Adiabatic connections for exact and approximate thermal density functional theory

Adiabatic connection approaches have a long history in ground-state density functional theory, and their use within the finite-temperature formalism provides similar insights about both exact and approximate exchange-correlation functionals. In particular, geometric and analytical interpretation of these expressions can provide new strategies around the added complications of exchange-correlation entropy and orderings of limits. In this talk, I will introduce the generalized thermal adiabatic connection (GTAC) approach and my group's work on establishing a finite-temperature strictly correlated electron (FT SCE) formalism. In addition, I will discuss how these two perspectives can be used for developing thermal density functional theory, whether as separate approaches or when paired for generating new approximations.