  We discuss the cooling efficiency of ultracold Fermi-Bose mixtures in
species-selective traps using a thermodynamical approach. The dynamics of
evaporative cooling trajectories is analyzed in the specific case of
bichromatic optical dipole traps also taking into account the effect of partial
spatial overlap between the Fermi gas and the thermal component of the Bose
gas. We show that large trapping frequency ratios between the Fermi and the
Bose species allow for the achievement of a deeper Fermi degeneracy,
consolidating in a thermodynamic setting earlier arguments based on more
restrictive assumptions. In particular, we confirm that the minimum temperature
of the mixture is obtained at the crossover between boson and fermion heat
capacities, and that below such a temperature sympathetic cooling vanishes.
When the effect of partial overlap is taken into account, optimal sympathetic
cooing of the Fermi species may be achieved by properly tuning the relative
trapping strength of the two species in a time-dependent fashion.
Alternatively, the dimensionality of the trap in the final stage of cooling can
be changed by increasing the confinement strength, which also results in a
crossover of the heat capacities at deeper Fermi degeneracies. This technique
may be extended to Fermi-Bose degenerate mixtures in optical lattices.
