At zero temperature, the Pauli potential—the functional derivative of the Pauli kinetic energy density functional—is the key to the accuracy of the orbital-free density functional theory (OF-DFT) as it is supposed to capture all the effects associated with the Pauli exclusion principle. Here, we extend this concept to finite temperature by defining Pauli free energy and the modified Pauli free energy, both representing the natural generalizations of the Pauli term from zero-$T$ to finite-$T$. We discuss their physical interpretation, the mathematical nuances, and the applicability, arguing that the modified Pauli potential should be used as an extension of the zero-$T$ counterpart within the OF-DFT framework. Through analytical and numerical methods, we then analyze some of the exact properties concerning the modified Pauli free- and kinetic-energy terms and examine the temperature dependence of the modified Pauli potential.

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• Electronic structure
• Fermions
• Warm-dense matter
• Density functional theory