  Although stellar radii from asteroseismic scaling relations agree at the
percent level with independent estimates for main sequence and most
first-ascent red giant branch stars, the scaling relations over-predict radii
at the tens of percent level for the most luminous stars ($R \gtrsim 30
R_{\odot}$). These evolved stars have significantly superadiabatic envelopes,
and the extent of these regions increase with increasing radius. However,
adiabaticity is assumed in the theoretical derivation of the scaling relations
as well as in corrections to the large frequency separation. Here, we show that
a part of the scaling relation radius inflation may arise from this assumption
of adiabaticity. With a new reduction of Kepler asteroseismic data, we find
that scaling relation radii and Gaia radii agree to within at least $2\%$ for
stars with $R \lesssim 30 R_{\odot}$, when treated under the adiabatic
assumption. The accuracy of scaling relation radii for stars with $50 R_{\odot}
\lesssim R \lesssim 100 R_{\odot}$, however, is not better than $10\%-15\%$
using adiabatic large frequency separation corrections. We find that up to one
third of this disagreement for stars with $R \approx 100 R_{\odot}$ could be
caused by the adiabatic assumption, and that this adiabatic error increases
with radius to reach $10\%$ at the tip of the red giant branch. We demonstrate
that, unlike the solar case, the superadiabatic gradient remains large very
deep in luminous stars. A large fraction of the acoustic cavity is also in the
optically thin atmosphere. The observed discrepancies may therefore reflect the
simplified treatment of convection and atmospheres.
