In this talk we want to study one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at elevated temperature. Inclusion of temperature guarantees differentiability of the universal functional by occupying all states and additionally not fully occupying the states in a fermionic system. We use convexity of the universal functional and invertibility of the potential-to-1RDM map to show that the subgradient contains only one element which is equivalent to differentiability.
This allows us to characterise the v-representable 1RDMs in this setting.
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