Henriksson, Andreas (2019) On the GibbsLiouville theorem in classical mechanics. [Preprint]
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Abstract
In this article, it is argued that the GibbsLiouville 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 GibbsLiouville 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 GibbsLiouville theorem.
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Item Type:  Preprint  

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Keywords:  Determinism; Information; GibbsLiouville 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://philsciarchive.pitt.edu/id/eprint/16620 
Available Versions of this Item

On the GibbsLiouville theorem in classical mechanics. (deposited 08 May 2019 01:48)

On the GibbsLiouville theorem in classical mechanics. (deposited 10 May 2019 01:05)

On the GibbsLiouville theorem in classical mechanics. (deposited 12 May 2019 01:59)
 On the GibbsLiouville theorem in classical mechanics. (deposited 08 Nov 2019 02:15) [Currently Displayed]

On the GibbsLiouville theorem in classical mechanics. (deposited 12 May 2019 01:59)

On the GibbsLiouville theorem in classical mechanics. (deposited 10 May 2019 01:05)
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