The Hungry Daemon: An energy-harvesting active particle must obey the Second Law of Thermodynamics

Thought experiments like Maxwell's Demon or the Feynman-Smoluchowski Ratchet can help in pursuing the microscopic origin of the Second Law of Thermodynamics. Here we present a more sophisticated physical system than a ratchet, consisting of a Hamiltonian active particle which can harvest energy from an environment which may be in thermal equilibrium at a single temperature. We show that while a phenomenological description would seem to allow the system to operate as a Perpetual Motion Machine of the Second Kind, a full mechanical analysis confirms that this is impossible, and that perpetual energy harvesting can only occur if the environment has an energetic population inversion similar to a lasing medium.