Abstract
In 1931--1932, Erwin Schrodinger studied a hot gas Gedankenexperiment (an instance of large deviations of the empirical distribution). Schrodinger's problem represents an early example of a fundame...
Highlights
In 1931--1932, Erwin Schr\o"dinger studied a hot gas Gedankenexperiment
A key motivation has been to highlight links between the classical early work in both topics and the more recent stochastic control viewpoint, which naturally lends itself to efficient computational schemes and interesting generalizations
The solution of Problem 4.1 exhibits the following remarkable reversibility property: Swapping the two marginal densities \rho 0 and \rho 1, the new solution is the time reversal of the previous one; cf. the title On the reversal of natural laws of [215]. These are the remarkable analogies to quantum mechanics which appeared to Schr\o"dinger to be very worthy of reflection
Summary
Several other significant contributions on this problem followed, including generalizations to multidimensional matrices such as [18, 108], and this line of research continues to this day; see, e.g., [76, 4, 234, 198, 25, 85] This large body of literature often ignores two papers by Erwin Schr\o"dinger from the early 1930s [215, 216] as well as important contributions by Robert Fortet (1938--1940) [105, 106] and Arne Beurling (1960) [27]. The only way to avoid total chaos, it seems to us, is to start with Erwin Schr\o"dinger's drama in the early 1930s
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