On the relation between the compressibility and the static structure factor of a fluid with a state-dependent pair-potential

It was assumed that both for a simple and a complex fluid the expression of the free-energy in terms of either its pair cf. or its direct cf. were mutually consistent. Since the expression in terms of the pair cf. was easily transposed to the case of a complex fluid with a state dependent pair-potential, an equivalent expression in terms of the direct cf. of the complex fluid was constructed. On this basis it was shown that the infinite wavelength limit of the static structure factor of the complex fluid was no longer proportional to its isothermal compressibility.