On the Gibbs-Liouville theorem in classical mechanics

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Abstract
In this article, it is argued that the Gibbs-Liouville theorem is a mathematical representation of the statement that closed classical systems evolve deterministically. From the perspective of an observer of the system, whose knowledge about the degrees of freedom of the system is complete, the statement of deterministic evolution is equivalent to the notion that the physical distinctions between the possible states of the system, or, in other words, the information possessed by the observer about the system, is never lost. Furthermore, it is shown that the Hamilton equations and the Hamilton principle on phase space follow directly from the differential representation of the Gibbs-Liouville theorem, i.e. that the divergence of the Hamiltonian phase flow velocity vanish. Finally, it is argued that the statements of invariance of the Poisson algebra and unitary evolution are equivalent representations of the Gibbs-Liouville theorem.
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First archival date: 2019-05-12
Latest version: 5 (2021-05-24)
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2019-05-12

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