  Szilard's now-famous single-molecule engine was only the first of three
constructions he introduced in 1929 to resolve several paradoxes arising from
Maxwell's demon. We analyze Szilard's remaining two demon models. We show that
the second one, though a markedly different implementation employing a
population of distinct molecular species and semi-permeable membranes, is
informationally and thermodynamically equivalent to an ideal gas of the
single-molecule engines. Since it is a gas of noninteracting particles one
concludes, following Boyd and Crutchfield, that (i) it reduces to a chaotic
dynamical system---called the Szilard Map, a composite of three piecewise
linear maps that implement the thermodynamic transformations of measurement,
control, and erasure; (ii) its transitory functioning as an engine that
converts disorganized heat energy to work is governed by the Kolmogorov-Sinai
entropy rate; (iii) the demon's minimum necessary "intelligence" for optimal
functioning is given by the engine's statistical complexity, and (iv) its
functioning saturates thermodynamic bounds and so it is a minimal, optimal
implementation. We show that Szilard's third model is rather different and
addresses the fundamental issue, raised by the first two, of measurement in and
by thermodynamic systems and entropy generation. Taken together, Szilard's
suite of constructions lays out a range of possible realizations of Maxwellian
demons that anticipated by almost two decades Shannon's and Wiener's concept of
information as surprise and cybernetics' notion of functional information.
This, in turn, gives new insight into engineering implementations of novel
nanoscale information engines that leverage microscopic fluctuations and into
the diversity of thermodynamic mechanisms and intrinsic computation harnessed
in physical, molecular, biochemical, and biological systems.
