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Related papers: An additive variant of Tsallis generalized entropy

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In this letter, we study the limit behavior of the evolution of Tsallis entropy in self-gravitating systems. The study is carried out under two different situations, drawing the same conclusion. No matter in the energy transfer process or…

Statistical Mechanics · Physics 2017-10-11 Yahui Zheng , Jiulin Du , Faku Liang

A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…

Chaotic Dynamics · Physics 2009-11-10 Henk van Beijeren

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

During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…

Statistical Mechanics · Physics 2009-11-07 Michael Nauenberg

In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…

Statistical Mechanics · Physics 2007-05-23 Lapo Casetti , Michael Kastner

We calculate the fluctuation of the energy of a system in Tsallis statistics following the finite heat bath canonical ensemble approach. We obtain this fluctuation as the second derivative of the logarithm of the partition function plus an…

Statistical Mechanics · Physics 2009-11-07 F. Q. Potiguar , U. M. S. Costa

Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in simple thermodynamic systems with temperature-independent heat capacities is TC/k. A…

General Physics · Physics 2009-11-13 David Sands

The thermodynamic stability conditions (TSC) of nonadditive and composable entropies are discussed. Generally the concavity of a nonadditive entropy with respect to internal energy is not necessarily equivalent to the corresponding TSC. It…

Statistical Mechanics · Physics 2009-11-10 Tatsuaki Wada

An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution,…

Statistical Mechanics · Physics 2026-05-29 Kenric P. Nelson

A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…

Statistical Mechanics · Physics 2010-08-18 B. N. Tiwari , Vinod Chandra , Subhashish Banerjee

We numerically determine the entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the…

Statistical Mechanics · Physics 2016-08-17 Yoshiyuki Chiba , Naoko Nakagawa

After introducing the fundamental properties of self-gravitating systems, we present an application of Tsallis' generalized entropy to the analysis of their thermodynamic nature. By extremizing the Tsallis entropy, we obtain an equation of…

Statistical Mechanics · Physics 2009-11-10 Masa-aki Sakagami , Atsushi Taruya

We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the…

Statistical Mechanics · Physics 2007-09-23 Michele Campisi

Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…

General Relativity and Quantum Cosmology · Physics 2009-11-11 J. P. Badiali

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 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

A few decades after Hill's work on nano-thermodynamics, the development of a thermodynamic framework, to account consistently for the fluctuations of small systems due to their interactions with the surrounding environment, is still…

Statistical Mechanics · Physics 2019-09-23 Salvatore Calabrese , Lamberto Rondoni , Amilcare Porporato

There exists only one generalization of the classical Boltzmann-Gibbs-Shannon entropy functional to a one-parametric family of additive entropy functionals. We find analytical solution to the corresponding extension of the classical…

Statistical Mechanics · Physics 2009-11-07 Alexander N. Gorban , Iliya V. Karlin , Hans Christian Ottinger

Starting with the additivity condition for Lyapunov functions of master equation, we derive a one-parametric family of entropy functions which may be appropriate for a description of certain effects of finiteness of statistical systems, in…

Statistical Mechanics · Physics 2009-11-07 Alexander N. Gorban , Iliya V. Karlin

A unified framework to describe the adiabatic class of ensembles in the generalized statistical mechanics based on Schwammle-Tsallis two parameter (q, q') entropy is proposed. The generalized form of the equipartition theorem, virial…

Statistical Mechanics · Physics 2013-08-09 R. Chandrashekar , J. Segar