] 2 9 A ug 2 00 3 Discrete - time ratchets , the Fokker - Planck equation and Parrondo ’ s paradox
نویسندگان
چکیده
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.
منابع مشابه
] 1 7 Fe b 20 03 Parrondo ’ s games as a discrete
We write the master equation describing the Parrondo’s games as a consistent discretization of the Fokker–Planck equation for an overdamped Brownian particle describing a ratchet. Our expressions, besides giving further insight on the relation between ratchets and Parrondo’s games, allow us to precisely relate the games probabilities and the ratchet potential such that periodic potentials corre...
متن کاملDiscrete-time ratchets, the Fokker-Planck equation and Parrondo’s paradox
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...
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We discuss in detail two recently proposed relations between the Parrondo’s games and the Fokker–Planck equation describing the flashing ratchet as the overdamped motion of a particle in a potential landscape. In both cases it is possible to relate exactly the probabilities of the games to the potential in which the overdamped particle moves. We will discuss under which conditions current-less ...
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