  We present an updated and improved equation of state (which we call the NDL
EoS) for use in neutron-star structure and supernova simulations. This EoS is
based upon a framework originally developed by Bowers & Wilson, but there are
numerous changes. Among them are: (1) a reformulation in the context of density
functional theory; (2) the possibility of the formation of material with a net
proton excess (Ye > 0.5); (3) an improved treatment of the nuclear statistical
equilibrium and the transition to heavy nuclei as the density approaches
nuclear matter density; (4) an improved treatment of the effects of pions in
the regime above nuclear matter density including the incorporation of all the
known mesonic and baryonic states at high temperature; (5) the effects of
3-body nuclear forces at high densities; and (6) the possibility of a
first-order or crossover transition to a QCD chiral symmetry restoration and
deconfinement phase at densities above nuclear matter density. This paper
details the physics of, and constraints on, this new EoS and describes its
implementation in numerical simulations. We show comparisons of this EoS with
other equations of state commonly used in supernova collapse simulations.
