Universal property of the information entropy in atoms, nuclei and atomic clusters

The position- and momentum-space information entropies of the electron distributions of atomic clusters are calculated using a Woods-Saxon single particle potential. The same entropies are also calculated for nuclear distributions according to the Skyrme parametrization of the nuclear mean field. It turns out that a similar functional form S=a+b ln N for the entropy as function of the number of particles N holds approximately for atoms, nuclei and atomic clusters. It is conjectured that this is a universal property of a many-fermion system in a mean field. It is also seen that there is an analogy of our expression for S to Boltzmann's thermodynamic entropy S=k ln W.