  In this paper, we reconsider the single interval R\'enyi entropy of a free
compact scalar on a torus. In this case, the contribution to the entropy could
be decomposed into classical part and quantum part. The classical part includes
the contribution from all the saddle points, while the quantum part is
universal. After considering a different monodromy condition from the one in
the literature, we re-evaluate the classical part of the R\'enyi entropy.
Moreover, we expand the entropy in the low temperature limit and find the
leading thermal correction term which is consistent with the universal behavior
suggested in arXiv:1403.0578 [hep-th]. Furthermore we investigate the large
interval behavior of the entanglement entropy and show that the universal
relation between the entanglement entropy and thermal entropy holds in this
case.
