Maxwell Demon that Can Work at Macroscopic Scales

Maxwell’s demons work by rectifying thermal fluctuations. They are not expected to function at macroscopic scales where fluctuations become negligible and dynamics become deterministic. We propose an electronic implementation of an autonomous Maxwell’s demon that indeed stops working in the regular macroscopic limit as the dynamics becomes deterministic. However, we find that if the power supplied to the demon is scaled up appropriately, the deterministic limit is avoided and the demon continues to work. The price to pay is a decreasing thermodynamic efficiency. Our Letter suggests that novel strategies may be found in nonequilibrium settings to bring to the macroscale nontrivial effects so far only observed at microscopic scales.

Figure 1

(a) Typical deterministic transfer function for the common implementation of a subthreshold CMOS inverter. (b) An external agent measures the fluctuating output voltage $v$ of a CMOS inverter and adjusts the input voltage as $v_{\mathrm{in}}=-\alpha v$, with $\alpha >0$. The histogram shows the Gaussian fluctuations at equilibrium ($V_1=V_2=0$). (c) A similar feedback protocol is implemented with an additional CMOS inverter.

Figure 2

Average electric current $⟨I_S⟩$ (in units of $q_e/{\tau }_0$) at steady state for the circuit of Fig. 1 as a function of the powering voltage biases $\mathrm{\Delta }{V}_S$ and $\mathrm{\Delta }{V}_D$ ($v_e=0.1$, $n=1$). The solid gray line marks the boundary between the $⟨I_S⟩<0$ (blue) and $⟨I_S⟩>0$ (red) regions, and the dashed line corresponds to the approximate analytical result of Eq. (9).

Figure 3

Efficiency as a function of the scale parameter $v_e^{-1}$ with the scaling strategy $\mathrm{\Delta }{V}_S=c{v}_e$ and $\mathrm{\Delta }{V}_D=2\log (1+2{\alpha }^2/c{v}_e)$ for $c=0.1$ and different values of ${\alpha }^2$. The results are obtained using the Gillespie algorithm. The dashed black line shows the scaling obtained from Eqs. (11) and (12).