  We study polar coding for stochastic processes with memory. For example, a
process may be defined by the joint distribution of the input and output of a
channel. The memory may be present in the channel, the input, or both. We show
that $\psi$-mixing processes polarize under the standard Ar\i{}kan transform,
under a mild condition. We further show that the rate of polarization of the
\emph{low-entropy} synthetic channels is roughly $O(2^{-\sqrt{N}})$, where $N$
is the blocklength. That is, essentially the same rate as in the memoryless
case.
