Wasserstein distance between noncommutative dynamical systems

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Wasserstein distance between noncommutative dynamical systems

Duvenhage, Rocco

Journal of mathematical analysis and applications, 11/2023, Volume: 527, Issue: 1

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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.

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