Statistics and dynamics

The classical statistics of Boltzmann and Gibbs will be discussed. As pointed out long ago by Einstein, there is a connection of the statistics applicable to a system and its underlying dynamics. This follows, for example, from the existence of quantum (Bose–Einstein or Fermi–Dirac) statistics, where the underlying dynamics is quite different from classical mechanics. In 1988 Tsallis proposed a very successful new statistics. Its connection with an underlying dynamics as well as with the nonextensivity of systems are still matters of active investigation.