Complete gradient estimates of quantum Markov semigroups

Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics.

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Journal Article | Published | English
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Abstract
In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.
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Date Published
2021-08-30
Journal Title
Communications in Mathematical Physics
Acknowledgement
Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.
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Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 2021. doi:10.1007/s00220-021-04199-4
Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4
Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04199-4.
M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” Communications in Mathematical Physics. Springer Nature, 2021.
Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics.
Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics, Springer Nature, 2021, doi:10.1007/s00220-021-04199-4.
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