Evolutionary games of condensates in coupled birth-death processes

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.

39 pages, 4 figures, 1 table

References in corpus (11)

• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Cyclic dominance in evolutionary games: A review
• Coevolutionary Dynamics: From Finite to Infinite Populations
• Fragmentation of Bose-Einstein Condensates
• Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Evolutionary game theory in growing populations
• Chemical warfare and survival strategies in bacterial range expansions
• Coexistence and Survival in Conservative Lotka-Volterra Networks
• Binary birth-death dynamics and the expansion of cooperation by means of self-organized growth
• Specialization and Bet Hedging in Heterogeneous Populations

Cited by in corpus (6)

• Stochastic population dynamics in spatially extended predator-prey systems
• Zealots tame oscillations in the spatial rock-paper-scissors game
• Biodiversity in models of cyclic dominance is preserved by heterogeneity in site-specific invasion rates
• Conditioned random walks and interaction-driven condensation
• Cooperation in Microbial Populations: Theory and Experimental Model Systems
• Slow-fast dynamics in stochastic Lotka-Volterra systems