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Socioeconomic agents as active matter and nucleation paths in active field theories
In this seminar, we will tackle two subjects whose common thread is active matter.
In a first part, I will focus on a socio-economic occupation model in the spirit of the Sakoda-Schelling model, historically introduced to shed light on segregation dynamics among human groups. For a large class of decision rules that drive the system out of equilibrium, we recover an equilibrium-like phase separation phenomenology (liquid-gas). Within the mean-field approximation I will show how the model can be mapped, to some extent, onto an active matter field description, paving the way for a unifying framework which considers population and price dynamics within a field theoretic approach.
In a second part, using the nucleation-induced active phase separation as a starting observation, I will ask a general question : How can one predict the final phase of a nonequilibrium system where several phases compete ? Since resorting to the free energy minimization is impossible, the transition depends crucially on the system’s dynamics. By using a minimum action method, I will pinpoint the first-order phase transition in some spatially-extended nonequilibrium systems. I will focus on the nonequilibrium extension of the Cahn-Hilliard dynamics, commonly used to describe active liquid-gas phase separation. The paths of the transitions and their critical nuclei are notably identified.
References
Socioeconomic agents as active matter in nonequilibrium Sakoda-Schelling models
R Zakine, J Garnier-Brun, AC Becharat, M Benzaquen
arXiv:2307.14270
Minimum Action Method for Nonequilibrium Phase Transitions
R Zakine, E Vanden-Eijnden
arXiv:2202.06936
Unveiling the Phase Diagram and Reaction Paths of the Active Model B with the Deep Minimum Action Method
R Zakine, E Simonnet, E Vanden-Eijnden
arXiv:2309.15033