Minimal Brownian ratchet: an exactly solvable model.


We develop an analytically solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations, we obtain the steady-state probabilities. Generally, the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space, we find the null curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force.

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@article{Lee2003MinimalBR, title={Minimal Brownian ratchet: an exactly solvable model.}, author={Youngki Lee and Andrew Allison and Derek Abbott and Harry Eugene Stanley}, journal={Physical review letters}, year={2003}, volume={91 22}, pages={220601} }