Generalized Theory of Condensing Systems. V

Abstract

Discussions are given of the validity of the G-condition, which was used as the start­ ing point of the theory of condensing systems in the author's previous papers, and which was considered to represent the essential features of the volume-dependent cluster integrals of the physical real systems. In particular, for classical systems with two-body forces of finite range, the concept of maximum length of a cluster is introduced, and, with the use of this, some theorems are established which are useful for testing the validity of (G· 3) [which is the third item of the G-condition and assumes the independence, upon u (volume per molecule), of the contribution per molecule to the (infinitely large) cluster integral in some range of values of u]. The validity of the assumptions in the theorems is discussed from the physical point of view. In this connection, some arguments are made about the analytical properties of the condensa­ tion point, strongly supporting the identity of the condensation point of the classical real system and that of the (0) -system (i. e. the system consisting of volume-independent cluster integrals). Some remarks are given on the G-condition in the case of the general system (quantal or classical). Finally, analytical examples of functions satisfying the G-condition are shown.