Modeling the Energy Characteristics of Ratchets by a Game-Theory Approach

Abstract

The hopping diffusion model is often used to describe the motion of Brownian ratchets. On the other hand, hopping diffusion is well modeled by Parrondo’s paradoxical game method. In this paper, this method is used to simulate the energy characteristics of ratchets. It is known that the most efficient ratchet models are those in which the periodic potential profile can block the backflow of particles and fluctuates for half a period. Therefore, we have considered a one-dimensional hopping diffusion model with two nonequivalent nodes in an elementary cell, the hops of a Brownian particle between which were specified by two sets of transition probabilities. These sets of probabilities corresponded to potential profiles of the desired shape, which periodically shifted relative to each other by half a period. The time dependencies of the work done by the particle against the load force (output energy) and the energy transferred to the particle when switching potentials (input energy) of the system were calculated. The ratchet efficiency (the ratio of output energy to input energy) was calculated as a function of the load force at the moments of potential switching. This value ceased to depend on the time when the process became steady. The simulation results showed that the selected sets of transition probabilities ensure high efficiency of the considered ratchets up to 70%. In this case, the dependence of the efficiency on the load force is a nonmonotonic function, the course of which is in good agreement with the known theoretical data.