Harnessing higher-dimensional fluctuations in an information engine

Abstract

We study the optimal performance of an information engine consisting of an overdamped Brownian bead confined in a controllable, $d$-dimensional harmonic trap and additionally subjected to gravity. The trap's center is updated dynamically via a feedback protocol designed such that no external work is done by the trap on the bead, while maximizing the extraction of gravitational potential energy and achieving directed motion. We show that performance strikingly improves when thermal fluctuations in directions perpendicular to gravity are harnessed. This improvement arises from feedback cooling of these transverse degrees of freedom, along which all heat is extracted; comparable performance can be achieved even without vertical measurements. This engine design modularizes the functions of harnessing fluctuations and storing free energy, drawing a close analogy to the Szilard engine.

Figures (4)

• Figure 1: Schematic for $d\!=\!2$: a Brownian bead (blue dot) at position $\boldsymbol{r} = (x,z)$ experiences the gravitational force in the $z$-direction and the action of a confining optical trap (red dot and area) centered at $\boldsymbol{\lambda}$.
• Figure 2: Schematic of the zero-work condition and the optimal feedback rule maximizing free-energy storage for $d\!=\!2$. The dashed circle shows possible updated positions $\boldsymbol{\lambda}_{n^++1}$ for the trap center, given $\boldsymbol{r}_{n+1}$ and $\boldsymbol{\lambda}_{n^+}$, for which no work is exerted on the bead. The updated trap center lies at the top of a hypersphere centered at $\boldsymbol{r}_{n+1}$ with radius $|\boldsymbol{r}_{n+1}-\boldsymbol{\lambda}_{n^+}|$.
• Figure 3: Information-engine output power $P_{\text{net}}$ as a function of sampling frequency $f_{\rm s}$, for $d\!=\!2$ (red) and $d\!=\!1$ (black). Solid curves: semi-analytic steady-state calculations [supp_mat IV and saha_maximizing_2021]. Dashed gray lines: analytic results in the low-sampling-frequency limit [supp_mat III] and the high-sampling-frequency limit \ref{['PSB25-new_clean:eq:max-output-power']}. The dotted vertical line indicates $f_{\rm s}=1$. We set $\delta_{\rm g} = 0.8$, the value that approximately maximizes the output power for $d\!=\!1$saha_maximizing_2021.
• Figure 4: Output power (a) and vertical velocity (b) as functions of the scaled gravitational force $\delta_{\rm g}$, in the high-sampling frequency limit, for different dimensions. Solid curves: analytic results \ref{['PSB25-new_clean:eq:max-output-power']} [supp_mat II]. Dashed curves: partial information engine from Eq. \ref{['PSB25-new_clean:eq:power-averaged']}. Dotted lines: asymptotic limit $d-1$ for $\delta_{\rm g} \to \infty$. Inset in (b): log-log plot highlighting the algebraic decay for large $\delta_{\rm g}$, whose analytic form is represented by dotted lines.