Can there be a second kind of entropy catastrophe in the melting of metastable solids?

We explore here the thermodynamic possibility of the superheating of alloys and the existence of a second order melting transition in metastable alloys subject to concentration fluctuations. Toward the purpose, a novel approach has been adopted which involves simultaneous consideration of the free energy and entropy changes associated with the melting of the fluctuated region. Similar to the well-known Kauzmann paradox in freezing, in principle, there exists an entropy catastrophe in the nucleation of melting in metastable solids, too. However, it would be experimentally difficult to realize the melting of metastable solids because of the tendency to equilibrate at elevated temperatures.