  We consider the thermodynamic limit of mean-field stochastic particle systems
on a complete graph. The evolution of occupation number at each vertex is
driven by particle exchange with its rate depending on the population of the
starting vertex and the destination vertex, including zero-range and
misanthrope process. We show that under a detailed balance condition and
suitable growth assumptions on the exchange rate, the evolution equation of the
law of the particle density can be seen as a generalised gradient flow equation
related to the large deviation rate functional.
  We show the variational convergence of the gradient structures based on the
energy dissipation principle, which coincides with the large deviation rate
function of the finite system. The convergence of the system in this
variational sense is established based on compactness of the density and flux
and $\Gamma$-lower-semicontinuity of the energy dissipation functional along
solutions to the continuity equation. The driving free energy
$\Gamma$-converges in the thermodynamic limit, after taking possible
condensation phenomena into account.
