  We show that, for fermionic atoms in a one-dimensional optical lattice, the
fraction of atoms in doubly occupied sites is a highly non-monotonic function
of temperature. We demonstrate that this property persists even in the presence
of realistic harmonic confinement, and that it leads to a suppression of
entropy at intermediate temperatures that offers a route to adiabatic cooling.
Our interpretation of the suppression is that such intermediate temperatures
are simultaneously too high for quantum coherence and too low for significant
thermal excitation of double occupancy thus offering a clear indicator of the
onset of quantum fluctuations.
