Run-and-tumble motion in a linear ratchet potential: Analytic solution, power extraction, and first-passage...

Area of Science:

• Statistical Mechanics
• Active Matter Physics
• Non-equilibrium Thermodynamics

Background:

• Run-and-tumble particles are a key model for active matter.
• Ratchet potentials break symmetry to rectify particle motion.
• Understanding energy transduction in active systems is crucial.

Purpose of the Study:

• To derive analytic results for active particles in a piecewise-linear ratchet potential.
• To investigate steady-state properties like probability density, current, and entropy production.
• To explore extractable power and thermodynamic efficiency for potential active engines.

Main Methods:

• Derivation of analytic solutions for system properties.
• Analysis of steady-state probability density and particle current.
• Calculation of entropy production, extractable power, and efficiency.

Main Results:

• Ratchet potential induces directed motion (current) that peaks with specific parameters.
• Extractable power and efficiency exhibit nonmonotonic dependence on system parameters.
• Entropy production can remain finite even at vanishing diffusion.
• Near-perfect efficiency is achievable for dry active particles in certain regimes.

Conclusions:

• This work provides exact solutions for active particle behavior in ratchet potentials.
• The findings facilitate the design of active engines by connecting theory with potential applications.
• Analytic results offer a foundation for understanding work extraction from active matter.