  We theoretically investigate the thermodynamics of an interacting
inhomogeneous two-component Fermi gas in an optical lattice. Motivated by a
recent experiment by L. Hackerm\"uller et al., Science, 327, 1621 (2010), we
study the effect of the interplay between thermodynamics and strong
correlations on the size of the fermionic cloud. We use dynamical mean-field
theory to compute the cloud size, which in the experiment shows an anomalous
expansion behavior upon increasing attractive interaction. We confirm this
qualitative effect but, assuming adiabaticity, we find quantitative agreement
only for weak interactions. For strong interactions we observe significant
non-equilibrium effects which we attribute to a dynamical arrest of the
particles due to increasing correlations.
