Wasserstein distance between noncommutative dynamical systems

被引：2
|
作者：
Duvenhage, Rocco [1 ]
机构：
[1] Univ Pretoria, Dept Phys, ZA-0002 Pretoria, South Africa
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 527卷 / 01期
关键词：
Optimal transport; Wasserstein distance; von Neumann algebras; States; Dynamical systems; Open systems; VON-NEUMANN-ALGEBRAS; VONNEUMANN-ALGEBRAS; QUANTUM; JOININGS; SEMIGROUPS; TRANSPORT; THEOREM;
D O I：
10.1016/j.jmaa.2023.127353
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce and study a class of quadratic Wasserstein distances on spaces consisting of generalized dynamical systems on a von Neumann algebra. We emphasize how symmetry of such a Wasserstein distance arises, but also study the asymmetric case. This setup is illustrated in the context of reduced dynamics, and a number of simple examples are also presented.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org /licenses /by-nc-nd /4 .0/).
引用
收藏
页数：26
相关论文
共 50 条
  • [1] Conductance and noncommutative dynamical systems
    Ramos, C. Correia
    Martins, Nuno
    Ramos, J. Sousa
    [J]. NONLINEAR DYNAMICS, 2006, 44 (1-4) : 127 - 134
  • [2] Conductance and Noncommutative Dynamical Systems
    C. Correia Ramos
    Nuno Martins
    J. Sousa Ramos
    [J]. Nonlinear Dynamics, 2006, 44 : 127 - 134
  • [3] The Gromov-Wasserstein Distance Between Spheres
    Arya, Shreya
    Auddy, Arnab
    Clark, Ranthony A.
    Lim, Sunhyuk
    Memoli, Facundo
    Packer, Daniel
    [J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2024,
  • [4] On the Wasserstein distance between mutually singular measures
    Buttazzo, Giuseppe
    Carlier, Guillaume
    Laborde, Maxime
    [J]. ADVANCES IN CALCULUS OF VARIATIONS, 2020, 13 (02) : 141 - 154
  • [5] Quantum Wasserstein distance between unitary operations
    Qiu, Xinyu
    Chen, Lin
    Zhao, Li -Jun
    [J]. PHYSICAL REVIEW A, 2024, 110 (01)
  • [6] ERGODIC THEOREMS FOR NONCOMMUTATIVE DYNAMICAL-SYSTEMS
    CONZE, JP
    DANGNGOC, N
    [J]. INVENTIONES MATHEMATICAE, 1978, 46 (01) : 1 - 15
  • [7] Wasserstein distances in the analysis of time series and dynamical systems
    Muskulus, Michael
    Verduyn-Lunel, Sjoerd
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2011, 240 (01) : 45 - 58
  • [8] Noncommutative Kahler structure on C*-dynamical systems
    Guin, Satyajit
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 2019, 146
  • [9] CALCULATION OF WASSERSTEIN DISTANCE BETWEEN PROBABILITY DISTRIBUTIONS ON LINE
    VALLANDE.SS
    [J]. TEORIYA VEROYATNOSTEI I YEYE PRIMENIYA, 1973, 18 (04): : 824 - 827
  • [10] Quantum Wasserstein distance of order 1 between channels
    Duvenhage, Rocco
    Mapaya, Mathumo
    [J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2023, 26 (03)
12345