Exponential Relative Entropy Decay Along Quantum Markov Semigroups
Operator Algebras
2025-06-27 v2 Mathematical Physics
math.MP
Quantum Physics
Abstract
We establish the equivalence between exponential decay of the relative entropy along a quantum Markov semigroup and the modified logarithmic Sobolev inequality for general von Neumann algebras. We also extend an intertwining criterion for the modified logarithmic Sobolev inequality to GNS-symmetric quantum Markov semigroups on infinite-dimensional von Neumann algebras.
Cite
@article{arxiv.2505.07549,
title = {Exponential Relative Entropy Decay Along Quantum Markov Semigroups},
author = {Melchior Wirth},
journal= {arXiv preprint arXiv:2505.07549},
year = {2025}
}
Comments
Error in Theorem 2.7 corrected