  We introduce a deterministic chaotic system---the Szilard Map---that
encapsulates the measurement, control, and erasure protocol by which Maxwellian
Demons extract work from a heat reservoir. Implementing the Demon's control
function in a dynamical embodiment, our construction symmetrizes Demon and
thermodynamic system, allowing one to explore their functionality and recover
the fundamental trade-off between the thermodynamic costs of dissipation due to
measurement and due to erasure. The map's degree of chaos---captured by the
Kolmogorov-Sinai entropy---is the rate of energy extraction from the heat bath.
Moreover, an engine's statistical complexity quantifies the minimum necessary
system memory for it to function. In this way, dynamical instability in the
control protocol plays an essential and constructive role in intelligent
thermodynamic systems.
