Approximate adiabatic connection from the exchange-correlation entropy for the uniform electron gas

Warm dense matter is a highly energetic state found in planetary cores and generated on the path to fusion during inertial confinement fusion experiments. Thermal density functional theory is a tool commonly used to investigate this complicated regime. The generalized thermal adiabatic connection can be used to gain insights into the temperature dependence of the exchange-correlation free energy. This work discusses the results from using the generalized thermal adiabatic connection to extract the exchange-correlation entropy and obtain approximate finite-temperature adiabatic connection curves for the uniform electron gas. The resulting approximate curves for warm dense regimes and comparisons with the finite temperature adiabatic connection will be presented, as well as new ideas for geometric interpretation.