Statistics of driven processes

Stefan Thurner

Stefan Thurner is full professor for Science of Complex Systems at the Medical University of Vienna, where he chairs Section for Science of Complex Systems. He is external professor at the Santa Fe Institute, senior researcher at IIASA, and president of the Complexity Science Hub Vienna (@CSHVienna).

Stefan obtained a PhD in theoretical physics from the Technical University of Vienna and a PhD in economics from the University of Vienna. He held postdoc positions at Humboldt University of Berlin and Boston University before joining the faculty of the University of Vienna and later Medical University. His habilitation is in theoretical physics. Stefan started his career with contributions to theroretical particle physics and gradually shifted his resarch focus to the understanding of complex systems.

Stefan has published more than 200 scientific articles in 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, buerocratic inefficiency, collective human behavior, efficiency of healthcare systems). 

His work has been covered extensively by the media such as the New York Times, BBC world, Nature, New Scientist, Physics World, and is featured in more than 400 newspaper, radio and television reports.


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

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