Parrondo's games and the zipping algorithm

TL;DR

This paper explores the connection between Parrondo's games, a type of stochastic process, and a compression-based method for measuring information transfer in thermal ratchets, revealing a qualitative link between gain and entropy.

Contribution

It introduces a novel analysis linking Parrondo's games with a zipping algorithm used for assessing information transfer in thermal ratchets.

Findings

Good qualitative agreement between gain and inverse entropy in Parrondo's games

Different versions of Parrondo's games show consistent results

The study highlights a relationship between stochastic gain and information entropy

Abstract

We study the relation between the discrete--time version of the flashing ratchet known as Parrondo's games and a compression technique used very recently with thermal ratchets for evaluating the transfer of information -- negentropy -- between the Brownian particle and the source of fluctuations. We present some results concerning different versions of Parrondo's games, showing all of them a good qualitative agreement between the gain and the inverse of the entropy.