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

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