Information engine fueled by first-passage times

TL;DR

The paper investigates an information engine powered by first-passage-time triggered feedback on an underdamped Brownian cantilever. It introduces protocol-based information measures $I(k)$ and $I_u(k)$ and derives fluctuation theorems that relate work, free energy, and information without relying on measurement outcomes, yielding a bound $\langle -w \rangle \le \langle \Delta I \rangle$ that is saturated in experiments. The authors present a general time-based framework applicable to arbitrary feedback protocols and continuous variables, enabling experimental tests of information-to-work conversion. This work advances the thermodynamics of information by providing a practical, protocol-centric approach to fluctuation relations and tight work bounds.

Abstract

Using a mechanical cantilever submitted to electrostatic feedback control, we investigate the thermodynamic properties of an information engine that extracts work from thermal fluctuations. The cantilever position is rapidly sampled and the feedback is triggered by the first passage of the system across a fixed threshold. The information $ΔI$ associated with the feedback is based on the first-passage-time distribution. In this setting, we derive and experimentally verify two distinct fluctuation theorems that involve $ΔI$ and give a tight bound on the work produced by the engine. Our results extend beyond the specific application to our experiment: we develop a general framework for obtaining fluctuation theorems and work bounds, formulated in terms of probability distributions of protocols rather than underlying measurement outcomes.

Figures (7)

• Figure 1: First-passage protocol. Initially, the demon is locked and the bead equilibrates in the potential $U_A(x)=U(x, -L)=\frac{1}{2}(x+L)^2$ for a time $\tau\gg \tau_r$. The demon is then activated and rapidly samples the bead position $x$. As soon as $x>h$ (which might occur at the first sampling), the potential is switched to $U_B(x)=U(x, +L)=\frac{1}{2}(x-L)^2$, the demon is locked and the protocol is repeated (with a symmetry $x\leftrightarrow-x$ to recover the same initial state).
• Figure 2: Probability distribution function (pdf) of extracted work, $P(-w)$, for $L=0.91$ and $h=0.30$. For each event, the number of readings $k$ performed before the switching is measured. The full pdf consists of a peak near $w_0=2Lh$ from events $k>0$ ($+$) and a tail from events $k=0$ ($\times$), as expected from theory. The finite sampling time $\delta t$ produces the spread around $w_0$ (rather than a Dirac distribution, $\blacktriangle$) shown in the inset, as the trigger does not occur exactly at $x(t_k)=h$.
• Figure 3: (a) Extracted mean work $\langle {-w} \rangle$ as a function of $L$ and $h$: experimental results (open markers, statistical uncertainty smaller than the symbol size), theoretical prediction (solid lines), and mean information upper bound $\langle {\Delta I} \rangle$ (filled markers, computed with Eqs. \ref{['eq:Delta_I1']} and \ref{['eq:Delta_Isup1']}). The bound $\langle {-w} \rangle\le\langle {\Delta I} \rangle$ is verified and nearly saturated in all the measurements: the efficiency $\langle {-w} \rangle/\langle {\Delta I} \rangle$ tends to 1 when $L$ and $h$ are large. In that limit, the demon is rarely triggered at the first measurement, thus $-w=\Delta I=w_0$ for most realizations. (b) Extracted mean power as a function of $L$ and $h$. The maximum power is reached for $L \sim h \sim 1$.
• Figure 4: (a) $\langle {\mathop{\mathrm{e}}\nolimits^{-w-\Delta I}} \rangle$ as a function of $L$ for different values of $h$. As predicted by Eq. \ref{['eq:ashida']}, this average is close to $1$ for all values of $L$ and $h$. (b) $\langle {\mathop{\mathrm{e}}\nolimits^{-w}} \rangle$ for $k=0$ ($\times$), $k>0$ ($+$) and over all $k$ ($\circ$) as a function of $L$, for $h=0.3$. As predicted by Eq. \ref{['eq:newFT']} (for all $k$) and Eq. \ref{['eq:CondAvg_k']} (for any specific $k$) these measured values match $\langle \mathop{\mathrm{e}}\nolimits^{\Delta I} \rangle$ (solid lines). Above $L=1.5$, the number of measured values corresponding to $k=0$ fall below 100, which is insufficient to estimate $\langle {\mathop{\mathrm{e}}\nolimits^{-w}} \rangle$ with good precision. Error bars correspond to the statistical uncertainty (standard deviation over square root of the sample number).
• Figure SM1: Experimental setup. The deflection $x$ of a cantilever is measured using an interferometer. $x$ is then used by the feedback loop to compute a voltage $V_\mathit{FB}(x)$ that generates a force on the cantilever, shifting the central position of the harmonic potential.