Evolutionary games of condensates in coupled birth-death processes

TL;DR

This paper applies evolutionary game theory to driven-dissipative bosonic systems to explain the formation and dynamics of multiple condensates, revealing entropy-driven selection and oscillatory behaviors.

Contribution

It introduces a novel approach linking evolutionary game theory to condensate formation in quantum systems, explaining condensate selection and dynamics.

Findings

Multiple condensates can form in driven-dissipative bosonic systems.

Relative entropy production determines condensate selection.

Condensate occupations can oscillate, exemplified by a rock-paper-scissors game.

Abstract

Condensation phenomena arise through a collective behaviour of particles. They are observed in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the energetic ground state in ultra-cold bosonic gases (Bose-Einstein condensation). Recently, it has been shown that a driven and dissipative system of bosons may form multiple condensates. Which states become the condensates has, however, remained elusive thus far. The dynamics of this condensation are described by coupled birth-death processes, which also occur in evolutionary game theory. Here, we apply concepts from evolutionary game theory to explain the formation of multiple condensates in such driven-dissipative bosonic systems. We show that vanishing of relative entropy production determines their selection. The condensation proceeds exponentially fast, but the system never comes to rest. Instead, the occupation numbers of condensates may oscillate, as we demonstrate for a rock-paper-scissors game of condensates.