Data from: The flashing Brownian ratchet and Parrondo’s paradox

A Brownian ratchet is a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. A flashing Brownian ratchet is a process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, producing directed motion. These processes have been of interest to physicists and biologists for nearly 25 years. The flashing Brownian ratchet is the process that motivated Parrondo’s paradox, in which two fair games of chance, when alternated, produce a winning game. Parrondo’s games are relatively simple, being discrete in time and space. The flashing Brownian ratchet is rather more complicated. We show how one can study the latter process numerically using a random walk approximation.

布朗棘轮（Brownian ratchet）是一类一维扩散过程，其运动轨迹会向周期性非对称锯齿势的势能极小值处漂移。闪烁布朗棘轮（flashing Brownian ratchet）则是一种在一维布朗运动与布朗棘轮两种状态间交替切换的过程，可产生定向运动。近25年来，这类过程一直受到物理学家与生物学家的广泛关注。闪烁布朗棘轮正是催生帕隆多悖论（Parrondo's paradox）的过程：该悖论指出，将两局公平的随机博弈交替进行，最终可得到一个必胜博弈。帕隆多博弈（Parrondo's games）相对简洁，其在时间与空间维度上均为离散形式。相较之下，闪烁布朗棘轮的机制要复杂得多。本文展示了如何通过随机游走近似（random walk approximation）对该过程开展数值研究。