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

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.

14 pages (main), 23 pages (total), 17 figures

References in corpus (24)

• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Sedimentation, trapping, and rectification of dilute bacteria
• Effective Interactions in Active Brownian Suspensions
• Self-Starting Micromotors in a Bacterial Bath
• Rectification of Swimming Bacteria and Self Driven Particle Systems by Arrays of Asymmetric Barriers
• Multidimensional Stationary Probability Distribution for Interacting Active Particles
• Directed transport of active particles over asymmetric energy barriers
• Run-and-Tumble Dynamics of Self-Propelled Particles in Confinement
• Activated escape of a self-propelled particle from a metastable state
• First-passage time of run-and-tumble particles
• Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap
• Non-crossing run-and-tumble particles on a line
• Analytic Solution of an Active Brownian Particle in a Harmonic Well
• The entropy production of an active particle in a box
• First passage in the presence of stochastic resetting and a potential barrier
• Transport of underdamped active particles in ratchet potentials
• Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries
• Positing the problem of stationary distributions of active particles as third-order differential equation
• Encounter-based model of a run-and-tumble particle
• Rectification in a mixture of active and passive particles subject to a ratchet potential
• Pushing run-and-tumble particles through a rugged channel
• Reentrant condensation transition in a model of driven scalar active matter with diffusivity edge
• Diffusion Properties of a Brownian Ratchet with Coulomb Friction

Cited by in corpus (7)

• Statistical mechanics of passive Brownian particles in a fluctuating harmonic trap
• Anomalous random flights and time-fractional run-and-tumble equations
• Ratchet-mediated resetting: Current, efficiency, and exact solution
• Run-and-tumble particles in slit geometry as a splitting probability problem
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory
• Local entropy production rate of run-and-tumble particles
• Inverse Clausius Thermodynamics in Run-and-Tumble Dynamics