New Paradoxical Games Based on Brownian Ratchets

Abstract

Two losing games, when alternated in a periodic or random fashion, can produce a winning game. This paradox occurs in a family of stochastic processes: if one combines two or more dynamics where a given quantity decreases, the result can be a dynamic system where this quantity increases. The paradox could be applied to a number of stochastic systems and has drawn the attention of researchers from different areas. In this paper we show how the phenomenon can be used to design Brownian or molecular motors, i.e., thermal engines that operate by rectifying fluctuations. We briefly review the literature on Brownian motors, pointing out that a new thermodynamics of Brownian motors will be fundamental to the understanding of most processes of energy transduction in molecular biology.

Quantum Parrondo's games

“…1 yield a situation where both games A and B are individually losing but the combination of A and B can produce a net positive payoff provided ǫ < 1/168 [24]. With the quantum version of the games the expectation value of the payoff (to O[ǫ]) for a single sequence of AAB can vary between 0.812 + 0.24ǫ and −0.812 + 0.03ǫ.…”

“…Winning and losing probabilities for game A and the history dependent game B from Parrondo, Harmer and Abbott [24].…”

“…In this, game A is the toss of a single biased coin while game B utilises two or more biased coins whose use depends on the game situation. The paradox requires a form of feedback, for example through the dependence on capital [23], through history dependent rules [24], or through spatial neighbour dependence [25]. In this paper game B is a history dependent game utilising four coins B 1 to B 4 as indicated in Fig.…”

“…The effect is named after its discoverer, Juan Parrondo [19,20], and can be mimiced in a physical system of a Brownian ratchet and pawl [21,22] which is apparently driven in one direction by the Brownian motion of surrounding particles. The classical Parrondo game is cast in the form of a gambling game utilising a set of biased coins [22,23,24]. In this, game A is the toss of a single biased coin while game B utilises two or more biased coins whose use depends on the game situation.…”

An optical model for implementing Parrondo’s game and designing stochastic game with long-term memory

“…Parrondo, Harmer and Abbott proposed a history-dependent game paradox [7] as an improvement of Parrondo's game [3]. Later on, the history-dependent game paradox was extended to couple two history-dependent games [8].…”