  We add an ensemble of nuclei to the equation of state for homogeneous
nucleonic matter to generate a new set of models suitable for astrophysical
simulations of core-collapse supernovae and neutron star mergers. We implement
empirical constraints from (i) nuclear mass measurements, (ii) proton-proton
scattering phase shifts, and (iii) neutron star observations. Our model is also
guided by microscopic many-body theory calculations based on realistic nuclear
forces, including the zero-temperature neutron matter equation of state from
quantum Monte Carlo simulations and thermal contributions to the free energy
from finite-temperature many-body perturbation theory. We ensure that the
parameters of our model can be varied while preserving thermodynamic
consistency and the connection to experimental or observational data, thus
providing a probability distribution of the astrophysical hot and dense matter
equation of state. We compare our results with those obtained from other
available equations of state. While our probability distributions indeed
represent a large number of possible equations of state, we cannot yet claim to
have fully explored all of the uncertainties, especially with regard to the
structure of nuclei in the hot and dense medium.
