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CRM > English > Activities > Is there a world beyond Shannon? - Entropies for complex systems
Is there a world beyond Shannon? - Entropies for complex systems
Place: Sala Prat de la Riba, Institut d'Estudis Catalans​carrer del Carme 47, 08001 Barcelona

Date: April 11th, 2013

Time: 19.00


About Stefan Thurner: Theoretical physicist and economist. Professor for Science of Complex Systems at the Medical University of Vienna, external professor at the Santa Fe Institute. He has worked on fundamental physics (topological excitations in quantum field theories, alternative entropy formulations), applied mathematics (wavelet statistics, fractal harmonic analysis, diffusion processes), complex systems (network theory, evolutionary systems), life sciences (heart beat dynamics, gene regulatory networks, cell motility, bioinformatics), econophysics (price formation, banking regulation, systemic risk) and lately in social sciences (opinion formation and bureaucratic inefficiency). This work has received broad interest from the media such as the New York Times, BBC world, Nature, New Scientist, and Physics World. He is Austrian delegate at the COST action initiative and holds 2 patents. He has also been active in quantitative financial consulting for financial institutions, mainly for automated trading strategies.​


Is there a world beyond Shannon? - Entropies for complex systems ​

In information theory the so-called 4 Shannon-Khinchin (SK) axioms uniquely determine Boltzmann-Gibbs entropy as the one and only possible entropy. Physics (and social systems in particular) are different from information theory in the sense that such systems can be non-ergodic. Many complex systems in fact are. To describe strongly interacting statistical non-ergodic systems (i.e. complex systems) within a thermodynamical framework, it becomes necessary to introduce generalized entropies. A number of such entropies have been proposed in the past. The understanding of the fundamental origin of these entropies and its deeper relations to complex systems has remained unclear. Non-ergodicity explicitly violates the fourth SK axiom. We show that violating this axiom and keeping the other three axioms intact, determines an explicit form of a more general entropy, $S\sim \sum_i \Gamma (d+1,1-c\log p_i)$, uniquely describing a statistical system; $c$ and $d$ are scaling exponents, Gamma is the incomplete Gamma function. All recently proposed entropies appear to be special cases. We prove that each (!) statistical system is uniquely characterized by the pair of the two scaling exponents (c,d), which define equivalence classes for all (!) interacting and non-interacting systems, and that no other possibilities for entropies exist. The corresponding distribution functions are special forms of so-called Lambert-W exponentials, containing as special cases Boltzmann, stretched exponential and Tsallis distributions(power-laws) all abundant in nature. We show how the phasespace volume of a system is related to its (generalized) entropy and illustrate this with physical examples of spin systems on constant-connectency networks and accelerating random walks.
The seminar is open to the public.

If you have any questions please contact:

Ms. Núria Hernandez
Activities Coordinator​ ​