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Demystifying Typicality

Published online by Cambridge University Press:  01 January 2022

Roman Frigg  and
Charlotte Werndl
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Abstract

A gas prepared in a nonequilibrium state will approach equilibrium and stay there. An influential contemporary approach to statistical mechanics explains this behavior in terms of typicality. However, this explanation has been criticized as mysterious as long as no connection with the dynamics of the system is established. We take this criticism as our point of departure. Our central claim is that Hamiltonians of gases that are epsilon-ergodic are typical with respect to the Whitney topology. Because equilibrium states are typical, it follows that typical initial conditions approach equilibrium and stay there.

Type
Physics
Information
Philosophy of Science , Volume 79 , Issue 5 , December 2012 , pp. 917 - 929
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

The authors are listed alphabetically; the work is fully collaborative. An earlier version of this article has been presented at the 2010 PSA meeting in Montreal, and we would like to thank the audience for a valuable discussion.

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