Self-organized criticality in atmospheric cascades

It is well known that energy spectra of particles from atmospheric family events which are observed by the emulsion chambers at mountain altitudes are essentially following power-like dependence. On the other hand the occurence of power-law distributions is a very common feature in nature and it is usually connected with such notions as criticality, fractals and chaotic dynamics and studied using generalized (nonextensive) maximum entropy formalism characterized by a nonextensivity parameter q. Such formalism leads in a natural way to power-laws in the frame of equilibrium processes [1]. For nonequilibrium phenomena the sources of power-law distributions are self-organized criticality [2] and stochastic multiplicative processes [3]. In the former nonequilibrium systems are continuously driven by their own internal dynamic to a critical state with power-laws omnipresent. In the later power-law is generated by the presence of underlying replication of events. All these approaches can be unified in terms of generalized nonextensive statistics mentioned above (widely known as Tsallis statistics) [1].