  We consider a simplified version of a solvable model by Mandal and Jarzynski,
which constructively demonstrates the interplay between work extraction and the
increase of the Shannon entropy of an information reservoir which is in contact
with the physical system. We extend Mandal and Jarzynski's main findings in
several directions: First, we allow sequences of correlated bits rather than
just independent bits. Secondly, at least for the case of binary information,
we show that, in fact, the Shannon entropy is only one measure of complexity of
the information that must increase in order for work to be extracted. The
extracted work can also be upper bounded in terms of the increase in other
quantities that measure complexity, like the predictability of future bits from
past ones. Third, we provide an extension to the case of non-binary information
(i.e., a larger alphabet), and finally, we extend the scope to the case where
the incoming bits (before the interaction) form an individual sequence, rather
than a random one. In this case, the entropy before the interaction can be
replaced by the Lempel-Ziv (LZ) complexity of the incoming sequence, a fact
that gives rise to an entropic meaning of the LZ complexity, not only in
information theory, but also in physics.
