<i>v</i> -representability on a one-dimensional torus at elevated temperatures

Abstract We extend a previous result (Sutter et al 2024 J. Phys. A: Math. Theor. 57 475202) to give an explicit form of the set of v -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. Since we find the necessary domain for densities to be the Sobolev space H 1 , this leads to a broader dual space for potentials than the usual L p spaces and encompasses distributions. By including temperature and thus considering all excited states in the Gibbs ensemble, Gâteaux differentiability of the thermal universal functional is achieved. This is equivalent to unique v -representability and we can prove that the given set of v -representable densities is even maximal.