  We evaluate the Wald Noether charge entropy for a black hole in generalized
theories of gravity. Expanding the Lagrangian to second order in gravitational
perturbations, we show that contributions to the entropy density originate only
from the coefficients of two-derivative terms. The same considerations are
extended to include matter fields and to show that arbitrary powers of matter
fields and their symmetrized covariant derivatives cannot contribute to the
entropy density. We also explain how to use the linearized gravitational field
equation rather than quadratic actions to obtain the same results. Several
explicit examples are presented that allow us to clarify subtle points in the
derivation and application of our method.
