A dual formula for the noncommutative transport distance

2021/04/24 by Melchior Wirth · 1 voice · 11 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Dual (grammatical number) #Mathematical physics #Mathematics #Noncommutative geometry #Physics #Random Matrices and Applications #Statistical physics #math-ph #math.MP #math.OA #math.OC

paper · pdf · open access · doi:10.1007/s10955-022-02911-9

published in Journal of Statistical Physics 187(2), 19 (Springer Science+Business Media)

arxiv published 2021/04/24 · arxiv created 2021/06/09 · openalex publication_date 2022/04/08 · arxiv updated 2022/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou-Brenier formulation of the Wasserstein distance in terms of subsolutions of Hamilton-Jacobi-Bellmann equation.

Citations

• Topics in Optimal Transportation
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
• A Noncommutative Transport Metric and Symmetric Quantum Markov Semigroups as Gradient Flows of the Entropy
• Concentration of quantum states from quantum functional and transportation cost inequalities

Discussions

• AUTOMATIC REPOST OF OLD TWEETS FROM TWITTER (X) FOR ARCHIVING PURPOSES [11.05.2021] --- New preprint on "A dual formula for the noncommutative transport distance" by M. Wirth - https://arxiv.org/abs/2 [bsky, 0 points, 0 comments]

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