Autonomous out-of-equilibrium Maxwell's demon for controlling the energy fluxes produced by thermal fluctuations

Abstract

An autonomous out of equilibrium Maxwell's demon is used to reverse the natural direction of the heat flux between two electric circuits kept at different temperatures and coupled by the electric thermal noise. The demon does not process any information, but it achieves its goal by using a frequency dependent coupling with the two reservoirs of the system. There is no energy flux between the demon and the system, but the total entropy production (system+demon) is positive. The demon can be power supplied by thermocouples. The system and the demon are ruled by equations similar to those of two coupled Brownian particles and of the Brownian gyrator. Thus our results pave the way to the application of autonomous out equilibrium Maxwell demons to coupled nanosystems at different temperatures.

Characterizing autonomous Maxwell demons

“…Thus, the only way to extract heat from a reservoir at temperature T 2 is to have access to a reservoir at a lower temperature (in this case, T 4 ). Indeed, this is also observed in the examples in [18,19].…”

“…Given a partition separating the degrees of freedom of the system from those of the demon, we can also identify an internal energy current J int between them. In this context, the following conditions were proposed in [18,19] to characterize a "nonequilibrium Maxwell demon":…”

“…Both of them are quantum systems, but this is not essential. The example provided in [19] is classical and consists of a circuit with several noisy resistors that play the role of the thermal reservoirs. However, as we will see, it is not necessary to consider quantum or classical fluctuations to achieve the conditions of the previous section (from where it follows that correlations between currents are also not essential).…”

“…Many model systems [8][9][10][11] as well as experiments [12][13][14][15][16][17] have realized such traditional demons. Recent interesting proposals have shown that similar effects can be achieved in linear systems out of equilibrium [18,19]. In these proposals, a new kind of demon is characterized ("nonequilibrium demons" or "N-demons") that cannot be interpreted in terms of measurements and feedback control, and in which the only resource is the access to a nonequilibrium distribution.…”

“…To emphasize this distinction, we take these proposals to their most essential form by considering thermal circuits in which one has access to the internal currents, in addition to the reservoir currents. From this it follows that, according to the criteria accepted in [18,19], a demon could be constructed using an extremely simple and deterministic thermal circuit. When stricter traditional criteria are used, then those simple setups are ruled out.…”