We use the Chapman–Enskog method to derive the Smoluchowski equation from the Kramers equation in a high friction limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and we consider a generalized class of Kramers equations...

We apply the broad histogram method to an Ising system in the context of the recently reformulated Generalized Thermostatistics, and we claim it to be a very efficient simulation tool for this non-extensive statistics. Results are obtained for the nearest-neighbour version of the Ising model for...

We discuss different interpretations of Tsallis functional in astrophysics. In principle, for t→+∞, a self-gravitating system should reach a statistical equilibrium state described by the Boltzmann distribution. However, this tendency is hampered by the escape of stars and the gravothermal...

We discuss the role of the initial conditions for the dynamical anomalies observed in the quasi-stationary states of the Hamiltonian mean field (HMF) model.

We discuss the nature of quasi-stationary states (QSS) with non-Boltzmannian distribution in systems with long-range interactions in relation with a process of incomplete violent relaxation based on the Vlasov equation. We discuss several attempts to characterize these QSS. We show that their...

We discuss the glassy dynamics recently found in the meta-equilibrium quasi-stationary states (QSS) of the HMF model. The relevance of the initial conditions and the connection with Tsallis nonextensive thermostatistics is also addressed.

The mean field XY Hamiltonian, a suitable model for studying long-range interactions in extended systems, presents, amongst other interesting features, slow relaxation and formation of quasi-stationary (QS) states. It is now known that, along these QS trajectories, the system visits critical...

We present the numerical study of the one-dimensional Potts model with power-law decaying ferromagnetic interactions. The largest cluster probability distribution is obtained by Monte Carlo simulations using the Swendsen–Wang cluster algorithm with cumulative probabilities. The finite-size...

We present a systematic study of the thermodynamics of two and three-dimensional generalized Lennard–Jones (LJ) systems focusing on the relationship between the range of the potential, the system density and its dimension. We found that the existence of negative specific heats depends on these...