Entanglement and relative entropy of a chiral fermion on the torus

We derive the entanglement entropy of chiral fermions on the circle at arbitrary temperature. The spin-sector contribution depends only on the total length of the entangling region, regardless of the configuration of the intervals. Thus mutual information is independent of the spin boundary conditions, a property that does not hold for higher R\'enyi mutual information. Together with the modular Hamiltonian, this provides a systematic way of obtaining relative entropy on the torus