  We present the virial equation of state of low-density nuclear matter
composed of neutrons, protons and alpha particles. The virial equation of state
is model-independent, and therefore sets a benchmark for all nuclear equations
of state at low densities. We calculate the second virial coefficients for
nucleon-nucleon, nucleon-alpha and alpha-alpha interactions directly from the
relevant binding energies and scattering phase shifts. The virial approach
systematically takes into account contributions from bound nuclei and the
resonant continuum, and consequently provides a framework to include
strong-interaction corrections to nuclear statistical equilibrium models. The
virial coefficients are used to make model-independent predictions for a
variety of properties of nuclear matter over a range of densities, temperatures
and compositions. Our results provide constraints on the physics of the
neutrinosphere in supernovae. The resulting alpha particle concentration
differs from all equations of state currently used in supernova simulations.
Finally, the virial equation of state greatly improves our conceptual
understanding of low-density nuclear matter.
