  We calculate the equation of state of asymmetric nuclear matter at finite
temperature based on chiral effective field theory interactions to
next-to-next-to-next-to-leading order. Our results assess the theoretical
uncertainties from the many-body calculation and the chiral expansion. Using a
Gaussian process emulator for the free energy, we derive the thermodynamic
properties of matter through consistent derivatives and use the Gaussian
process to access arbitrary proton fraction and temperature. This enables a
first nonparametric calculation of the equation of state in beta equilibrium,
and of the speed of sound and the symmetry energy at finite temperature.
Moreover, our results show that the thermal part of the pressure decreases with
increasing densities.
