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Metal ions can be separated from one another by complexation with organic ligands–the chelating agent– to form uncharged chelates. Here, the chelating agent must contain hydrophobic groups and behave as a weak acid, losing a proton to bind with the metal. Since most organic ligands used in this process are insoluble or undergo oxidation in the aqueous phase, the chelating agent is initially added to the organic phase and extracted into the aqueous phase. The metal-ligand complex is...
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Machine-learning-derived protocols for information-based work extraction from active particles.

Grzegorz Szamel1

  • 1Colorado State University, Department of Chemistry, Fort Collins, Colorado 80523, USA.

Physical Review. E
|April 18, 2026
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Summary
This summary is machine-generated.

Researchers extracted useful work from active particles by adjusting potential stiffness. Machine learning found novel protocols, exceeding conventional limits by leveraging the system's nonequilibrium nature.

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Area of Science:

  • Statistical mechanics
  • Active matter physics
  • Machine learning applications

Background:

  • Active particles exhibit self-propulsion, deviating from equilibrium thermodynamics.
  • Extracting useful work from nonequilibrium systems is a key challenge.
  • Feedback control and information measurement are crucial for work extraction.

Purpose of the Study:

  • To propose and analyze a novel process for extracting useful work from a single active particle.
  • To investigate the role of potential stiffness adjustments in work extraction.
  • To employ machine learning to discover optimal control protocols for maximizing work output.

Main Methods:

  • Analytical derivation of work extraction using stepwise stiffness changes.
  • Application of a machine learning procedure to find time-dependent stiffness protocols.
  • Analysis of particle dynamics in a harmonic potential with controlled stiffness.

Main Results:

  • Demonstrated analytical feasibility of work extraction via stepwise stiffness changes.
  • Identified machine-learned protocols featuring counterintuitive initial stiffness jumps.
  • Achieved significantly enhanced useful work extraction compared to conventional methods.
  • Observed extracted work exceeding limits predicted by the conventional second law for feedback-controlled processes.

Conclusions:

  • The proposed process effectively extracts useful work from active particles.
  • Machine learning uncovers advanced protocols that optimize work extraction.
  • The enhanced work extraction is attributed to the system's inherent nonequilibrium characteristics.