Motility and energetics of randomly flashing ratchets

We consider randomly flashing ratchets, where the potential acting can be switched to another at random time instants with Poisson statistics. Using coupled Fokker-Planck equations, we formulate explicit expressions of mean velocity, dispersion and quantities measuring thermodynamics. How potential landscapes and transitions affect the motility and energetics is exemplified by numerical calculations on random on-off ratchets. Randomly flashing ratchets with shifted sawtooth potentials are further discussed. We find that the dynamics and output power of such system present symmetry w.r.t. the shift between the two potentials Delta(max) + Delta(min), which is the sum of the shift between the two peaks (Delta(max)) and the shift between the two bottoms (Delta(min)). The mean velocity and output power both reach the optimal performance at Delta(max) + Delta(min) = 1, provided that the asymmetry alpha(i) of potential U-i implies a positive flux respectively, i.e., alpha(i) > 0.5 for i = 1, 2.

Automated summary

Through numerical calculations, we found that the dynamics and output power of randomly flashing ratchets exhibit symmetry with respect to the shift between the two potentials Delta(max) + Delta(min), where Delta(max) and Delta(min) are the shifts between the two peaks and two bottoms respectively. The mean velocity and output power reach optimal performance when Delta(max) + Delta(min) = 1.