On-Chip Maxwell’s Demon as an Information-Powered Refrigerator

We present an experimental realization of an autonomous Maxwell’s demon, which extracts microscopic information from a system and reduces its entropy by applying feedback. It is based on two capacitively coupled single-electron devices, both integrated on the same electronic circuit. This setup allows a detailed analysis of the thermodynamics of both the demon and the system as well as their mutual information exchange. The operation of the demon is directly observed as a temperature drop in the system. We also observe a simultaneous temperature rise in the demon arising from the thermodynamic cost of generating the mutual information.

Figure 1

Operation principle. (a) The demon monitors the system (a single-electron transistor) for electrons that tunnel into (panel 1) or out of (panel 3) the island. It then immediately performs a feedback by applying a positive charge to trap (panel 2) or negative charge to repel (panel 4) the electrons. Coulomb blockade ensures that only either one or zero electrons reside in the system island. The electrons are always tunneling against the potential induced by the demon, and therefore the system cools down. (b) Energetics of the system under voltage bias $V$ in the experimental and autonomous realization of the cycle in (a) with another single-electron structure operating as the demon. The conduction electrons of the system follow Fermi distribution, providing electrons that can overcome the energy cost $J-eV/2$, where $J$ is the coupling energy between the system and the demon; however, in doing so, the system cools down by an equal amount. The energy $J$ is dissipated by the demon as it reacts, changing the projected energy cost experienced by the electron tunneling in the system from $-J-eV/2$ to $J-eV/2$. Note that here the system island is drawn without Fermi distribution for simplicity. Also, the described operation could, in principle, be performed nonautonomously by externally measuring the system state and changing the energy of the system as feedback; see, e.g., Ref. [25].

Figure 2

Experimental realization. (a) A scanning electron micrograph of the structure. False color identifies the system island (light blue), its left lead (dark blue), and right lead (dark green), as well as the demon island (orange) and its leads (red). The system temperature deviations from their base value, $\mathrm{\Delta }{T}_L$, $\mathrm{\Delta }{T}_R$, and $\mathrm{\Delta }{T}_d$, are measured at the indicated locations (see Supplemental Material for details of measurement setup [32]). (b) $I$ at $V=120\mu \mathrm{V}$. When $N_g$ is an integer, $I$ is modulated by $n_g$ as in a standard SET. When $N_g\sim 0.5$, $I$ is smaller due to demon interaction. (c) $\mathrm{\Delta }{T}_d$ at $V=120\mu \mathrm{V}$. When $n_g$, $N_g\sim 0.5$, $\mathrm{\Delta }{T}_d$ elevates due to the information flow between the system and the demon. Measured data in (b) and (c) are shown on the left and numerically obtained predictions on the right.

Figure 3

Operation as a Maxwell’s demon and as a one-sided refrigerator. Quantities shown are $I$ (black), $\mathrm{\Delta }{T}_L$ (blue), $\mathrm{\Delta }{T}_R$ (green), $\mathrm{\Delta }{T}_d$ (red), with parameter values $V=20\mu \mathrm{V}$, $T_{0,s}=77\mathrm{mK}$, and $T_{0,d}=55\mathrm{mK}$. (a) Measurement at $N_g=0.5$ (Maxwell’s demon). Both $T_L$ and $T_R$ decrease, indicating overall cooling of the system. This is justified by the mutual information transfer between the system and the demon, which in turn generates heat in the demon, observed as elevated $T_d$. (b) Measurement at $N_g=0$ (SET refrigeration [41, 42]). Either $\mathrm{\Delta }{T}_L$ or $\mathrm{\Delta }{T}_R$ can be negative, however, not simultaneously: overall heat is generated in the system. Measured data (symbols) are shown on the left and numerically obtained predictions (lines) on the right. (c) Energetics at different operation points, indicated as numbers in (a) and (b). At the operation point 1, the demon is interacting with the system as in Fig. 1. At operation points 2–4, the demon is inactive.

Figure 4

Bias dependence. Here, $n_g=0.5$, $N_g=0.5$, and $T_{0,d}=55\mathrm{mK}$. The data points (symbols) are obtained by averaging over 210 repetitions. (a) $\mathrm{\Delta }{T}_L$ (blue squares), $\mathrm{\Delta }{T}_R$ (green circles), and $\mathrm{\Delta }{T}_d$ (red diamonds) with their respective prediction with $T_{0,s}=77\mathrm{mK}$ (dashed lines) and $T_{0,s}=62\mathrm{mK}$ (solid lines). Inset: $I$ in the same measurement. Applying voltage increases the number of electrons passing through the system and in turn the information flow between the system and the demon. This is observed as increased $T_d$. (b) Numerical comparison between ${\dot{Q}}_d/k_B{T}_d$ and ${\dot{I}}_{m,d}$, demonstrating that the two quantities match. (c) Enlarged view of the measured $\mathrm{\Delta }{T}_L$ (blue squares) and $\mathrm{\Delta }{T}_R$ (green circles). Increasing voltage bias further enhances the entropy decrease in the system up to about $\pm 20\mu \mathrm{V}$. The model assumes a perfectly symmetric system and therefore predicts equal $\mathrm{\Delta }{T}_L$ and $\mathrm{\Delta }{T}_R$ with the fit $T_{0,s}=62\mathrm{mK}$ (solid line).