happens by shedding individual particles, is trailing the kinetic energy evolution till the last stages, when the core rapidly disappears.

Such molecular dynamics characteristics of the equilibrium or the metastable uniform and core-halo states as kinetic energy, wall pressure, number of core particles, particle-particle radial distribution function and velocity distribution function, are found to be equal within the statistical uncertainty of the molecular dynamics measurements to the corresponding mean field predictions.

The long collapse time observed in our simulations appears to be an explanation for the apparent discrepancy between the phase diagram presented in [@pet] and the mean field phase diagram (see, for example, [@chi]). The relaxation time allowed in [@pet] before the measurements of what was considered to be a steady state, $t_{rel}=3N/|EN|^{3/2}$, which is apparently equivalent to $\t_{rel}<1$, is by far insufficient for a system to collapse. Therefore, the discontinuities in caloric curves $\beta$ vs $\e$, typical for collapse and explosion gravitational transitions, were not observed in [@pet].

Although we considered systems only with the soft Coulomb potential, we speculate that a likewise similarity between the mean field and molecular dynamics equilibrium properties of the core-halo state exists for all ”soft” long-range (like a Fourier-truncated Coulomb) potentials. This 