  The total derivatives in the gravitational action are usually disregarded as
non-producing any non-trivial dynamics. In the context of the gravitational
entropy, within Wald's approach, these terms are considered irrelevant as
non-contributing to the entropy. On the other hand, the total derivatives are
usually present in the trace anomaly in dimensions higher than 2. As the trace
anomaly is related to the logarithmic term in the entanglement entropy it is
natural to ask whether the total derivatives make any essential contribution to
the entropy or they can be totally ignored. In this note we analyze this
question for some particular examples of total derivatives. Rather
surprisingly, in all cases that we consider the total derivatives produce
non-trivial contributions to the entropy. Some of them are non-vanishing even
if the extrinsic curvature of the surface is zero. We suggest that this may
explain the earlier observed discrepancy between the holographic entanglement
entropy and Wald's entropy.
