<特集：モデル> ギブスのカノニカル・アンサンブル : 何に支えられたモデルだったのか

Abstract

Ensemble is an important model in statistical mechanics that Gibbs used in his Elementary Principles. Few studies, however, have been made at analyzing his foundational arguments on ensemble. In this article, I compare Gibbs's derivation of the canonical ensemble with that in modern statistical mechanics, and argue that the former is based on mechanical reasoning, while the latter is based on a thermodynamical and quantum mechanical one. What the canonical ensemble represents, therefore, is different in each type of derivation. The modern canonical ensemble represents the probability of a system with a certain energy. On the other hand, Gibbs's canonical ensemble represents how systems of the ensemble distribute in phase space.