Rudolf Hanel

A comprehensive classification of complex statistical systems and an axiomatic derivation of their entropy and distribution functions

To characterize strongly interacting statistical systems within a thermodynamical framework - complex systems in particular - it might be necessary to introduce generalized entropies,

Generalized entropies and the transformation group of superstatistics

S_g

Statistical detection of systematic election irregularities

. A series of such entropies have been proposed in the past, mainly to accommodate important empirical distribution functions to a maximum ignorance principle. Until now the understanding of the fundamental origin of these entropies and its deeper relations to complex systems is limited. Here we explore this questions from first principles. We start by observing that the 4th Khinchin axiom (separability axiom) is violated by strongly interacting systems in general and ask about the consequences of violating the 4th axiom while assuming the first three Khinchin axioms (K1-K3) to hold and

Peer-review in a world with rational scientists: Toward selection of the average

S_g=\sum_ig(p_i)

Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example

. We prove by simple scaling arguments that under these requirements {\em each} statistical system is uniquely characterized by a distinct pair of scaling exponents

On the robustness of q-expectation values and Rényi entropy

(c,d)

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems

in the large size limit. The exponents define equivalence classes for all interacting and non interacting systems. This allows to derive a unique entropy,

Stability criteria for q-expectation values

S_{c,d}\propto \sum_i \Gamma(d+1, 1- c \ln p_i)

Generalized (c,d)-Entropy and Aging Random Walks

, which covers all entropies which respect K1-K3 and can be written as

Generalized entropies and logarithms and their duality relations

S_g=\sum_ig(p_i)