Statistical Mechanics of Finite Systems: Asymptotic Expansions. I. Two Petit Canonical Ensembles—(N, V, T) and (N, p, T) Systems

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Abstract
The statistical mechanics of a finite system differs from that of an infinite system in details of calculation, possession of additional variables and modification of fundamental relations, i.e., altered thermodynamics. Results become size‐dependent, and ensemble‐dependent. As examples of the general situation for finite systems, two petit canonical ensembles are examined here in relation to the grand canonical ensemble. The full asymptotic expansion is obtained for a one‐phase region of one‐component systems for each ensemble; all terms can be calculated within a grand canonical ensemble formalism. An analysis is made of both size dependence and the modified thermodynamics resulting from various approximations. The method presented represents both an approach to the study the general problems of the statical mechanical treatment of finite systems as well as a practical device for calculation in particular problems of small systems.