Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox
arXiv:cond-mat/0308609 · doi:10.1098/rspa.2004.1283
Abstract
Parrondo'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 (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.
17 pages, 5 figures
References in corpus (10)
- Brownian motors: noisy transport far from equilibrium
- New paradoxical games based on Brownian ratchets
- Quantum Parrondo's Games
- Winning combinations of history-dependent games
- Optimal strategies in collective Parrondo games
- Quantum coherence, correlated noise and Parrondo games
- Minimal Brownian Ratchet: An Exactly Solvable Model
- Parrondo's games as a discrete ratchet
- A Fokker--Planck description for Parrondo's games
- On Parrondo's paradox: how to construct unfair games by composing fair games
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- Quantum Zeno effect and nonclassicality in a PT symmetric system of coupled cavities
- Optimal potentials for temperature ratchets
- A q-deformed logistic map and its implications
- Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics
- Extended Parrondo's Game and Brownian Ratchets: Strong and Weak Parrondo Effect
- Winning in Sequential Parrondo Games by Players with Short-Term Memory
- Enhancement of Geometric Phase by Frustration of Decoherence: A Parrondo like Effect
- Exact probability distribution functions for Parrondo's games
- Parrondo-like behavior in continuous-time random walks with memory
- The flashing ratchet and unidirectional transport of matter
- A new generalization of Parrondo's games to three players and its application in genetic switches
- Analytical aspects of the Brownian motor effect in randomly flashing ratchets