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Explaining Thermodynamic-Like Behaviour In Terms of Epsilon-Ergodicity

Frigg, Roman and Werndl, Charlotte (2011) Explaining Thermodynamic-Like Behaviour In Terms of Epsilon-Ergodicity. [Preprint]

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Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic.

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Item Type: Preprint
Additional Information: Forthcoming in: Philosophy of Science
Keywords: thermodynamic-like behaviour; approach to equilibrium; epsilon-ergodicity; statistical mechanics; ergodic theory; Boltzmann
Subjects: Specific Sciences > Physics > Classical Physics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Charlotte Werndl
Date Deposited: 06 Oct 2011 11:32
Last Modified: 06 Oct 2011 11:32
Item ID: 8826

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