  We analyze an engine whose working fluid consists of a single quantum
particle, paralleling Szilard's construction of a classical single-particle
engine. Following his resolution of Maxwell's Second Law paradox using the
latter, which turned on physically instantiating the demon (control subsystem),
the quantum engine's design mirrors the classically-chaotic Szilard Map that
operates a thermodynamic cycle of measurement, thermal-energy extraction, and
memory reset. Focusing on the thermodynamic costs to observe and control the
particle and comparing these in the quantum and classical limits, we detail the
thermodynamic tradeoffs behind Landauer's Principle for
information-processing-induced thermodynamic dissipation in the quantum and
classical regimes. In particular, and as found with the classical engine, we
show that the sum of the thermodynamic costs over a cycle obeys a generalized
Landauer Principle, exactly balancing energy extraction from the heat bath.
Thus, the quantum engine obeys the Second Law. However, the quantum engine does
so via substantially different mechanisms: classically measurement and erasure
determine the thermodynamics, while in the quantum implementation the cost of
partition insertion is key.
