Abstract: Schrödinger studied in the 1930s a thought experiment about hot gas in which a cloud of particles evolves in time from an initial distribution to another one, possibly quite different from the initial one. He posed the problem of determining the most likely evolution among the many possible ones, a problem now known as the Schrödinger bridge problem. H. Föllmer later in the 1980s framed the problem as an entropy regularized variational problem. The Schrödinger problem underlies a number…