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.
Classical mechanics as nonlinear quantum mechanics
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abstract
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.
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quant-ph 1years
2026 1verdicts
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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.