Machine-learning-derived protocols for information-based work extraction from active particles

Abstract

We propose and analyze a process that extracts useful work from a single active particle maintained at constant temperature in a harmonic potential by measuring the relative sign of the self-propulsion and the confining force and then adjusting the stiffness of the potential. First, we show analytically that useful work can be extracted by stepwise changes of the stiffness. Then, we use a machine learning procedure to find time-dependent stiffness change protocols. We find that these protocols involve discontinuous initial changes of the stiffness opposite to the expected direction resembling the jumps analytically found by Garcia-Millan et al. [Phys. Rev. Lett. 135, 088301 (2025)] in a different information-based work extraction process. The learned protocols allow to extract significantly larger amounts of useful work. The work extracted exceeds that allowed by the second law for feedback processes, which can be rationalized by the non-equilibrium character of the system considered.

Figures (4)

• Figure 1: Work extraction. The demon measures the relative sign between the self-propulsion and the confining force. When the self-propulsion (shown as the arrow attached to the particle) is aligned with the confining force, $xf<0$, the potential stiffness is increased. Conversely, when the self-propulsion is anti-aligned with the confining force, $xf>0$, the potential stiffness is decreased. At the end of the extraction process, the stiffness returns to its original value.
• Figure 2: (a) Long-time limit of average useful work, $-\left<W\right>$, extracted by means of stepwise changes of the harmonic potential stiffness, as a function of persistence time, $\tau_p$. (b) Average useful work extracted using learned stiffness protocols for a large but finite process time, $t_f=256$, as a function of persistence time, $\tau_p$. Using learned potential results in a significantly larger extracted work. Initial and final stiffness $k=1$, self-propulsion strength $a=10$, temperature $T=1$ and friction constant $\gamma=1$.
• Figure 3: Time-dependence of learned stiffness protocols for various lengths of the extraction process. Upper panel (a) presents protocols for $xf$ being negative at the initial time and lower panel (b) presents protocols for $xf$ being initially positive. Solid lines: $t_f=4$, dashed lines: $t_f=16$, dot-dashed lines: $t_f=64$. Note discontinuous jumps at the initial and final times. The jumps at $t=0$ are larger than jumps at $t=t_f$ and are in the direction opposite to the one expected, as also found in Ref. GarciaMillan2025. Initial and final stiffness $k=1$, persistence time $\tau_p=0.4$, self-propulsion strength $a=10$, temperature $T=1$ and friction constant $\gamma=1$.
• Figure 4: Average useful work, $-\left<W\right>$, as a function of length of the extraction process, $t_f$. Squares: useful work extracted for $xf$ being negative at the initial time, diamonds: useful work for $xf$ being initially positive, circles: useful work averaged over the two measurement outcomes. Initial and final stiffness $k=1$, persistence time $\tau_p=0.4$, self-propulsion strength $a=10$, temperature $T=1$ and friction constant $\gamma=1$.