Journal Article

Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics

John Earman and Miklós Rédei

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 47, issue 1, pages 63-78
Published in print March 1996 | ISSN: 0007-0882
e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/47.1.63
Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics

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We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statistical mechanics. Our claim is based on the observations that dynamical systems for which statistical mechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behaviour for the finite set of observables that matter, but the behaviour must ensure that the approach to equilibrium for these observables is on the appropriate time-scale.

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Subjects: Philosophy of Science ; Science and Mathematics

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