03862nam a22006135i 4500 978-3-031-50466-2 DE-He213 20251030113054.0 cr nn 008mamaa 240919s2024 sz | s |||| 0|eng d 9783031504662 978-3-031-50466-2 10.1007/978-3-031-50466-2 doi QA1-939 PB bicssc MAT000000 bisacsh PB thema Optimal Transport on Quantum Structures [electronic resource] / edited by Jan Maas, Simone Rademacher, Tamás Titkos, Dániel Virosztek. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 321 p. 8 illus., 2 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Bolyai Society Mathematical Studies, 2947-9460 ; 29 Preface -- Chapter 1. An Introduction to Optimal Transport and Wasserstein Gradient Flows by Alessio Figalli -- Chapter 2. Dynamics and Quantum Optimal Transport:Three Lectures on Quantum Entropy and Quantum Markov Semigroups by Eric A. Carlen -- Chapter 3. Quantum Couplings and Many-body Problems by Francois Golse -- Chapter 4. Quantum Channels and Qubits by Giacomo De Palma and Dario Trevisan -- Chapter 5. Entropic Regularised Optimal Transport in a Noncommutative Setting by Lorenzo Portinale -- Chapter 6. Logarithmic Sobolev Inequalities for Finite Dimensional Quantum Markov Chains by Cambyse Rouzé. The flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flows dynamics and quantum optimal transport quantum couplings and many-body problems quantum channels and qubits These notes are based on lectures given by the authors at the "Optimal Transport on Quantum Structures" School held at the Erdös Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport. Mathematics. 65523 Mathematical analysis. 64178 Global analysis (Mathematics). 69682 Manifolds (Mathematics). 69683 Measure theory. 71216 Mathematics. 65523 Analysis. Global Analysis and Analysis on Manifolds. 69685 Measure and Integration. 71219 Maas, Jan. editor. edt http://id.loc.gov/vocabulary/relators/edt 84651 Rademacher, Simone. editor. edt http://id.loc.gov/vocabulary/relators/edt 84652 Titkos, Tamás. editor. edt http://id.loc.gov/vocabulary/relators/edt 84653 Virosztek, Dániel. editor. edt http://id.loc.gov/vocabulary/relators/edt 84654 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031504655 Printed edition: 9783031504679 Printed edition: 9783031504686 Bolyai Society Mathematical Studies, 2947-9460 ; 29 84655 https://doi.org/10.1007/978-3-031-50466-2 ZDB-2-SMA ZDB-2-SXMS 63542 63542