Classical grand canonical ensemble

range	$N\in\mathbb N$
definiendum	$(\ \langle \mathcal M_N, H_N,\pi_N,\pi_{N,0},{\hat\rho}_N,{\hat\rho}_{N,0} \rangle\ )_N \in \mathrm{it}$
postulate	$\forall N.\ \langle \mathcal M_N, H_N,\pi_N,\pi_{N,0},{\hat\rho}_N,{\hat\rho}_{N,0} \rangle$ … classical canonical ensemble

A sequence of phase spaces with their partition functions, one for each particle number.

todo: the $N$ th manifold is a submanifold of the $N+1$ 'th.