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

TL;DR

This paper provides an exact analytical study of run-and-tumble particles in a ratchet potential, revealing optimal conditions for current, power, and efficiency, and deriving first-passage properties to aid active engine design.

Contribution

It offers the first exact solutions for steady-state, power, efficiency, and first-passage metrics of active particles in a ratchet, linking active matter physics with engine applications.

Findings

Positive current peaks at finite diffusion, ratchet height, and propulsion speed.

Power and efficiency exhibit nonmonotonic dependence on parameters.

Near-perfect efficiency power extraction is possible in certain regimes.

Abstract

We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and thermodynamic efficiency. The ratchet's broken spatial symmetry rectifies the particles' self-propelled motion, resulting in a positive current that peaks at finite values of the diffusion strength, ratchet height, and particle self-propulsion speed. Similar nonmonotonic behaviour is also observed for the extractable power and efficiency. We find the optimal apex position for generating maximum current varies with diffusion, and that entropy production can have nonmonotonic dependence on diffusion. In particular, for vanishing diffusion, entropy production remains finite when particle self-propulsion is weaker than the ratchet force. Furthermore, power extraction with near-perfect efficiency is achievable in certain parameter regimes due to the simplifications afforded by modelling "dry" active particles. In the final part, we derive mean first-passage times and splitting probabilities for different boundary and initial conditions. This work connects the study of work extraction from active matter with exactly solvable active particle models and will therefore facilitate the design of active engines through these analytic results.