Free entropy and related quantities are controlled along Wasserstein geodesics for full types, and an explicit counterexample shows non-commutative laws cannot simultaneously realize entropy and Wasserstein distance in large-n random matrix models.
On ultraproduct embeddings and amenability for tracial von neumann algebras.International Mathematics Research Notices, 2021(4):2882–2918, 10 2020
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Information geometry for types in the large-$n$ limit of random matrices
Free entropy and related quantities are controlled along Wasserstein geodesics for full types, and an explicit counterexample shows non-commutative laws cannot simultaneously realize entropy and Wasserstein distance in large-n random matrix models.