Some entropic inequalities for primitive KMS symmetric quantum Markov semigroups

@misc{liu2026some,
  title = {{Some entropic inequalities for primitive KMS symmetric quantum Markov semigroups}},
  author = {Zhengwei Liu and Jincheng Wan and Jinsong Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13726},
  eprint = {2609.13726},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13726},
}

TY  - UNPB
TI  - Some entropic inequalities for primitive KMS symmetric quantum Markov semigroups
AU  - Zhengwei Liu
AU  - Jincheng Wan
AU  - Jinsong Wu
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13726
UR  - https://arxiv.org/abs/2609.13726
AB  - In this note, we prove that every primitive KMS-symmetric quantum Markov semigroup on a finite-dimensional matrix algebra satisfies a modified logarithmic Sobolev inequality (MLSI). We also construct a primitive quantum Markov semigroup without KMS symmetry that fails MLSI, and a primitive KMS-symmetric quantum Markov semigroup that fails complete MLSI (CMLSI). The latter construction also provides a non-primitive KMS-symmetric quantum Markov semigroup without MLSI. For the graph-based KMS-symmetric quantum Markov semigroups studied here, we prove MLSI and CMLSI when the underlying graph is connected and has at least three vertices. Finally, we establish CMLSI for a class of primitive bimodule KMS-symmetric quantum Markov semigroups arising from fermionic systems.
ER  -