• Corpus ID: 252519642

Complete order and relative entropy decay rates

@inproceedings{Gao2022CompleteOA,
  title={Complete order and relative entropy decay rates},
  author={Li Gao and Marius Junge and Nicholas Laracuente and Haojian Li},
  year={2022}
}

• Li Gao, M. Junge, +1 author Haojian Li
• Published 22 September 2022
• Mathematics

We prove that the complete modified log-Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its completely bounded mixing time. This implies that the complete modified log-Sobolev constant is comparable to spectral gap up to a constant as logarithm of dimension or index. The quantum version of a classical birth-death process shows that this bound is tight. Such an estimate is obtained for GNS-symmetric quantum Markov semigroups on general von Neumann algebras. As an application, we obtain that every subLaplacian given by a Hörmander system on a compact manifold satisfies a uniform modified log-Sobolev inequality for all matrix-valued functions.