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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