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arXiv · 2505.07549

Exponential Relative Entropy Decay Along Quantum Markov Semigroups

Melchior Wirth
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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.

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Melchior Wirth. 2025-05-12. Exponential Relative Entropy Decay Along Quantum Markov Semigroups. https://arxiv.org/abs/2505.07549

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