  Sequences of experimental ground-state energies are mapped onto concave
patterns cured from convexities due to pairing and/or shell effects. The same
patterns, completed by a list of excitation energies, can be used to give
numerical estimates of the grand potential $\Omega(\beta,\mu)$ for a mixture of
nuclei at low or moderate temperatures $T=\beta^{-1}$ and at many chemical
potentials $\mu.$ The average nucleon number $<{\bf A} >(\beta,\mu)$ then
becomes a continuous variable, allowing extrapolations towards nuclear masses
closer to drip lines. We study the possible concavity of several
thermodynamical functions, such as the free energy and the average energy, as
functions of $<{\bf A} >.$ Concavity, when present in such functions, allows
trivial interpolations and extrapolations providing upper and lower bounds,
respectively, to binding energies. Such bounds define an error bar for the
prediction of binding energies. An extrapolation scheme for such concave
functions is tested. We conclude with numerical estimates of the binding
energies of a few nuclei closer to drip lines.
