  (Pu) has an unusually rich phase diagram that includes seven distinct solid
state phases and an unusually large 25% collapse in volume from its delta phase
to its low temperature alpha phase via a series of structural transitions.
Despite considerable advances in our understanding of strong electronic
correlations within various structural phases of Pu and other actinides, the
thermodynamic mechanism responsible for driving the volume collapse has
continued to remain a mystery. Here we utilize the unique sensitivity of
magnetostriction measurements to unstable f electron shells to uncover the
crucial role played by electronic entropy in stabilizing delta-Pu against
volume collapse. We find that in contrast to valence fluctuating rare earths,
which typically have a single f electron shell instability whose excitations
drive the volume in a single direction in temperature and magnetic field,
delta-Pu exhibits two such instabilities whose excitations drive the volume in
opposite directions while producing an abundance of entropy at elevated
temperatures. The two instabilities imply a near degeneracy between several
different configurations of the 5f atomic shell, giving rise to a considerably
richer behavior than found in rare earth metals. We use heat capacity
measurements to establish a robust thermodynamic connection between the two
excitation energies, the atomic volume, and the previously reported excess
entropy of delta-Pu at elevated temperatures.
