<一般論文> アンサンブル理論と熱力学的アナロジーの系譜 : ギブスの統計力学についての一考察

Abstract

This paper shows that JosiahWillard Gibbs (1839–1903) integrated Helmholtzian thermodynamic analogies with the Boltzmann-Maxwellian ensemble approach in his book Elementary principles in statistical mechanics (1902). On one hand, Gibbs took over the ensemble concept from Maxwell and Boltzmann, who developed it in the 1870s and 1880s. A lecture note taken by a Gibbs' student reveals that Gibbs finished his theory of statistical mechanics following the Boltzmann-Maxwell line almost completely by 1895. On the other hand, Gibbs made analogies with thermodynamics in Helmholtz's sense; in 1884 Helmholtz suggested the idea of monocyclic systems to establish the fact that there are formal and operational correspondences between mechanics and thermodynamics. In the same year, Boltzmann extended the domain of monocyclic systems by means of ensembles, but he made only formal analogies. The lecture note also mentions formal analogies. In the Elementary principles, Gibbs applied the ensemble concept to make both formal and operational analogies, as can be seen in Helmholtz. Although there is no direct evidence that Gibbs studied Helmholtz's monocyclic systems, a detailed analysis allows us to interpret Gibbs' theory as succeeding Helmholtz' thermodynamic analogies.