  Inspired by the available examples of Microcanonical Szil\'ard Engines and by
the original Szil\'ard Engine, we devise a system with two degrees of freedom
whose ensemble average energy, starting with a microcanical ensemble, decreases
after a cyclic variation of its external parameters. We use the Ergodic
Adiabatic Theorem to motivate our cycle and numerical simulations to check the
decrement in the average energy. We then compare our system to the
aforementioned Szil\'ard Engines, Microcanonical or not, and speculate about
symmetry breaking being the cause of energy extraction in cyclic processes,
even when non-integrability and chaos are present.
