On the clustering phase transition in self-gravitating N-body systems

The thermodynamic behaviour of self-gravitating N-body systems has been wor ked out by borrowing a standard method from molecular dynamics. The link be tween dynamics and thermodynamics is made in the microcanonical ensemble of statistical mechanics. Through the computation of basic thermodynamic obse rvables and of the equation of state in the P - V plane, the clustering pha se transition appears to be of the second-order type. The dynamical - micro canonical averages are compared with their corresponding canonical ensemble averages, obtained through standard Monte Carlo computations. The latter s eem to have completely lost any information about the phase transition. Fin ally, our results obtained in a 'microscopic' framework - are compared with some existing theoretical predictions - obtained in a 'macroscopic' (therm odynamic) framework: qualitative and quantitative agreement is found, with an interesting exception.