Nano-plasmas produced, e.g. in clusters after short-pulse laser irradiation, can show collective excitations as derived from the time evolution of fluctuations in thermodynamic equilibrium. Molecular dynamical simulations are performed for various cluster sizes. New data are obtained for the minimum value of the stationary cluster charge. The bi-local auto-correlation function gives the spatial structure of the eigenmodes, for which energy eigenvalues are obtained. Varying the cluster size, starting from a few-particles cluster, the emergence of macroscopic properties like collective excitations is shown.