On the semiclassical regularity of thermal equilibria

We study the regularity properties of fermionic equilibrium states at finite positive temperature and show that they satisfy certain semiclassical bounds. As a corollary, we identify explicitly a class of positive temperature states satisfying the regularity assumptions of [J.J. Chong, L. Lafleche, C. Saffirio: arXiv:2103.10946 (2021)].