Given an isolated $N$-particle dynamical system with only two body interaction, that is

$$H=\sum_{i=1}^N\frac{\mathbf{p}_i^2}{2m}+\sum_{i<j}V(\mathbf{r}_i-\mathbf{r}_j)$$

In the thermodynamic limit, that is $N\gg 1$ and $N/V=$constant, it seems that not all two body interaction can make system approach thermal equilibrium automatically. For example, if the interaction is inverse square attractive force, we know the system cannot approach thermal equilibrium.

Although there is [Boltzmann's H-theorem](https://en.wikipedia.org/wiki/H-theorem) to derive the second law of thermodynamics, it relies on the [Boltzmann equation](https://en.wikipedia.org/wiki/Boltzmann_equation) which is derived from [Liouville's equation](https://en.wikipedia.org/wiki/Liouville's_equation) in approximation of low density and short range interaction.

My question:

1. Does it mean that any isolated system with low density and short range interaction can approach thermal equilibrium automatically? If not, what's the counterexample?

2. For long range interaction or high density isolated system, what's the necessary and sufficient conditions for such system can approach thermal equilibrium automatically? What's about coulomb interaction?

3. How to prove rigorously that a pure self-gravitational system cannot approach equilibrium? I only heard the hand-waving argument that gravity has the effect of clot, but I never see the rigorous proof.

I know there is maximal entropy postulate in microscopic ensemble.I just want to find the range of application of this postulate. I'm always curious about the above questions but I never saw the discussion in any textbook of statistical mechanics. You can also cite the literature in which I can find the answer.