Motivation

L. Boltzmann and J.W. Gibbs in the 19th century settled the frame of statistical mechanics, with the concept of extensive entropy, and state probability with exponential weight (p ~exp(-beta E) with beta = 1/kT), satisfying the ergodicity hypothesis. However, all systems do not satisfy these hypotheses, in particular systems with long-range forces, and in particular with self-gravity. There is a vast class of nonequilibrium phenomena (some metastable and stationary states) which appears to be described by nonextensive statistical mechanics, based on generalized entropic form, like the Tsallis or Renyi entropies. (click on the image to download the poster)

Many applications of non-extensive statistical mechanics have been studied: turbulence, anomalous diffusion, economy, cosmic ray fluxes, bacterial development, self-organized criticality, self-gravitating systems.. All these phenomena share long-range correlations in space/time, or fractal boundary conditions, or some mechanism creating a scale-invariant hierarchical structure. Such phenomena occur in non-linear dynamical systems, when the Lyapunov factors approach zero and departure from initial conditions is no longer exponential. At the boundary of chaos, generalisations of the entropy, for instance in terms of q-entropy, to take into account its pseudo-extensivity, have encountered success in dealing with these non-linear systems. The meeting will focus on recent progress in particular on statistical mechanics of self-gravity, turbulence and stock markets. The main topics will be: Statistical mechanics of collisionless stellar systems Interstellar medium, self-gravity and fractal structure Turbulence, chaos, and generalized thermodynamics Statistical mechanics of stock markets