  Motivated by recent progress on the motive power of information in quantum
thermodynamics, we put forth an operational resource theory of Maxwell's
demons. We show that the resourceful ({\em daemonic}) states can be partitioned
into at most nine irreducible subsets. The sets can be classified by a rank
akin to the Schmidt rank for entanglement theory. Moreover, we show that there
exists a natural monotone, called the wickedness, which quantifies the
multilevel resource content of the states. The present resource theory is shown
to share deep connections with the resource theory of thermodynamics. In
particular, the nine irreducible sets are found to be characterized by well
defined temperatures which, however, are not monotonic in the wickedness. This
result, as we demonstrate, is found to have dramatic consequences for
Landauer's erasure principle. Our analysis therefore settles a longstanding
debate surrounding the identity of Maxwell's demons and the operational
significance of other related fundamental thermodynamic entities.
