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When do Gibbsian phase averages and Boltzmannian equilibrium values agree?

Frigg, Roman (2020) When do Gibbsian phase averages and Boltzmannian equilibrium values agree? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. ISSN 1355-2198

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Identification Number: 10.1016/j.shpsb.2020.05.003

Abstract

This paper aims to shed light on the relation between Boltzmannian statistical mechanics and Gibbsian statistical mechanics by studying the Mechanical Averaging Principle, which says that, under certain conditions, Boltzmannian equilibrium values and Gibbsian phase averages are approximately equal. What are these conditions? We identify three conditions each of which is individually sufficient (but not necessary) for Boltzmannian equilibrium values to be approximately equal to Gibbsian phase averages: the Khinchin condition, and two conditions that result from two new theorems, the Average Equivalence Theorem and the Cancelling Out Theorem. These conditions are not trivially satisfied, and there are core models of statistical mechanics, the six-vertex model and the Ising model, in which they can fail.

Item Type: Article
Official URL: https://www.sciencedirect.com/journal/studies-in-h...
Additional Information: © 2020 Elsevier Ltd
Divisions: Philosophy, Logic and Scientific Method
Subjects: Q Science > QC Physics
Date Deposited: 04 May 2020 09:15
Last Modified: 20 Oct 2020 07:41
URI: http://eprints.lse.ac.uk/id/eprint/104221

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