The thermal history of melts leads to three liquid states above the melting temperatures Tm containing clusters—bound colloids with two opposite values of enthalpy +Δεlg × ΔHm and −Δεlg × ΔHm and zero. All colloid bonds disconnect at Tn+ > Tm and give rise in congruent materials, through a first-order transition at TLL = Tn+, forming a homogeneous liquid, containing tiny superatoms, built by short-range order. In non-congruent materials, (Tn+) and (TLL) are separated, Tn+ being the temperature of a second order and TLL the temperature of a first-order phase transition. (Tn+) and (TLL) are predicted from the knowledge of solidus and liquidus temperatures using non-classical homogenous nucleation. The first-order transition at TLL gives rise by cooling to a new liquid state containing colloids. Each colloid is a superatom, melted by homogeneous disintegration of nuclei instead of surface melting, and with a Gibbs free energy equal to that of a liquid droplet containing the same magic atom number. Internal and external bond number of colloids increases at Tn+ or from Tn+ to Tg. These liquid enthalpies reveal the natural presence of colloid–colloid bonding and antibonding in glass-forming melts. The Mpemba effect and its inverse exist in all melts and is due to the presence of these three liquid states.