  We discuss, in the context of energy flow in high-dimensional systems and
Kolmogorov-Arnol'd-Moser (KAM) theory, the behavior of a chain of rotators
(rotors) which is purely Hamiltonian, apart from dissipation at just one end.
We derive bounds on the dissipation rate which become arbitrarily small in
certain physical regimes, and we present numerical evidence that these bounds
are sharp. We relate this to the decoupling of non-resonant terms as is known
in KAM problems.
