2013/10/06 by Charlotte Werndl, Werndl, Charlotte
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic Dynamics (nlin.CD) #Classical Physics (physics.class-ph) #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Statistical Mechanics and Entropy #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1310.1573
openalex publication_date 2013/10/06 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
A popular view in contemporary Boltzmannian statistical mechanics is to\ninterpret the measures as typicality measures. In measure-theoretic dynamical\nsystems theory measures can similarly be interpreted as typicality measures.\nHowever, a justification why these measures are a good choice of typicality\nmeasures is missing, and the paper attempts to fill this gap. The paper first\nargues that Pitowsky's (2012) justification of typicality measures does not fit\nthe bill. Then a first proposal of how to justify typicality measures is\npresented. The main premises are that typicality measures are invariant and are\nrelated to the initial probability distribution of interest (which are\ntranslation-continuous or translation-close). The conclusion are two theorems\nwhich show that the standard measures of statistical mechanics and dynamical\nsystems are typicality measures. There may be other typicality measures, but\nthey agree about judgements of typicality. Finally, it is proven that if\nsystems are ergodic or epsilon-ergodic, there are uniqueness results about\ntypicality measures.\n