Thermal properties of the Rényi entropies of free bosons and fermions

We generalize techniques previously used to compute ground-state properties of one-dimensional noninteracting quantum gases to obtain exact results at finite temperature. We compute the order-n Rényi entropy to all orders in the fugacity in one, two, and three spatial dimensions. In arbitrary spatial dimensions, we provide closed-form expressions for its virial expansion up to next-to-leading order. In all of our results, we find explicit volume scaling in the high-temperature limit