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We develop a cavity-based method which allows to extract thermodynamicproperties from position information in hard-sphere/disk systems. So far, thereare 'available-volume' and 'free-volume' methods. We add a third one, which wecall 'available-volume-after-takeout', and which is shown to be mathematicallyequivalent to the others. In applications, where data sets are finite, allthree methods show limitations, and they do this in different parameter ranges.We illustrate the principal equivalence and the limitations on data frommolecular dynamics -- In particular, we test robustness against missing data.We have in mind experimental limitations where there is a small polydispersity,say 4% in the particle radii, but individual radii cannot be determined. Weobserve that, depending on the used method, the errors in such a situation areeasily 100% for the pressure and 10kT for the chemical potentials. Our work ismeant as guideline to the experimentalist for choosing the right one of thethree methods, in order to keep the outcome of experimental data analysismeaningful.

Cavity averages for hard spheres in the presence of polydispersity and incomplete data