Human-Scale Brownian Ratchet: A Historical Thought Experiment

We present an experimental realization at macroscopic scale of the storied Brownian ratchet, which is an illustration of the Maxwell’s demon. In our mechanism, the rotation of a centimeter-scale 1D Brownian object in a granular gas is detected by an electromechanical converter (dynamo), generating a voltage proportional to its angular velocity. The current generated by this random rotation is rectified by an electronic device (demon), such that only positive current passes. Eventually, work can be produced. The advantage of such a macroscopic setup is to allow measurement of all the observables with time: useful power (work), heat taken from the bath, and finally the efficiency of the equivalent heat engine. The feedback allowing the conversion from heat into work expresses as a bias on the Brownian motion.

Figure 1

Sketch of the experimental system. The beads are vibrated vertically in a vessel by an electromagnetic shaker. A blade is immersed in the grains, fastened on the shaft of a small dc motor.

Figure 2

Electrical circuit associated with the probe. The motor $\mathcal{M}$ is represented in a dashed rectangle by an ideal voltage source $e$ and its internal resistance $r$. The demon $\mathcal{D}$ is composed of a comparator, at the terminals of the motor, triggering a switch that allows the current to pass or not in the load resistance $R$, depending on the polarity of $u_1$.

Figure 3

1 h time samples of angular trajectories of the rotor, with the demon active (red) or inactive (blue).

Figure 4

Variance of the angular increments ${\delta }_{\tau }\theta$ over the time-lag $\tau$ with demon (red line with symbols) or without (blue line). As an eye guide, doted lines of slopes 1 and 2 are drawn. The inset shows $(1/\tau )(⟨{\delta }_{\tau }{\theta }^2⟩-⟨{\delta }_{\tau }\theta {⟩}^2)$ against $\tau$. Vertical dashed lines figure the velocity correlation time, ${\tau }^{*}\simeq 18\mathrm{ms}$.

Figure 5

Histograms of the rotor’s speed. A very slight depletion can be seen on the right wing, when the demon is active (red), in comparison to the case where the demon is off (blue).

Figure 6

Normalized histograms of the heat and work per time unit, $\dot{q}$ (orange doted line) and $\dot{w}$ (green line). Averaged heat and work per time unit are $⟨\dot{q}⟩=⟨ei⟩\simeq 6.6\mu \mathrm{W}$ and $⟨\dot{w}⟩=R⟨i^2⟩\simeq 4.2\mu \mathrm{W}$.