Observations of isolated neutron stars place constraints on the equation of state ( EOS ) of cold , neutron-rich matter , while nuclear physics experiments probe the EOS of hot , symmetric matter .
Many dynamical phenomena , such as core-collapse supernovae , the formation and cooling of proto-neutron stars , and neutron star mergers , lie between these two regimes and depend on the EOS at finite temperatures for matter with varying proton fractions .
In this paper , we introduce a new framework to accurately calculate the thermal pressure of neutron-proton-electron matter at arbitrary density , temperature , and proton fraction .
This framework can be expressed using a set of five physically-motivated parameters that span a narrow range of values for realistic EOS and are able to capture the leading-order effects of degenerate matter on the thermal pressure .
We base two of these parameters on a new approximation of the Dirac effective mass , with which we reproduce the thermal pressure to within \lesssim 30 \% for a variety of realistic EOS at densities of interest .
Three additional parameters , based on the behavior of the symmetry energy near the nuclear saturation density , allow for the extrapolation of any cold EOS in \beta -equilibrium to arbitrary proton fractions .
Our model thus allows a user to extend any cold nucleonic EOS , including piecewise-polytropes , to arbitrary temperature and proton fraction , for use in calculations and numerical simulations of astrophysical phenomena .
We find that our formalism is able to reproduce realistic finite-temperature EOS with errors of \lesssim 20 \% and offers a 1 - 3 orders-of-magnitude improvement over existing ideal-fluid models .