Brownian motion and gambling: from ratchets to paradoxical games

Abstract

Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this paper we review this paradox, from Brownian ratchets to the most recent studies on collective games, providing some intuitive explanations of the unexpected phenomena that we will find along the way.

arXiv comment25 pages, 11 figures

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• Multiplex decomposition of non-Markovian dynamics and the hidden layer reconstruction problem
• Genuine Parrondo's paradox in quantum walks with time-dependent coin operators
• Noise, Synchrony and Correlations at the Edge of Chaos
• Transverse rectification of disorder-induced fluctuations in a driven system
• Extended Parrondo's Game and Brownian Ratchets: Strong and Weak Parrondo Effect
• Cold atom realizations of Brownian motors
• Quantum Parrondo's game with random strategies
• Order from chaos in quantum walks on cyclic graphs
• Collective decision making and paradoxical games
• Reversals of chance in paradoxical games
• Winning in Sequential Parrondo Games by Players with Short-Term Memory
• Some limit laws for quantum walks with applications to a version of the Parrondo paradox
• Physics at the FQMT'04 conference
• Higher-order evolutionary dynamics with game transitions
• Parrondo's paradox in quantum walks with inhomogeneous coins
• A Markovian slot machine and Parrondo's paradox
• Parrondo's effects with aperiodic protocols
• Parrondo games as disordered systems
• Selective altruism in collective games
• Local detailed balance for active particle models
• Price of information in games of chance: a statistical physics approach
• A Rayleigh criterion for mechanical instability: inducing activity by chemo-mechanical coupling
• Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware