Maxwell demon no-go theorem for multichannel scattering

Recent implementations of Maxwell demons and other devices exhibiting asymmetric response to particles incident from opposite directions have raised conceptual and practical interest. According to quantum-scattering-theory selection rules, demons necessitate, among other conditions, non-local and non-Hermitian potentials. These potentials arise as effective interactions for a single asymptotic channel within a multichannel (large, Hermitian) system. However we find that, regardless of the complexity of the large Hamiltonian, the demon behavior cannot be approached in this way. We discuss the consequences and possible resolutions of the ensuing paradox. We also introduce and examine a parameter to quantify the distance to demon behavior and propose a way to construct devices as close to a demonic behaviour as possible in a quantum-optical setup.