Allison mixtures: Where random digits obey thermodynamic principles

摘要

Parrondo's paradox is a well-known situation where losing strategies can be combined to win, and is based on a thermodynamic Brownian ratchet principle. We demonstrate a new extension of Parrondo's paradox called the Allison mixture where it is possible to paradoxically generate random sequences with nonzero autocovariance, out of sub-sequences of zero autocovariance. We explain the effect with a ratchet analogy and show the behavior of random digits follows a thermodynamic analogy. As Kish-based cipher techniques rely on the Second Law for their security, this raises the tantalizing open question of whether the Allison mixture can be exploited for new Kish-inspired digital security schemes.