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We describe some analogy between optimal transport and the Schr\"odinger problem where the transport cost is replaced by an entropic cost with a reference path measure.
On the translocation of masses
L. Kantorovitch · 1942
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E. Nelson · 1967
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Une initiation aux inégalités de Sobolev logarithmiques
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A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
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A survey of the Schrödinger problem and some of its connections with optimal transport
C. Léonard · 2014
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Iterative Bregman projections for regularized transportation problems
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C. Léonard · 2012
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On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint
Y. Chen, T. Georgiou, and M. Pavon
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Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates
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