  Due to the Unruh effect, accelerated and inertial observers differ in their
description of a given quantum state. The implications of this effect are
explored for the entropy assigned by such observers to localized objects that
may cross the associated Rindler horizon. It is shown that the assigned
entropies differ radically in the limit where the number of internal states $n$
becomes large. In particular, the entropy assigned by the accelerated observer
is a bounded function of $n$. General arguments are given along with explicit
calculations for free fields. The implications for discussions of the
generalized second law and proposed entropy bounds are also discussed.
