  We consider a finite chain of non-linear oscillators coupled at its ends to
two infinite heat baths which are at different temperatures. Using our earlier
results about the existence of a stationary state, we show rigorously that for
arbitrary temperature differences and arbitrary couplings, such a system has a
unique stationary state. (This extends our earlier results for small
temperature differences.) In all these cases, any initial state will converge
(at an unknown rate) to the stationary state. We show that this stationary
state continually produces entropy. The rate of entropy production is strictly
negative when the temperatures are unequal and is proportional to the mean
energy flux through the system.
