  We consider open quantum systems consisting of a finite system of independent
fermions with arbitrary Hamiltonian coupled to one or more equilibrium fermion
reservoirs (which need not be in equilibrium with each other). A strong form of
the third law of thermodynamics, $S(T) \rightarrow 0$ as $T\rightarrow 0$, is
proven for fully open quantum systems in thermal equilibrium with their
environment, defined as systems where all states are broadened due to
environmental coupling. For generic open quantum systems, it is shown that
$S(T)\rightarrow g\ln 2$ as $T\rightarrow 0$, where $g$ is the number of
localized states lying exactly at the chemical potential of the reservoir. For
driven open quantum systems in a nonequilibrium steady state, it is shown that
the local entropy $S({\bf x}; T) \rightarrow 0$ as $T({\bf x})\rightarrow 0$,
except for cases of measure zero arising due to localized states, where $T({\bf
x})$ is the temperature measured by a local thermometer.
