Classical probabilistic transport equations are reformulated as quantum systems whose wave function obeys Schrödinger evolution and whose observables include non-commuting operators for statistical quantities.
Mauroy, Koopman operator framework for spectral analysis and identification of infinite-dimensional sys- tems, Mathematics9, 2495 (2021)
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Quantum mechanics for classical transport equations
Classical probabilistic transport equations are reformulated as quantum systems whose wave function obeys Schrödinger evolution and whose observables include non-commuting operators for statistical quantities.