Electronic Maxwell demon in the coherent strong-coupling regime

Abstract

We consider an external feedback control loop implementing the action of a Maxwell demon. Applying control actions that are conditioned on measurement outcomes, the demon may transport electrons against a bias voltage and thereby effectively converts information into electric power. While the underlying model -a feedback-controlled quantum dot that is coupled to two electronic leads -is well explored in the limit of small tunnel couplings, we can address the strong-coupling regime with a fermionic reaction-coordinate mapping. This exact mapping transforms the setup into a serial triple quantum dot coupled to two leads. We find that a continuous projective measurement of the central dot occupation would lead to a complete suppression of electronic transport due to the quantum Zeno effect. In contrast, by using a microscopic detector model we can implement a weak measurement, which allows for closure of the control loop without transport blockade. Then, in the weak-coupling regime, the energy flows associated with the feedback loop are negligible, and dominantly the information gained in the measurement induces a bound for the generated electric power. In the strong coupling limit, the protocol may require more energy for operating the control loop than electric power produced, such that the whole device is no longer information-dominated and can thus not be interpreted as a Maxwell demon.

Operational approach to quantum stochastic thermodynamics

“…One route could be to enlarge the system space by incorporating explicitly the most dominant degrees of freedom of the environment into the dynamics -a strategy which was directly or indirectly proposed in Refs. [146,147,[151][152][153][154][155][156][157]. Preliminary results also show that this is not even necessary if we do not consider real-time feedback control [158].…”

Maxwell’s demon in the quantum-Zeno regime and beyond

“…In principle, one could argue that a negative feedback energy D < E 0 fb could be stored or used by a smart demon for another application. However, a detailed discussion of this issue could become possible when specifying the measurement apparatus [51][52][53].…”

Pushing the limits of the reaction-coordinate mapping

“…On the one hand, they raise hopes of relying on the combination of 'reaction-coordinate mapping' and 'weak-coupling master equations' beyond the strict range of applicability of the latter. Although the mapping had been successfully applied to open-systems strongly coupled to highly structured environments 19,[23][24][25][26][27][28]30,[32][33][34]77 , our findings suggest that non-Markovian noise featuring broader power spectra may also be modelled in the exact same manner. On the other hand, however, weak-coupling master equations should not be trusted beyond their strict range of applicability when calculating boundary heat currents-even if these appear to be thermodynamically consistent, they may be serious overestimations.…”

“…On the other hand, however, weak-coupling master equations should not be trusted beyond their strict range of applicability when calculating boundary heat currents-even if these appear to be thermodynamically consistent, they may be serious overestimations. It is pertinent to keep this it in mind when using the reaction-coordinate mapping to extend quantum thermodynamics into the strong coupling regime, an interesting line which currently attracts an increasing attention 20,[24][25][26]32,33,77 . Put simply, being able to replicate accurately the exact numerical propagation of an open system with the reaction-coordinate technique does not guarantee that the boundary heat (or particle) currents calculated from the corresponding master equation are equally accurate.…”