We derive a quantum theory of evaporative cooling for a degenerate Fermi ga
s: with two constituents and show that the optimum cooling trajectory is in
fluenced significantly by the quantum statistics of the particles. The cool
ing efficiency is reduced at low temperatures due to Pauli blocking of avai
lable final states in each binary collision event. We compare the theoretic
al optimum trajectory with experimental data on cooling a quantum degenerat
e cloud of potassium-40, and show that temperatures as low as 0.3 times the
Fermi temperature can now be achieved.