  A direct connection of information entropy $S$ and kinetic energy $T$ is
obtained for nuclei and atomic clusters, which establishes $T$ as a measure of
the information in a distribution. It is conjectured that this is a universal
property for fermionic many-body systems. We also check rigorous inequalities
previously found to hold between S and T for atoms and verify that they hold
for nuclei and atomic clusters as well. These inequalities give a relationship
of Shannon's information entropy in position-space with an experimental
quantity i.e. the rms radius of nuclei and clusters.
