  We study the unitary time evolution of a simple quantum Hamiltonian
describing a heat engine coupled to two heat baths. The engine is modeled as a
three-level system. Each heat bath consists of a single harmonic oscillator.
The engine is operated via time-dependent external fields. The S-matrix of the
thermodynamic cycle is obtained in analytic form. We conjecture that the
spectrum of this S-matrix contains a continuous part, and that this is a
requirement for the operation as a heat engine. Energy currents flow in both
directions through the engine. The balance of these currents determines whether
the engine performs work or whether its operation requires the application of
external forces.
