Chemistry, Physics and Technology of Surface

ISSN 2518-1238 (Online), ISSN 2079-1704 (Print)

In spite of the widespread opinion about the negative effect of chaos on the nature and human life, there exist examples of its constructive role in various processes. Among them, a prominent position is occupied by the processes in which thermal noise causes not only Brownian motion but also drift of nanoparticles as a result of unbiased non-equilibrium perturbations of various nature in systems with broken spatial and/or temporal symmetry. Such processes are relevant to the operation of Brownian motors, or ratchets, actively studied in the past decades. In the present paper, the working principles of systems of this kind are explained based on the author’s approach which unifies the treatment of different ratchet effect manifestations in the models of fluctuating potential, catalytic wheel, and electroconformational coupling. Another manifestation of this effect is provided by the paradoxical games proposed by Parrondo in which chaos appears in random tosses of a die and the ratchet effect arises from a certain alternation of game strategies ensuring an average win. The paper presents the simplest version of Parrondo’s game; it consists in the alternation of two antisymmetric games, with the rules depending on the parity of the capital possessed by the player before the next toss. The dependence of the average win on the number of tosses is calculated by computer simulation and compared with the result of the catalytic wheel model valid in the adiabatic approximation. The theoretical win calculated by this model agrees well with the numerical simulation result for the game concerned. The attractiveness of the treatment of the ratchet effect in terms of game theory stems from the possibility to visualize the theoretical framework and to study the laws of Brownian motor operation by simple modelling methods.

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