Complexions of an Assembly of Quasi-Independent Localized Systems

The total number of complexions is computed exactly for an isolated assembly of N quasiindependent localized systems with equally-spaced energy levels. This number Ω(N), is equal to Σt{Nk} where each term depends on a particular set of energy-level occupation numbers, Nk, allowed by the energy and system-number conservation conditions. In thermodynamic calculations, the approximation is usually made of replacing Ω by the maximum term in this sum tmax. A procedure is proposed for obtaining the exact value of tmax for integral N. The error made in the approximation is then calculated, and χ = ln tmax/lnΩ is computed for N = 2r. For N = 212 = 4096 one finds that (χ−1) is less than 0.005. An approximate analytic form for χ valid for higher N is also given.