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The entropy-temperature curves are calculated for non-interacting fermions ina 3D optical lattice. These curves facilitate understanding of how adiabaticchanges in the lattice depth affect the temperature, and we demonstrate regimeswhere the atomic sample can be significantly heated or cooled. When the Fermienergy of the system is near the location of a band gap the cooling regimesdisappear for all temperatures and the system can only be heated by latticeloading. For samples with greater than one fermion per site we find thatlattice loading can lead to a large increase in the degeneracy of the system.We study the scaling properties of the system in the degenerate regimes andassess the effects of non-adiabatic loading.Comment: 6 pages, 4 figure

Adiabatic cooling of fermions in an optical lattice