expectation, this gives a lower bound on the complete modified logarithmic Sobolev constant in terms of the GNS spectral gap. The bounds allow initial entanglement with an external environment and are independent of its system size. Applications to alternating reservoir pulses and continuously coupled energy ladders give bounds with optimal size dependence.
ER  -