Date: April 11th, 2013
Time: 19.00
Speaker
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.
Information
The seminar is open to the public.
If you have any questions please contact:
Ms. Núria Hernandez
nhernandez@crm.cat
Activities Coordinator