Henriksson, Andreas (2019) On the Gibbs-Liouville theorem in classical mechanics. [Preprint]

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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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Item Type:	Preprint
Creators:	Creators Email ORCID Henriksson, Andreas andreas.henriksson@skole.rogfk.no 0000-0001-9014-4320
Keywords:	Determinism; Information; Gibbs-Liouville theorem; Hamilton equations; Hamilton principle; Poisson algebra; Unitarity
Subjects:	Specific Sciences > Physics > Classical Physics
Depositing User:	Mr. Andreas Henriksson
Date Deposited:	08 Nov 2019 02:15
Last Modified:	08 Nov 2019 02:15
Item ID:	16620
Subjects:	Specific Sciences > Physics > Classical Physics
Date:	9 May 2019
URI:	http://philsci-archive.pitt.edu/id/eprint/16620

Available Versions of this Item

• On the Gibbs-Liouville theorem in classical mechanics. (deposited 08 May 2019 01:48)
  • On the Gibbs-Liouville theorem in classical mechanics. (deposited 10 May 2019 01:05)
    • On the Gibbs-Liouville theorem in classical mechanics. (deposited 12 May 2019 01:59)
      • On the Gibbs-Liouville theorem in classical mechanics. (deposited 08 Nov 2019 02:15) [Currently Displayed]

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