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Related papers: Tsallis entropy and generalized Shannon additivity

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The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…

Probability · Mathematics 2015-06-22 Jin-Li Guo , Qi Suo

Recently, Suyari has proposed a generalization of Shannon-Khinchin axioms, which determines a class of entropies containing the well-known Tsalis and Havrda-Charvat entropies [H. Suyari, IEEE Trans. Inf. Theory, vol. 50, pp. 1783-1787, Aug.…

Mathematical Physics · Physics 2012-12-03 Velimir M. Ilic , Miomir S. Stankovic , Edin H. Mulalic

The property of Tsallis entropy is examined when considering tow systems with different temperatures to be in contact with each other and to reach the thermal equilibrium. It is verified that the total Tsallis entropy of the two systems…

Statistical Mechanics · Physics 2015-08-10 Jiulin Du

There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…

Information Theory · Computer Science 2017-08-22 John C. Baez , Tobias Fritz , Tom Leinster

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…

Classical Physics · Physics 2016-11-15 B. H. Lavenda , J. Dunning-Davies

Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined…

Statistical Mechanics · Physics 2007-05-23 Hiroki Suyari , Makoto Tsukada

In this paper we give an interpretation of Tsallis' nonextensive statistical mechanics based upon the information-theoretic point of view of Luzzi et al. [cond-mat/0306217; cond-mat/0306247; cond-mat/0307325], suggesting Tsallis' entropy to…

Statistical Mechanics · Physics 2015-06-24 F. Sattin

Entropy is a key measure in studies related to information theory and its many applications. Campbell of the first time recognized that exponential of Shannons entropy is just the size of the sample space when the distribution is uniform.…

Information Theory · Computer Science 2016-08-15 Dhanesh Garg , Staish Kumar

The exact solution of a particular form of the stationary state generalized Fokker-Planck equations, which is given under certain conditions by the classical Tsallis distribution, is compared with the solution of the MAXENT equations…

Statistical Mechanics · Physics 2013-02-01 J. M. Conroy , H. G. Miller

We study the evolution of Tsallis entropy along the heat flow and establish its concavity in arbitrary dimensions. Extending prior results that were restricted to the one-dimensional setting, we prove that the Tsallis entropy is concave in…

Information Theory · Computer Science 2026-04-24 Lukang Sun

Nonextensive entropies are divided into three classes, each of which is characterized by Shannon additivity and pseudoadditivity. One of the three classes has properties of both additivities. The remaining classes have only one property of…

Mathematical Physics · Physics 2007-05-23 Hiroki Suyari

We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…

Quantum Physics · Physics 2007-05-23 C. G. Chakrabarti , Indranil Chakrabarty

This article extends the non-extensive entropy of Tsallis and uses this entropy to model an energy producing system in an absorbing heat bath. This modified non-extensive entropy is superficially identical to the one proposed by Tsallis,…

Statistical Mechanics · Physics 2007-05-23 Mark Fleischer

Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we…

Statistical Mechanics · Physics 2017-05-19 Nikos Kalogeropoulos

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.

Classical Analysis and ODEs · Mathematics 2013-01-08 S. Furuichi , N. Minculete , F. -C. Mitroi

The aim of the present paper is to present a careful and accessible discussion of the formal aspects of Boltzmann-Gibbs and Tsallis entropies. We begin with a brief overview of Boltzmann-Gibbs entropy, highlighting its main properties and…

Statistical Mechanics · Physics 2025-10-23 Kelvin dos Santos Alves , Rogerio Teixeira Cavalcanti

Tsallis relative operator entropy is defined as a parametric extension of the relative operator entropy. Some properties of the Tsallis relative operator entropy are investigated. Also some operator inequalities related to the Tsallis…

Functional Analysis · Mathematics 2010-03-29 S. Furuichi , K. Yanagi , K. Kuriyama

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…

Statistical Mechanics · Physics 2009-11-11 Sumiyoshi Abe , Yutaka Nakada

We generalize the completely monotone conjecture ([CG15]) from Shannon entropy to the Tsallis entropy up for orders up to at least four. To this end, we employ the algorithm ([J\"un16, JM06a]) which employs the technique of systematic…

Analysis of PDEs · Mathematics 2022-12-20 Li-Chang Hung

We consider the Shannon-Khinchin axiomatic systems for the characterization of generalized entropies such as Sharma-Mital and Frank-Daffertshofer entropy. We provide the generalization of Shannon-Khinchin axioms and give the corresponding…

Mathematical Physics · Physics 2015-06-17 Velimir M. Ilic , Miomir S. Stankovic