Laboratoire de Physique Théorique
Toulouse - UMR 5152

Hamiltonian systems with long-range interactions show a relaxation towards quasi-stationary states whose lifetime increases with system size. The state to which relaxation occurs strongly depends on the initial condition. For certain classes of initial conditions one can show that a maximum entropy principle introduced long ago by Lynden-Bell for gravitational systems predicts the presence of phase transitions in a control parameter space which includes features of the initial condition. Predictions of this theory check well with numerical experiments. We also propose an alternative explanation of the presence of quasi-stationary states and of the phase transitions based on the properties of the dynamics of a single particle.

 REFERENCES

 A. Antoniazzi, F. Califano, D. Fanelli, S. Ruffo : "Exploring the thermodynamic limit of Hamiltonian models : convergence to the Vlasov equation", Phys. Rev. Lett., 98, 150602 (2007).
 A. Antoniazzi, D. Fanelli, S. Ruffo and Y.Y. Yamaguchi :"Nonequilibrium tricritical point in a system with long-range interactions", Phys. Rev. Lett., 99, 040601 (2007).
 R. Bachelard, C. Chandre, D. Fanelli, X. Leoncini and S. Ruffo :"Abundance of regular orbits and out-of-equilibrium phase transitions in the therodynamic limit for long-range systems", Phys. Rev. Lett, 101, 260603 (2008).