This paper is a review of results which have been recently obtained by applying
mathematical concepts drawn, in particular, from differential geometry and topology, to the …

There is no compelling reason imposing that the methods of statistical mechanics should be
restricted to the dynamical systems which follow the usual Boltzmann–Gibbs prescriptions …

Metaphors, generalizations and unifications are natural and desirable ingredients of the
evolution of scientific theories and concepts. Physics, in particular, obviously walks along …

Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book
discusses fundamental properties of transient and stationary solutions, emphasizing the …

Boltzmann''s formula S= In [W (E)] defines the microcanonical ensemble. The usual
textbooks on statistical mechanics start with the microensemble but rather quickly switch to …

Phase transitions are among the most impressive phenomena occurring in nature. They are
an example of emergent behavior, ie, of collective properties having no direct counterpart in …

We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-
Field model, a prototype for long-range interactions in N-particle dynamics. In particular, we …

We study the dynamics of a system of N classical spins with infinite-range interaction. We
show that, if the thermodynamic limit is taken before the infinite-time limit, the system does …

Under certain conditions, the rate of increase of the statistical entropy of a simple, fully
chaotic, conservative system is known to be given by a single number, characteristic of this …

We study the link between relaxation to the equilibrium and anomalous superdiffusive
motion in a classical N-body Hamiltonian system with long-range interaction showing a …