Together with Jasper Hoeksema and Chin 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. As a consequence of the variational convergence result, we show the propagation of chaos of the Markov processes to the limiting equation and the -convergence of the energy functional. The latter convergence is consistent with related results for reversible coagulation-fragmentation equations and reveals the connection of stochastic processes to the long-time condensation phenomena in the limit equation.