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Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

van Lith, Janneke (2001) Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics. [Preprint]

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    Abstract

    The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well-known that this account is problematic. <P> This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.


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    Item Type: Preprint
    Keywords: ergodic theory, statistical mechanics, stationarity, equilibrium, interpretation of probability
    Subjects: Specific Sciences > Probability/Statistics
    Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
    Depositing User: Janneke van Lith
    Date Deposited: 15 Aug 2001
    Last Modified: 07 Oct 2010 11:10
    Item ID: 367
    URI: http://philsci-archive.pitt.edu/id/eprint/367

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