  We compute the four-derivative corrections to the geometry, extremality
bound, and thermodynamic quantities of AdS-Reissner-Nordstr{\"o}m black holes
for general dimensions and horizon geometries. We confirm the universal
relationship between the extremality shift at fixed charge and the shift of the
microcanonical entropy, and discuss the consequences of this relation for the
Weak Gravity Conjecture in AdS. The thermodynamic corrections are calculated
using two different methods: first by explicitly solving the higher-derivative
equations of motion and second, by evaluating the higher-derivative Euclidean
on-shell action on the leading-order solution. In both cases we find agreement,
up to the addition of a Casimir energy in odd dimensions. We derive the bounds
on the four-derivative Wilson coefficients implied by the conjectured
positivity of the leading corrections to the microcanonical entropy of
thermodynamically stable black holes. These include the requirement that the
coefficient of Riemann-squared is positive, meaning that the positivity of the
entropy shift is related to the condition that $c - a$ is positive in the dual
CFT. We discuss implications for the deviation of $\eta/s$ from its universal
value and a potential lower bound.
