v-Representability on a one-dimensional torus at elevated temperatures
Abstract
We extend a previous result [Sutter et al., J. Phys. A: Math. Theor. 57, 475202 (2024)] to give an explicit form of the set of -representable densities on the one-dimensional torus with any fixed number of particles in contact with a heat bath at finite temperature. The particle interaction has to satisfy some mild assumptions but is kept entirely general otherwise. For densities, we consider the Sobolev space and exploit the convexity of the functionals. This leads to a broader set of potentials than the usual spaces and encompasses distributions. By including temperature and thus considering all excited states in the Gibbs ensemble, G\^ateaux differentiability of the thermal universal functional is guaranteed. This yields -representability and it is demonstrated that the given set of -representable densities is even maximal.
Keywords
Cite
@article{arxiv.2508.07784,
title = {v-Representability on a one-dimensional torus at elevated temperatures},
author = {Sarina M. Sutter and Markus Penz and Michael Ruggenthaler and Robert van Leeuwen and Klaas J. H. Giesbertz},
journal= {arXiv preprint arXiv:2508.07784},
year = {2026}
}