  The thermodynamics of the inhomogeneous one-dimensional repulsive fermionic
Hubbard model with parabolic confinement is studied by a density-functional
theory approach, based on Mermin's generalization to finite temperatures. A
local-density approximation (LDA), based on exact results for the homogeneous
model, is used to approximate the correlation part in the Helmholtz
free-energy, comprising the thermodynamic Bethe ansatz LDA (TBALDA). The
general presentation of the method is given and some properties of the
homogeneous model that are relevant to the DFT approach are analyzed. Extensive
comparison between TBALDA and numerical exact diagonalization results for
thermodynamic properties of small inhomogeneous chains is discussed. In the
remaining, a classical thermodynamic treatment of the confined system is
developed with the focus on global properties of large systems. A unusual
behavior under isentropic expansion is found and discussed.
