Solutions of Koopman-von Neumann equations, their superpositions, and uncertainties

Abstract:The so-called Koopman-von Neumann (KvN) formulation brings classical mechanics to Hilbert space, but many techniques familiar from quantum mechanics remain missing. We use the gauge freedom of the KvN equation to derive separable solutions of the KvN equation, and by extension the classical Liouville equation. The canonical ensemble solution of statistical mechanics is shown to arise from separable solutions. We discuss the Hermiticity of the Liouvillian operator, and treat a case where its spectrum is discrete. Finally, we analyze an uncertainty relation between the so-called dynamical time and the Liouvillian, and argue that such a relation is natural and can be understood entirely within a classical framework.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Classical Physics (physics.class-ph)

arXiv:2512.11148 [quant-ph]

(or arXiv:2512.11148v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2512.11148 Focus to learn more arXiv-issued DOI via DataCite

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