Equivalent formulations and implications of Debye randomness for amorphous systems

It is shown that amorphous samples are Debye (D) random when some average quantities are equal to the corresponding averages evaluated over the largest available sets. The physical consistency of this condition requires that the interphase specific surfaces are proportional to the product of the corresponding volume fractions. The coefficient of proportionality μ is the only parameter which appears in the correlation function, whose analytical expression is simply exp(-μr), independently of the number of the phases constituting the D-random sample. Furthermore, D randomness amounts to requiring that the system of linear differential equations be linear and that its form remain invariant when two phases are combined into a single one.