1. See, for example, T. L. Hill,Introduction to Statistical Thermodynamics(Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1960), pp. 343–344.
2. It is essential thatxbe a “proper” thermodynamic variable. Thusxmust be proportional ton(f,Tconstant) and fx must be of ordernkT. For example,3for a random coil, the end-to-end lengthlwith ends on a given line is “proper” but the end-to-end lengthrwith free ends is not (rαn12). The lengthlof a random coil is, however, a “degenerate” case in that l = 0 when f = 0. We are primarily interested in macromolecular phase transitions (at f = 0) in this paper. When one phase is a random coil with l = 0, the situation is somewhat analogous to the ideal Bose-Einstein condensation where the condensed phase has zero volume. In summary: although random coils represent a degenerate case here and we do not have them primarily in mind, it is not necessary to exclude them from the discussion.
3. See Chap. 13 of reference 1.
4. See, for example, T. L. Hill,Statistical Mechanics(McGraw-Hill Book Company, Inc., New York, 1956), Appendix 9.