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Discrete-time ratchets, the Fokker-Planck equation and Parrondo's Paradox

AuthorsAmengual, Pau; Allison, Andrew; Toral, Raúl ; Abbott, Derek
KeywordsParrondo's Paradox
Fokker-Planck Equation
Brownian Ratchet
Issue Date8-Aug-2004
PublisherRoyal Society (Great Britain)
CitationProceedings of the Royal Society of London A 460(2048): 2269-2284 (2004)
AbstractParrondo’s games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker–Planck equation, that rigorously establish the connection between Parrondo’s games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo’s games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.
Description16 pages (final publisher version), 17 pages, 5 figures (attached post-print version).-- Published online 5 May 2004.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0308609
Publisher version (URL)http://dx.doi.org/10.1098/rspa.2004.1283
Appears in Collections:(IFISC) Artículos
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