Avoid low-temperature edge effects by extrapolating the free-energy grid

Determine whether extrapolating the Helmholtz free-energy grid beyond its current temperature and density boundaries can avoid the low-temperature edge effects that produce poor thermodynamic consistency in the derived pressure, entropy, and energy within the original equation-of-state domain.

Background

The F-derived equation-of-state tables remain thermodynamically inconsistent near their lower and upper temperature boundaries because numerical differentiation of the free energy is unreliable at the table edges. In simulations of cold, low-mass planets, outer layers can enter the low-temperature region and produce spurious radius decreases and luminosity increases, so results below approximately 10^{2.5} K are not currently reliable.

The paper proposes extending the F(rho,T) grid slightly beyond the existing boundaries and then deriving pressure, entropy, and internal energy within the original table domain from the extrapolated free energy. Whether this procedure actually removes the edge effects is left unresolved and identified as future work.