A resource theory of Maxwell's demons

TL;DR

This paper develops an operational resource theory for Maxwell's demons, classifies their states into nine irreducible sets, and introduces a monotone called wickedness to quantify their resource content, revealing deep links with thermodynamics.

Contribution

It introduces a novel resource theory for Maxwell's demons, classifies their states into irreducible sets, and connects these to thermodynamic concepts like temperature and wickedness.

Findings

Nine irreducible state sets classified by a Schmidt-like rank.

Existence of a monotone called wickedness to quantify resource content.

Implications for Landauer's erasure principle and thermodynamic debates.

Abstract

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.