English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The notion of entropy is ubiquitous both in natural and social sciences. Inthe last two decades, a considerable effort has been devoted to the study ofnew entropic forms, which generalize the standard Boltzmann-Gibbs (BG) entropyand are widely applicable in thermodynamics, quantum mechanics and informationtheory. In [23], by extending previous ideas of Shannon [38], [39], Khinchinproposed an axiomatic definition of the BG entropy, based on four requirements,nowadays known as the Shannon-Khinchin (SK) axioms.  The purpose of this paper is twofold. First, we show that there exists anintrinsic group-theoretical structure behind the notion of entropy. It comesfrom the requirement of composability of an entropy with respect to the unionof two statistically independent subsystems, that we propose in an axiomaticformulation. Second, we show that there exists a simple universal class ofadmissible entropies. This class contains many well known examples of entropiesand infinitely many new ones, a priori multi-parametric. Due to its specificrelation with the universal formal group, the new family of entropiesintroduced in this work will be called the universal-group entropy. A newexample of multi-parametric entropy is explicitly constructed.

Beyond the Shannon-Khinchin Formulation: The Composability Axiom and the Universal Group Entropy