Epsilon-ergodicity and the success of equilibrium statistical mechanics

Philosophy of Science 65 (4):688-708 (1998)
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Abstract

Why does classical equilibrium statistical mechanics work? Malament and Zabell (1980) noticed that, for ergodic dynamical systems, the unique absolutely continuous invariant probability measure is the microcanonical. Earman and Rédei (1996) replied that systems of interest are very probably not ergodic, so that absolutely continuous invariant probability measures very distant from the microcanonical exist. In response I define the generalized properties of epsilon-ergodicity and epsilon-continuity, I review computational evidence indicating that systems of interest are epsilon-ergodic, I adapt Malament and Zabell’s defense of absolute continuity to support epsilon-continuity, and I prove that, for epsilon-ergodic systems, every epsilon-continuous invariant probability measure is very close to the microcanonical.

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Peter Vranas
University of Wisconsin, Madison

Citations of this work

The “Past Hypothesis”: Not even false.John Earman - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (3):399-430.
Time in Thermodynamics.Jill North - 2011 - In Criag Callender (ed.), The Oxford Handbook of Philosophy of Time. Oxford University Press. pp. 312--350.

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