  Observed self-gravitating systems reveal often fragmented non-equilibrium
structures that feature characteristic long-range correlations. However, models
accounting for non-linear structure growth are not always consistent with
observations and a better understanding of self-gravitating $N$-body systems
appears necessary. Because unstable gravitating systems are sensitive to
non-gravitational perturbations we study the effect of different dissipative
factors as well as different small and large scale boundary conditions on
idealized $N$-body systems. We find, in the interval of negative specific heat,
equilibrium properties differing from theoretical predictions made for
gravo-thermal systems, substantiating the importance of microscopic physics and
the lack of consistent theoretical tools to describe self-gravitating gas.
Also, in the interval of negative specific heat, yet outside of equilibrium,
unforced systems fragment and establish transient long-range correlations. The
strength of these correlations depends on the degree of granularity, suggesting
to make the resolution of mass and force coherent. Finally, persistent
correlations appear in model systems subject to an energy flow.
