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

@article{Tempesta2014BeyondTS, title={Beyond the Shannon-Khinchin Formulation: The Composability Axiom and the Universal Group Entropy}, author={Piergiulio Tempesta}, journal={arXiv: Mathematical Physics}, year={2014} }

## 44 Citations

### Formal groups and Z-entropies

- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2016

It is proved that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies called the Z-entropies, which arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts.

### Group Entropies: From Phase Space Geometry to Entropy Functionals via Group Theory

- Computer ScienceEntropy
- 2018

The group theoretic entropies make use of formal group theory to replace the additivity axiom with a more general composability axiom, and explain why groupEntropies may be particularly relevant from an information-theoretical perspective.

### A theorem on the existence of trace-form generalized entropies

- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

An analytic technique is proposed, which allows to generate many new examples of entropic functionals generalizing the standard Boltzmann–Gibbs entropy. Our approach is based on the existence of a…

### Uniqueness and characterization theorems for generalized entropies

- Computer ScienceArXiv
- 2017

It is proved that, under mild regularity assumptions, the only composable generalized entropy in trace form is the Tsallis one-parameter family (which contains Boltzmann–Gibbs as a particular case), which leads to the use of generalized entropies that are not of trace form in the study of complex systems.

### A System of Billiard and Its Application to Information-Theoretic Entropy

- Mathematics, Computer ScienceArXiv
- 2020

The Ihara entropy is a weakly decomposable entropy whose composition law is given by the Lazard formal group law and fulfils the generalized Shannon-Khinchin axioms.

### Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere

- PhysicsEntropy
- 2019

The present review focuses on nonadditive entropies generalizing Boltzmann–Gibbs statistical mechanics and their predictions, verifications, and applications in physics and elsewhere.

### Change the coefficients of conditional entropies in extensivity

- MathematicsJournal of Mathematical Physics
- 2021

The impossibility to replace the coefficients with a non-power function of the probabilities of the events $X=n$ is proved and the difference between the value at the joint law of $(X,Y) and that at the law of $X$ for a general functional is estimated.

### A family of generalized quantum entropies: definition and properties

- Computer ScienceQuantum Inf. Process.
- 2016

A quantum version of the generalized generalized entropies, introduced by Salicrú et al, is presented and it is exhibited that majorization plays a key role in explaining most of their common features.

### On the equivalence between four versions of thermostatistics based on strongly pseudo-additive entropies

- Computer Science
- 2019

This paper establishes the equivalence between four different thermostatistics formalisms based on Renyi and SPA entropies coupled with linear and escort constraints and provides the transformation formulas, which obtain a general framework applicable to the wide class of entropie and constraints previously discussed in the literature.

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An analytic technique is proposed, which allows to generate many new examples of entropic functionals generalizing the standard Boltzmann–Gibbs entropy. Our approach is based on the existence of a…

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