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不对称锯齿势的极小值方向漂移。闪烁布朗棘轮（flashing Brownian ratchet）是一种在两种运行模式间交替切换的过程：其一为一维布朗运动，其二为布朗棘轮，该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博悖论（Parrondo’s paradox）的原型过程：两个公平的随机博弈，在交替进行时反而会转化为获胜博弈。帕隆博博弈相对简洁，其时间与空间维度均为离散形式；而闪烁布朗棘轮则要复杂得多。本文将展示如何通过随机游走近似，对该过程开展数值研究。