The foundational role of ergodic theory

Foundations of Science 11 (4):323-347 (2005)
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The foundation of statistical mechanics and the explanation of the success of its methods rest on the fact that the theoretical values of physical quantities (phase averages) may be compared with the results of experimental measurements (infinite time averages). In the 1930s, this problem, called the ergodic problem, was dealt with by ergodic theory that tried to resolve the problem by making reference above all to considerations of a dynamic nature. In the present paper, this solution will be analyzed first, highlighting the fact that its very general nature does not duly consider the specificities of the systems of statistical mechanics. Second, Khinchin’s approach will be presented, that starting with more specific assumptions about the nature of systems, achieves an asymptotic version of the result obtained with ergodic theory. Third, the statistical meaning of Khinchin’s approach will be analyzed and a comparison between this and the point of view of ergodic theory is proposed. It will be demonstrated that the difference consists principally of two different perspectives on the ergodic problem: that of ergodic theory puts the state of equilibrium at the center, while Khinchin’s attempts to generalize the result to non-equilibrium states



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Massimiliano Badino
Università degli Studi di Verona

Citations of this work

The ergodic hierarchy.Roman Frigg & Joseph Berkovitz - 2011 - Stanford Encyclopedia of Philosophy.
Philosophy of statistical mechanics.Lawrence Sklar - 2008 - Stanford Encyclopedia of Philosophy.
When do Gibbsian phase averages and Boltzmannian equilibrium values agree?Charlotte Werndl & Roman Frigg - 2020 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 72:46-69.
Bridging Conceptual Gaps: The Kolmogorov-Sinai Entropy.Massimiliano Badino - forthcoming - Isonomía. Revista de Teoría y Filosofía Del Derecho.

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References found in this work

Physics and Chance.Lawrence Sklar - 1995 - British Journal for the Philosophy of Science 46 (1):145-149.
The Kind of Motion We Call Heat.S. G. Brush - 1982 - British Journal for the Philosophy of Science 33 (2):165-186.

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