preprint
Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
Eric A.
Carlen
author
Jan
Maas
author 4C5696CE-F248-11E8-B48F-1D18A9856A870000-0002-0845-1338
JaMa
department
We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates.
ArXiv2018
eng
1811.04572
E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems.” ArXiv, 2018.
Carlen, Eric A., and Jan Maas. <i>Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems</i>. ArXiv, 2018.
E.A. Carlen, J. Maas, (2018).
Carlen EA, Maas J. 2018. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems.
Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. 2018.
Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems.” ArXiv, 2018.
Carlen, E. A., & Maas, J. (2018). Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems. ArXiv.
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