Nonadditive Entropies and Complex Systems

Entropies for complex systems: generalized-generalized entropies

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to – justified or not – hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann) we demonstrate how the corresponding entropy has to look like, given the form of the corresponding distribution functions. By two natural assumptions that (i) t...

Some Coding Theorems for Nonadditive Generalized Mean-Value Entropies

We give an optimality characterization of nonadditive generalizedmean-value entropies from suitable nonadditive and generalized mean-value properties of the measure of average length. The results obtained cover many results obtained by other authors as particular cases, as well as the ordinary length due to Shannon 1948. Themain instrument is the l ni function of the word lengths in obtaining t...

Nonadditive entropies yield probability distributions with biases not warranted by the data.

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann-Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types ...

Complex fuzzy linear systems

Entropies and Co-Entropies of Coverings with Application to Incomplete Information Systems

Different generalizations to the case of coverings of the standard approach to entropy applied to partitions of a finite universe X are explored. In the first approach any covering is represented by an identity resolution of fuzzy sets on X and a corresponding probability distribution with associated entropy is defined. A second approach is based on a probability distribution generated by the c...