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.
A free probability analogue of the Wasserstein metric on the trace-state space.Geometric and Functional Analysis, 11:1125–1138, 2001
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Free information geometry and the model theory of noncommutative stochastic processes
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.