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On the ergodic theorem and information loss in statistical mechanics

Henriksson, Andreas (2019) On the ergodic theorem and information loss in statistical mechanics. [Preprint]

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Abstract

In this article, it is argued that, for a classical Hamiltonian system which is closed, the ergodic theorem emerge from the Gibbs-Liouville theorem in the limit that the system has evolved for an infinitely long period of time. In this limit, from the perspective of an ignorant observer, who do not have perfect knowledge about the complete set of degrees of freedom for the system, distinctions between the possible states of the system, i.e. the information content, is lost leading to the notion of statistical equilibrium where states are assigned equal probabilities. Finally, by linking the concept of entropy, which gives a measure for the amount of uncertainty, with the concept of information, the second law of thermodynamics is expressed in terms of the tendency of an observer to loose information over time.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Henriksson, Andreasandreas.henriksson@skole.rogfk.no0000-0001-9014-4320
Keywords: Gibbs-Liouville theorem; Ergodic theorem; Statistical equilibrium; Second law of thermodynamics
Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Mr. Andreas Henriksson
Date Deposited: 10 May 2019 01:00
Last Modified: 10 May 2019 01:00
Item ID: 15987
Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: 8 May 2019
URI: http://philsci-archive.pitt.edu/id/eprint/15987

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