  We examine the properties of the isospin-asymmetry expansion of the nuclear
equation of state from chiral two- and three-body forces. We focus on
extracting the high-order symmetry energy coefficients that consist of both
normal terms (occurring with even powers of the isospin asymmetry) as well as
terms involving the logarithm of the isospin asymmetry that are formally
nonanalytic around the expansion point of isospin-symmetric nuclear matter.
These coefficients are extracted from numerically precise perturbation theory
calculations of the equation of state coupled with a new set of finite
difference formulas that achieve stability by explicitly removing the effects
of higher-order terms in the expansion. We consider contributions to the
symmetry energy coefficients from both two- and three-body interactions. It is
found that the coefficients of the logarithmic terms are generically larger in
magnitude than those of the normal terms from second-order perturbation theory
diagrams, but overall the normal terms give larger contributions to the ground
state energy. The high-order isospin-asymmetry terms are especially relevant at
large densities where they affect the proton fraction in beta-equilibrium
matter.
