Systems chemistry and Parrondo’s paradox: computational models of thermal cycling

Osipovitch, Daniel C.; Barratt, Carl; Schwartz, Pauline M.

doi:10.1039/b900288j

Cited by 36 publications

(27 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, if (ρ, φ) = (1/3, 1/2) (and ε = 0), our results show that there is a globally asymptotically stable equilibrium with game B eventually played forever. This is contrary to a computational result of Dinís and Parrondo [11], who found the pattern [1,40] in this case (i.e., AB 40 AB 40 AB 40 · · · ). The anomaly is likely attributable to roundoff error; 64-bit arithmetic (C++) is insufficient here.…”

Section: Introductioncontrasting

confidence: 99%

A discrete dynamical system for the greedy strategy at collective Parrondo games

Ethier

2011

Dynamical Systems

View full text Add to dashboard Cite

We consider a collective version of Parrondo's games with probabilities parameterized by 2 (0, 1) in which a fraction 2 (0, 1] of an infinite number of players collectively choose and individually play at each turn the game that yields the maximum average profit at that turn. Dinı´s and Parrondo [L. Dinı´s and J.M.R. Parrondo, Optimal strategies in collective Parrondo games, Europhys. Lett. 63 (2003), pp. 319-325] and Van den Broeck and Cleuren [C. Van den Broeck and B. Cleuren, Parrondo games with strategy, in Noise in Complex Systems and

show abstract

Section: Introductioncontrasting

confidence: 99%

A discrete dynamical system for the greedy strategy at collective Parrondo games

Ethier

2011

Dynamical Systems

View full text Add to dashboard Cite

show abstract

“…The games have also received attention in many other fields [7], ranging from Brownian ratchets [8,9], nonlinear dynamics [10][11][12][13], biology [14,15], chemistry [16], and economics [17]. Different variants of the original Parrondo's games have been developed, including historydependent Parrondo's game [18], Parrondo's game with self-transition [4] and multi-player version of Parrondo's game [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Extended Parrondo's game and Brownian ratchets: Strong and weak Parrondo effect

Szeto

2014

Phys. Rev. E

View full text Add to dashboard Cite

Inspired by the flashing ratchet, Parrondo's game presents an apparently paradoxical situation. Parrondo's game consists of two individual games, game A and game B. Game A is a slightly losing coin-tossing game. Game B has two coins, with an integer parameter M. If the current cumulative capital (in discrete unit) is a multiple of M, an unfavorable coin p(b) is used, otherwise a favorable p(g) coin is used. Paradoxically, a combination of game A and game B could lead to a winning game, which is the Parrondo effect. We extend the original Parrondo's game to include the possibility of M being either M(1) or M(2). Also, we distinguish between strong Parrondo effect, i.e., two losing games combine to form a winning game, and weak Parrondo effect, i.e., two games combine to form a better-performing game. We find that when M(2) is not a multiple of M(1), the combination of B(M(1)) and B(M(2)) has strong and weak Parrondo effect for some subsets in the parameter space (p(b),p(g)), while there is neither strong nor weak effect when M(2) is a multiple of M(1). Furthermore, when M(2) is not a multiple of M(1), a stochastic mixture of game A may cancel the strong and weak Parrondo effect. Following a discretization scheme in the literature of Parrondo's game, we establish a link between our extended Parrondo's game with the analysis of discrete Brownian ratchet. We find a relation between the Parrondo effect of our extended model to the macroscopic bias in a discrete ratchet. The slope of a ratchet potential can be mapped to the fair game condition in the extended model, so that under some conditions, the macroscopic bias in a discrete ratchet can provide a good predictor for the game performance of the extended model. On the other hand, our extended model suggests a design of a ratchet in which the potential is a mixture of two periodic potentials.

show abstract

“…Increasing our understanding of how to control decoherence is one of the motivating factors behind these developments in quantum game theory. It has been shown [77] that Parrondo's original games can be rather elegantly described in terms Onsager rate equations [78,79] -indeed the possibility of Parrondo-like effects in chemical kinetics has been explored in a computational chemistry setting [80]. Parrondo effects have also inspired work in the study of negative mobility phenomena [81], reliability theory [82], noise induced synchronization [83], spatial patterns via switching [84], and in controlling chaos [85,86].…”

Section: Developments In Parrondo's Paradox and Related Phenomenamentioning

confidence: 99%

Asymmetry and Disorder: A Decade of Parrondo's Paradox

Abbott

2010

Fluct. Noise Lett.

View full text Add to dashboard Cite

In 1996, Parrondo's games were first constructed using a simple coin tossing scenario, demonstrating the paradoxical situation where individually losing games combine to win. Parrondo's principle has become paradigmatic for situations where losing strategies or deleterious effects can combine to win. Intriguingly, there are deep connections between the Parrondo effect and a range of physical phenomena, as it turns out that Parrondo's original games are a discrete-time and discrete-space version of a flashing Brownian ratchet. This has been formally established via discretization of the Fokker-Planck equation. Over the past decade, many examples ranging from physics to population genetics have been reported in the literature pointing to the generality of Parrondo's principle. In general terms, the Parrondo effect occurs where there is a nonlinear interaction of random behavior with an asymmetry, and can be mathematically understood in terms of a convex linear combination. Many effects, where randomness plays a constructive role, such as stochastic resonance, volatility pumping, the Brazil nut paradox, etc., can be viewed as being in the class of Parrondian phenomena. We will briefly review the history of Parrondo's paradox, recent developments, and connections to related phenomena.

show abstract

Systems chemistry and Parrondo’s paradox: computational models of thermal cycling

Cited by 36 publications

References 19 publications

A discrete dynamical system for the greedy strategy at collective Parrondo games

A discrete dynamical system for the greedy strategy at collective Parrondo games

Extended Parrondo's game and Brownian ratchets: Strong and weak Parrondo effect

Asymmetry and Disorder: A Decade of Parrondo's Paradox

Contact Info

Product

Resources

About