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We explore the properties of run-and-tumble particles moving in apiecewise-linear "ratchet" potential by deriving analytic results for thesystem's steady-state probability density, current, entropy production rate,extractable power, and thermodynamic efficiency. The ratchet's broken spatialsymmetry rectifies the particles' self-propelled motion, resulting in apositive current that peaks at finite values of the diffusion strength, ratchetheight, and particle self-propulsion speed. Similar nonmonotonic behaviour isalso observed for the extractable power and efficiency. We find the optimalapex position for generating maximum current varies with diffusion, and thatentropy production can have nonmonotonic dependence on diffusion. Inparticular, for vanishing diffusion, entropy production remains finite whenparticle self-propulsion is weaker than the ratchet force. Furthermore, powerextraction with near-perfect efficiency is achievable in certain parameterregimes due to the simplifications afforded by modelling "dry" activeparticles. In the final part, we derive mean first-passage times and splittingprobabilities for different boundary and initial conditions. This work connectsthe study of work extraction from active matter with exactly solvable activeparticle models and will therefore facilitate the design of active enginesthrough these analytic results.

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