Langevin dynamics or stochastic gradient flow for grand canonical ensemble

Question

We know that for a measure exp(-U(X)) (canonical ensemble), we can use the dynamic dX=-DU(X)+ noise to sample the measure as t goes to infinity.

Is there any dynamic corresponding to the grand canonical ensemble, where the particle number is also random? The partition function is usually written as $\sum_{n} \frac{z^n}{n!} \exp(-U(x_1,...,x_n))$.

Thanks!