  We perform a quantitative simulation of the repulsive Fermi-Hubbard model
using an ultracold gas trapped in an optical lattice. The entropy of the system
is determined by comparing accurate measurements of the equilibrium double
occupancy with theoretical calculations over a wide range of parameters. We
demonstrate the applicability of both high-temperature series and dynamical
mean-field theory to obtain quantitative agreement with the experimental data.
The reliability of the entropy determination is confirmed by a comprehensive
analysis of all systematic errors. In the center of the Mott insulating cloud
we obtain an entropy per atom as low as 0.77kB which is about twice as large as
the entropy at the Neel transition. The corresponding temperature depends on
the atom number and for small fillings reaches values on the order of the
tunneling energy.
