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The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…

Statistical Mechanics · Physics 2015-06-24 Jan Naudts

In order to study as a whole a wide part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the $h$-derivative, which generalizes the conventional Newton--Leibniz calculus. This new entropy,…

Statistical Mechanics · Physics 2023-06-14 Jin-Wen Kang , Ke-Ming Shen , Ben-Wei Zhang

The coupled entropy, $H_\kappa,$ is proven to uniquely satisfy the requirement that a generalized entropy be a measure of the uncertainty at the scale, $\sigma,$ for a class of non-exponential distributions. The coupled stretched…

Statistical Mechanics · Physics 2026-01-14 Kenric P. Nelson

The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…

Machine Learning · Statistics 2025-11-25 Kenric P. Nelson

We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…

Data Analysis, Statistics and Probability · Physics 2007-10-24 Peter Sunehag

We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…

Disordered Systems and Neural Networks · Physics 2007-11-20 Fariel Shafee

The Tsallis entropy given for a positive parameter $\alpha$ can be considered as a modification of the classical Shannon entropy. For the latter, corresponding to $\alpha=1$, there exist many axiomatic characterizations. One of them based…

Mathematical Physics · Physics 2017-04-27 Sonja Jäckle , Karsten Keller

We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…

Dynamical Systems · Mathematics 2025-04-18 Tianyu Wang , Weisheng Wu

We compute the entanglement entropy of a wide class of exactly solvable models which may be characterized as describing matter coupled to gauge fields. Our principle result is an entanglement sum rule which states that entropy of the full…

Strongly Correlated Electrons · Physics 2013-09-11 Brian Swingle

When at equilibrium, large-scale systems obey conventional thermodynamics because they belong to microscopic configurations (or states) that are typical. Crucially, the typical states usually represent only a small fraction of the total…

Statistical Mechanics · Physics 2025-01-14 Bernat Corominas-Murtra , Rudolf Hanel , Petr Jizba

The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…

Quantum Physics · Physics 2021-04-09 M. X. Luo , X. Wang

We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…

Statistical Mechanics · Physics 2007-05-23 Rudolf Hanel , Stefan Thurner

The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…

Statistical Mechanics · Physics 2007-05-23 Qiuping A. Wang

We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using…

Statistical Mechanics · Physics 2007-05-23 Oscar Sotolongo-Costa , Alejandro Gonzalez Gonzalez , Francois Brouers

The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy, and a complete proof of the uniqueness theorem for the…

Statistical Mechanics · Physics 2009-10-31 Sumiyoshi Abe

Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, where the number of accessible configurations $W(N)$ grows exponentially with the number of degrees of freedom~$N$.…

Statistical Mechanics · Physics 2026-03-05 Henrik Jeldtoft Jensen , Petr Jizba , Piergiulio Tempesta

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…

Quantum Physics · Physics 2014-02-19 F. Dupuis , L. Kraemer , P. Faist , J. M. Renes , R. Renner

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…

Statistical Mechanics · Physics 2009-10-31 R. Salazar , R. Toral

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…

Statistical Mechanics · Physics 2016-04-13 Gabriele Sicuro , Piergiulio Tempesta

This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…

Mathematical Physics · Physics 2024-05-02 Supriyo Dutta , Shigeru Furuichi , Partha Guha