An optical model for an analogy of Parrondo game and designing Brownian ratchets

TL;DR

This paper develops an optical model simulating Parrondo's game and Brownian ratchets, revealing their equivalence and exploring how correlations and entanglement influence game outcomes and particle motion.

Contribution

It introduces a physical optical analogy for Parrondo's game and Brownian ratchets, including long-term memory and entanglement, to better understand their dynamics and paradoxical behaviors.

Findings

The two games are essentially the same and not paradoxical.

Correlations can turn losing games into winning or oscillating outcomes.

The optical model helps explain anomalous Brownian particle motion.

Abstract

An optical model of classical photons propagating through array of many beam splitters is developed to give a physical analogy of Parrondo's game and Parrondo-Harmer-Abbott game. We showed both the two games are reasonable game without so-called game paradox and they are essentially the same. We designed the games with long-term memory on loop lattice and history-entangled game. The strong correlation between nearest two rounds of game can make the combination of two losing game win, lose or oscillate between win and loss. The periodic potential in Brownian ratchet is analogous to a long chain of beam splitters. The coupling between two neighboring potential wells is equivalent to two coupled beam splitters. This correspondence may help us to understand the anomalous motion of exceptional Brownian particles moving in the opposite direction to the majority. We designed the capital wave for a game by introducing correlations into independent capitals instead of sub-games. Playing entangled quantum states in many coupled classical games obey the same rules for manipulating quantum states in many body physics.