Preprint: Variational convergence for an irreversible exchange-driven stochastic particle system
Substantially revised and extended, 2025-07-06
Together with Jasper Hoeksema and Chun Yin Lam, we considerably extended and updated the previous version of the arXiv preprint 2401.06696. We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations known as the exchange-driven growth model, which has two conserved quantities. As a bounded perturbation of the reversible kernel, the variational formulation is a generalization of the gradient flow formulation of the reversible process and can be interpreted as the large deviation functional of the Markov jump process.
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