  Warm dense matter is a highly energetic phase characterized by strong
correlations, thermal effects, and quantum mechanical electrons. Thermal
density functional theory is commonly used in simulations of this challenging
phase, driving the development of temperature-dependent approximations to the
exchange-correlation free energy. Approaches using the adiabatic connection
formula are well known at zero temperature and have been recently leveraged at
non-zero temperatures as well. In this work, a generalized thermal adiabatic
connection (GTAC) formula is proposed, introducing a fictitious temperature
parameter. This allows extraction of the exchange-correlation entropy $S_{xc}$
using simulated interaction strength scaling. This procedure, in turn, provides
an avenue for approximating the exchange-correlation entropy in a way that
preserves consistency with a chosen ground-state approximation. In addition,
analysis of $S_{xc}$ as a function of interaction strength suggests new forms
for approximations and GTAC itself offers a new framework for exploring both
the exact and approximate interplay of temperature, density, and interaction
strength across a wide range of conditions.
