The Canonical Ensemble and the Central Limit Theorem

TL;DR

This paper explores how the central limit theorem applied to the canonical ensemble offers new insights into statistical mechanics, supported by numerical illustrations and an educational laboratory experiment.

Contribution

It introduces a novel theoretical connection between the central limit theorem and the canonical ensemble, with practical educational applications.

Findings

Numerical demonstrations of the central limit theorem in the canonical ensemble

A proposed undergraduate laboratory experiment for teaching statistical mechanics

Enhanced conceptual understanding of statistical mechanics principles

Abstract

Some of the more powerful results of mathematical statistics are becoming of increasing importance in statistical mechanics. Here the use of the central limit theorem in conjunction with the canonical ensemble is shown to lead to an interesting and important new insight into results associated with the canonical ensemble. This theoretical work is illustrated numerically and it is shown how this numerical work can form the basis of an undergraduate laboratory experiment which should help to implant ideas of statistical mechanics in students' minds.