  We consider a system model of a general finite-state machine (ratchet) that
simultaneously interacts with three kinds of reservoirs: a heat reservoir, a
work reservoir, and an information reservoir, the latter being taken to be a
running digital tape whose symbols interact sequentially with the machine. As
has been shown in earlier work, this finite-state machine can act as a demon
(with memory), which creates a net flow of energy from the heat reservoir into
the work reservoir (thus extracting useful work) at the price of increasing the
entropy of the information reservoir. Under very few assumptions, we propose a
simple derivation of a family of inequalities that relate the work extraction
with the entropy production. These inequalities can be seen as either upper
bounds on the extractable work or as lower bounds on the entropy production,
depending on the point of view. Many of these bounds are relatively easy to
calculate and they are tight in the sense that equality can be approached
arbitrarily closely. In their basic forms, these inequalities are applicable to
any finite number of cycles (and not only asymptotically), and for a general
input information sequence (possibly correlated), which is not necessarily
assumed even stationary. Several known results are obtained as special cases.
