Badino, Massimiliano (2005) The Foundational Role of Ergodic Theory. [Preprint]
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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 Thirties, this problem, called the ergodic problem, was dealt with by an 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, A.I. Khinchin’s approach will be presented, that starting with the 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 the 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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|Additional Information:||Accepted for publication on Foundations of Science|
|Keywords:||ergodic theory, ergodic problem, statistical mechanics, Khinchin.|
|Subjects:||Specific Sciences > Physics > Statistical Mechanics/Thermodynamics|
|Depositing User:||Dr. Massimiliano Badino|
|Date Deposited:||25 Apr 2005|
|Last Modified:||07 Oct 2010 11:13|
Available Versions of this Item
- The Foundational Role of Ergodic Theory. (deposited 24 Apr 2005)
- The Foundational Role of Ergodic Theory. (deposited 25 Apr 2005)[Currently Displayed]
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