Allison mixtures: Where random digits obey thermodynamic principles

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 subsequences 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.