  We study a chain of four interacting rotors (rotators) connected at both ends
to stochastic heat baths at different temperatures. We show that for
non-degenerate interaction potentials the system relaxes, at a stretched
exponential rate, to a non-equilibrium steady state (NESS). Rotors with high
energy tend to decouple from their neighbors due to fast oscillation of the
forces. Because of this, the energy of the central two rotors, which interact
with the heat baths only through the external rotors, can take a very long time
to dissipate. By appropriately averaging the oscillatory forces, we estimate
the dissipation rate and construct a Lyapunov function. Compared to the chain
of length three (considered previously by C. Poquet and the current authors),
the new difficulty with four rotors is the appearance of resonances when both
central rotors are fast. We deal with these resonances using the rapid
thermalization of the two external rotors.
