Evolutionary games of condensates in coupled birth–death processes

• Published in: Nature communications Vol. 6; no. 1; p. 6977
• Main Authors: Knebel, Johannes, Weber, Markus F., Krüger, Torben, Frey, Erwin
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 24.04.2015; Nature Publishing Group; Nature Pub. Group
• Subjects: 639/766/36/1125; 639/766/483/640; Algorithms; Biological Evolution; Birth; Bosons; Chemical Phenomena; Condensates; Condensation; Entropy; Evolution; Game Theory; Gases; Humanities and Social Sciences; Markov processes; Mass transport; multidisciplinary; Occupations; Science; Science (multidisciplinary); Traffic jams; Transportation models
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/ncomms7977

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 the 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. A driven-dissipative system of non-interacting bosons may form multiple condensates—a dynamics described by birth–death processes that also occur in evolutionary game theory. Here, the authors apply game theory to show how the vanishing of relative entropy production governs condensate selection.