The entropy of hot matter produced in medium energy nuclear collisions is inferred from recent data on light fragment cross sections. A previously suggested model is used to fit the abundances of both the deuterons, and the deuteronlike pairings contained in higher mass clusters, with a single parameter. The model takes into account finite density effects in six-dimensional phase space. The entropy rises monotonically with energy, as expected, but remains rather high even at the lower energies. Surprisingly the measured entropy always lies above the theoretically expected value (about 3.3) at the critical point of the liquid-gas phase transition which, it is argued, depends only upon the gross features of the nuclear matter equation of state.