A novel free entropy functional χ_chron^U is defined using chronological formulas that is concave along Wasserstein geodesics and whose heat evolution satisfies the evolution variational inequality as the metric gradient flow.
Tracial non-commutative smooth functions and the free Wasserstein manifold.Dissertationes Mathematicae, 580:1–150, 2022
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A novel free entropy functional χ_chron^U is defined using chronological formulas that is concave along Wasserstein geodesics and whose heat evolution satisfies the evolution variational inequality as the metric gradient flow.