We present a first-principles statistical mechanics theory that incorporates the calculation of electronic total energies in the local density approximation, configurational entropies, vibrational modes and relaxation effects in disordered systems. Applications of the theory to the binary Au-Ni system are given using the linear muffin-tin orbital method for the total energy calculations, the cluster variation method for the description of the configurational entropy and the Debye-Gruneisen approximation for the vibrational modes. The solubilities of both ends of the phase diagram, calculated with no adjustable parameters, are compared with experiment.