We construct a new class of phenomenological equations of state for homogeneous matter for use in simulations of hot and dense matter in local thermodynamic equilibrium. We construct a functional form which respects experimental, observational and theoretical constraints on the nature of matter in various density and temperature regimes. Our equation of state matches (i) the virial coefficients expected from nucleon-nucleon scattering phase shifts, (ii) experimental measurements of nuclear masses and charge radii, (iii) observations of neutron star radii, (iv) theory results on the equation of state of neutron matter near the saturation density, and (v) theory results on the evolution of the EOS at finite temperatures near the saturation density. Our analytical model allows one to compute the variation in the thermodynamic quantities based on the uncertainties in the nature of the nucleon-nucleon interaction. Finally, we perform a correction to ensure the equation of state is causal at all densities, temperatures, and electron fractions.
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