Exact local entropy of a nonequilibrium quantum system

The statistical mechanics of a system of independent fermions or bosons in a nonequilibrium steady state is analyzed using the density operator in the scattering basis. An exact result for the local entropy is obtained, and identities and inequalities corresponding to the first, second, and third laws of thermodynamics are derived. The second law takes the form of a hierarchy of inequalities relating the exact scattering entropy to entropy formulas based on local measurements that implicitly involve incomplete information.