CSH President Stefan Thurner’s talk is part of the IFISC Colloquia on Complex Systems, which take place at the Edifici Instituts Universitaris de Recerca, Campus Universitat de les Illes Balears, in Palma de Mallorca, Spain.
We present a simple theory for driven out-of-equilibrium systems — alias complex systems. Driven systems that are composed of a driving- and a relaxation process, generically produce power law distributions for low driving rates. The theory allows us to relate the driving rate with the dynamical origin of a number of distribution functions that occur in complex systems over and over again, including the power law, the Gamma, the Weibull, the Tsallis, the stretched exponential, the log-normal and many more. We present simple examples, such as the statistics of search processes, sentence formation, fragmentation phenomena, self-organized critical systems, and the energy distribution of cosmic rays.