ABSTRACT / Driven complex systems abound practically everywhere. We show that the underlying statistics of many of these can be undserstood by so-called sample space reducing (SSR) processes that offer an intuitive understanding of the origin and ubiquity of fat tailed distributions in countless systems, including power-laws. SSR processes are mathematically simple and offer an exact alternative to Boltzmann equation based approaches to non-equailibrium systems. We show that in many situations the statistics of driven systems is determined by the driving process and is universal with respect to the specific relaxation dynamics. With simple driving process we can naturally derive Zipf’s law, exact power-laws, exponential, Gamma, normal, Weibull, Gompertz, Pareto and other distributions. We discuss a number of examples of SRR processes that range from fragmentation processes, diffusion on networks, language formation, cascading and search processes, as well as the derivation of the equivalent of the Maxwell Botzmann distribution for inelastically colliding particles in a box.
BIO / Stefan Thurner is full professor for Science of Complex Systems at the Medical University of Vienna, where he chairs the Section for Science of Complex Systems. He is external professor at the Santa Fe Institute and President of the Complexity Science Hub Vienna. Stefan started his career with contributions to theoretical particle physics and gradually shifted his focus to the understanding of complex systems. He has published more than 240 scientific articles ranging from fundamental physics (topological excitations in quantum field theories, statistics and entropy of complex systems), applied mathematics (wavelet statistics, fractal harmonic analysis, anomalous diffusion), network theory, evolutionary systems, life sciences (network medicine, gene regulatory networks, bioinformatics, heart beat dynamics, cell motility), economics and finance (price formation, regulation, systemic risk) and lately in social sciences (opinion formation, bureaucratic inefficiency, collective human behavior, efficiency of healthcare systems). He holds two patents.