Skye: A Differentiable Equation of State
  Stellar evolution and numerical hydrodynamics simulations depend critically
on access to fast, accurate, thermodynamically consistent equations of state.
We present Skye, a new equation of state for fully-ionized matter. Skye
includes the effects of positrons, relativity, electron degeneracy, Coulomb
interactions, non-linear mixing effects, and quantum corrections. Skye
determines the point of Coulomb crystallization in a self-consistent manner,
accounting for mixing and composition effects automatically. A defining feature
of this equation of state is that it uses analytic free energy terms and
provides thermodynamic quantities using automatic differentiation machinery.
Because of this, Skye is easily extended to include new effects by simply
writing new terms in the free energy. We also introduce a novel thermodynamic
extrapolation scheme for extending analytic fits to the free energy beyond the
range of the fitting data while preserving desirable properties like positive
entropy and sound speed. We demonstrate Skye in action in the MESA stellar
evolution software instrument by computing white dwarf cooling curves.
