  We calculate several thermodynamic quantities for repulsively interacting
one-dimensional fermions.We solve the Hubbard model at both zero and finite
temperatures using the Bethe-ansatz method. For arbitrary values of the
chemical potential, we calculate the particle number density, the double
occupancy, various compressibilities, and the entropy as a function of
temperature and interaction. We find that these thermodynamic quantities show a
characteristic behavior so that measurements of these quantities can be used as
a detection of temperature, the metal-insulator transition, and metallic and
insulating phases in the trap environment. Further, we discuss an experimental
scheme to extract these thermodynamic quantities from the column density
profiles. The entropy and the compressibility of the entire trapped atomic
cloud also reveal characteristic features indicating whether insulating and/or
metallic phases coexist in the trap.
