  The purpose of this paper is to point out a new connection between
information theory and dynamical systems. In the information theory side, we
consider rate distortion theory, which studies lossy data compression of
stochastic processes under distortion constraints. In the dynamical systems
side, we consider mean dimension theory, which studies how many parameters per
second we need to describe a dynamical system. The main results are new
variational principles connecting rate distortion function to metric mean
dimension.
