The theory of large deviations is concerned with the exponential decay of probabilities of
large fluctuations in random systems. These probabilities are important in many fields of …

For systems with long-range interactions, the two-body potential decays at large distances
as V (r)∼ 1/rα, with α≤ d, where d is the space dimension. Examples are: gravitational …

Abstract Systems with long-range (LR) forces, for which the interaction potential decays with
the interparticle distance with an exponent smaller than the dimensionality of the embedding …

The theoretical study of the self-organization of two-dimensional and geophysical turbulent
flows is addressed based on statistical mechanics methods. This review is a self-contained …

We discuss the nature of phase transitions in self-gravitating systems. We show the
connection between the binary star model of Padmanabhan, the thermodynamics of stellar …

We review simple aspects of the thermodynamic and dynamical properties of systems with
long-range pairwise interactions (LRI), which decay as 1/rd+ σ at large distances r in d …

Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic
functions, eg, of the canonical free energy. Given a certain physical system, it is of interest to …

The phase structure and critical phenomena of the 3+ 1 dimensional charged black holes in
asymptotically flat spacetime are investigated within the Rényi statistics. As the nonextensive …

We discuss the dynamics and thermodynamics of the Hamiltonian Mean Field model (HMF)
which is a prototypical system with long-range interactions. The HMF model can be seen as …

We discuss a method to solve models with long-range interactions in the microcanonical
and canonical ensemble. The method closely follows the one introduced by RS Ellis …