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Justifying Typicality Measures of Boltzmannian Statistical Mechanics and Dynamical Systems

Werndl, Charlotte (2013) Justifying Typicality Measures of Boltzmannian Statistical Mechanics and Dynamical Systems. [Preprint]

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Abstract

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper
attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main premises are that typicality measures are invariant and are related to
the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusion are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there
are uniqueness results about typicality measures.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Werndl, Charlottec.s.werndl@lse.ac.uk
Keywords: typicality, probability, Boltzmann, statistical mechanics, dynamical systems, ergodic, epsilon-ergodic, translation-continuous, translation-close
Subjects: Specific Sciences > Physics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Charlotte Werndl
Date Deposited: 02 Sep 2013 18:11
Last Modified: 02 Sep 2013 18:11
Item ID: 9976
Subjects: Specific Sciences > Physics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: 2013
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/9976

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