  We use guiding principles from nonequilibrium thermodynamics to develop an
admissible set of 13 moment equations for rarefied gas flows. The main benefits
of our thermodynamic approach are an explicit entropy expression fulfilling an
$H$ theorem and a sound Hamiltonian formulation of the reversible free flight
transport. To calculate the entropy and to find explicit closure
approximations, we propose a simple set of approximate 13 parameter solutions
to Boltzmann's kinetic equation. We discuss how standard hydrodynamics is
recovered as a limiting case.
