  This letter exposes a tight connection between the thermodynamic efficiency
of information processing and predictive inference. A generalized lower bound
on dissipation is derived for partially observable information engines which
are allowed to use temperature differences. It is shown that the retention of
irrelevant information limits efficiency. A data representation strategy is
derived from optimizing a fundamental physical limit to information processing:
minimizing the lower bound on dissipation leads to a data compression method
that maximally retains relevant, predictive, information. In that sense,
predictive inference emerges as the strategy that least precludes energy
efficiency.
