  An ergodic process $P$ is constructed such that the divergence-rate $D(P ||
P^*)$ is zero, yet $P$ is not equal to its time-reversed process $P^*$. The
process $P$ is constructed as a special realization of the universal coding
found by Xu. This result shows that there exist time-asymmetric processes that
are indistinguishable under time-reversal and that can, in principle, be
generated with zero dissipation.
