  We study higher derivative corrections to black brane thermodynamics and
their implications for the weak gravity conjecture for $p$-form gauge fields.
In particular we show that higher derivative corrections decrease
tension-to-charge ratios of extremal black branes as implied by the weak
gravity conjecture, if four-derivative couplings follow scattering positivity
bounds. We also demonstrate that entropy corrections in the micro canonical
ensemble are positive under the same assumptions. This extends earlier works in
the Einstein-Maxwell theory to $p$-form gauge fields in general spacetime
dimensions.
