  The local entropy of a nonequilibrium system of independent fermions is
investigated, and analyzed in the context of the laws of thermodynamics. It is
shown that the local temperature and chemical potential can only be expressed
in terms of derivatives of the local entropy for linear deviations from local
equilibrium. The first law of thermodynamics is shown to lead to an inequality,
not an equality, for the change in the local entropy as the nonequilibrium
state of the system is changed. The maximum entropy principle (second law of
thermodynamics) is proven: a nonequilibrium distribution has a local entropy
less than or equal to a local equilibrium distribution satisfying the same
constraints. It is shown that the local entropy of the system tends to zero
when the local temperature tends to zero, consistent with the third law of
thermodynamics.
