Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems

E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.

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Author
Carlen, Eric A.; Maas, JanIST Austria
Department
Abstract
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.
Publishing Year
Date Published
2020-01-01
Journal Title
Journal of Statistical Physics
Volume
178
Issue
2
Page
319-378
ISSN
eISSN
IST-REx-ID

Cite this

Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. 2020;178(2):319-378. doi:10.1007/s10955-019-02434-w
Carlen, E. A., & Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics, 178(2), 319–378. https://doi.org/10.1007/s10955-019-02434-w
Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” Journal of Statistical Physics 178, no. 2 (2020): 319–78. https://doi.org/10.1007/s10955-019-02434-w.
E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems,” Journal of Statistical Physics, vol. 178, no. 2, pp. 319–378, 2020.
Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378.
Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” Journal of Statistical Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w.
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