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Underdamped active Brownian heat engine.

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Active Brownian engines convert reservoir energy into work. An effective temperature, crucial for thermodynamic validity and efficiency bounds, exists when forces on the particle are uncorrelated with its position.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Physics

Background:

  • Active Brownian engines utilize energy from self-propelling molecules in non-equilibrium reservoirs.
  • These engines transform reservoir energy into useful work.
  • Thermodynamic consistency, particularly the second law, requires assigning an effective temperature to the reservoir.

Purpose of the Study:

  • To investigate the conditions under which an effective temperature can be defined for active Brownian engines.
  • To determine the implications of effective temperature for engine efficiency bounds.
  • To analyze the role of correlations between bath forces and particle position.

Main Methods:

  • Modeling active Brownian engines using an underdamped Brownian particle in a power-law potential.
  • Analyzing the conditions for the existence of an effective temperature.
  • Examining the relationship between noise autocorrelation, friction kernel, and force-position correlations.

Main Results:

  • An effective temperature exists if the total force on the particle is uncorrelated with its position.
  • This condition is generally met when noise autocorrelation and friction kernel are proportional (fluctuation-dissipation theorem).
  • Even when proportionality is broken, an effective temperature can be defined in specific, fine-tuned parameter regimes, demonstrated with a harmonic potential example.

Conclusions:

  • The thermodynamic validity and efficiency limits of active Brownian engines depend on the existence of an effective temperature.
  • The correlation between bath forces and particle position is key to defining this effective temperature.
  • The study highlights conditions and specific cases where thermodynamic principles can be applied to non-equilibrium systems.