Duvenhage, Rocco de Villiers2024-03-272024-03-272023-11Duvenhage, R. 2023, 'Wasserstein distance between noncommutative dynamical systems', Journal of Mathematical Analysis and Applications, vol. 527, art. 127353, pp. 1-26. https://DOI.org/10.1016/j.jmaa.2023.127353.0022-247X10.1016/j.jmaa.2023.127353http://hdl.handle.net/2263/95367We 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.en© 2023 The Author(s). This is an open access article under the CC BY-NC-ND license.Optimal transportWasserstein distance vonWasserstein distanceVon Neumann algebrasStatesDynamical systemsOpen systemsArticle