Partial energy fluctuations are known tools to reconstruct microcanonical
heat capacities. For experimental applications, approximations have been
developed to infer fluctuations at freeze out from the observed fragment
partitions. The accuracy of this procedure as well as the underlying
independent fragment approximation is under debate already at the level of
equilibrated systems. Using a well controlled computer experiment, the Lattice
Gas model, we critically discuss the thermodynamic conditions under which
fragment partitions can be used to reconstruct the thermodynamics of an
equilibrated system.Comment: version accepted for publication in Phys.Rev.