  To describe high energy collisions one widely uses thermodynamical methods
and concepts which follow the classical Boltzmann-Gibbs (BG) approach. In many
cases, however, either some deviations from the expected behaviour are observed
experimentally or it is known that the conditions necessary for BG to apply are
satisfied only approximately. In other branches of physics where such
situations are ubiquitous, the popular remedy is to resort, instead, to the so
called nonextensive statistics, the most popular example of which is Tsallis
statistics. We shall provide here an overview of possible imprints of
non-extensitivity existing both in high energy cosmic ray physics and in
multiparticle production processes in hadronic collisions, in particular in
heavy ion collisions. Some novel proposition for the interpretation of the
nonextensitivity parameter q present in such circumstances will be discussed in
more detail.
