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This study explores a geometric Brownian information engine (GBIE) with feedback control, optimizing work extraction from Brownian particles. Maximum work is achieved when feedback site (xf) is twice the measurement distance (xm), regardless of entropy.

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Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • Information Theory

Background:

  • Brownian motion is fundamental to understanding particle dynamics in confined systems.
  • Information engines leverage gathered information to perform work, a key concept in thermodynamics.
  • Geometric confinement and feedback control introduce complexities in energy and information transfer.

Purpose of the Study:

  • To investigate a geometric Brownian information engine (GBIE) with error-free feedback control.
  • To determine optimal operating conditions for maximizing extractable work from Brownian particles.
  • To analyze the influence of feedback parameters and entropic forces on engine performance and particle dynamics.

Main Methods:

  • Theoretical analysis of a geometric Brownian information engine model.
  • Investigation of particle dynamics under geometric confinement and feedback control.
  • Parameter space exploration to identify conditions for maximum work output and efficacy.

Main Results:

  • Extractable work is maximized when the feedback site (xf) is twice the measurement distance (xm), specifically at xm ≈ 0.6σ.
  • Transverse bias force (G) influences entropic contributions and particle distribution width (σ).
  • Maximum engine efficacy is achieved when confinement lengthscale aligns with feedback direction, showing a crossover from 2 to 11/9.

Conclusions:

  • Optimal work extraction in GBIE depends on specific relationships between measurement and feedback distances.
  • Entropic effects, while reducing achievable work, enhance unidirectional particle passage and average displacement.
  • Engine efficacy is tunable via feedback control and confinement geometry, with implications for information-to-work conversion efficiency.