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An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…

Mathematical Physics · Physics 2007-05-23 V. Garcia-Morales , J. Pellicer

Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical…

Statistical Mechanics · Physics 2016-05-05 Peter Hänggi , Stefan Hilbert , Jörn Dunkel

Schmidt et al (Phys Rev Lett 86, 1191 (2001)) observe and analyze a negative specific heat in Na clusters. The analysis is done within the framework of Boltzmann-Gibbs equilibrium statistical mechanics. We argue that this is not the only…

Statistical Mechanics · Physics 2007-05-23 C. Tsallis , B. J. C. Cabral , A. Rapisarda , V. Latora

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined…

Statistical Mechanics · Physics 2023-08-03 Zi-Kui Liu

We explore the thermodynamics of a novel solution for the Reissner-Nordstr\"{o}m-Anti-de Sitter (AdS) black hole, uniquely incorporating the Gauss-Bonnet term. Unlike previous studies that primarily focused on standard General Relativity or…

General Relativity and Quantum Cosmology · Physics 2025-10-24 M. Z. Bhatti , Kazuharu Bamba , I. Siddique , Bander Almutairi , Z. Yousaf

In this work, Gibbs paradox was discussed from the view of observer. The limitations of real observer are analyzed quantitatively. The entropy of mixing was found to be determined by both the identification ability and the information…

Classical Physics · Physics 2016-12-12 Liangsuo Shu , Xiaokang Liu , Suyi Huang , Shiping Jin

Large entropy fluctuations in a nonequilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2-freedom model with the so-called Gauss time-reversible thermostat. The local fluctuations (on a…

Chaotic Dynamics · Physics 2009-10-31 Boris Chirikov

Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…

Statistical Mechanics · Physics 2015-03-19 Stefan Thurner , Rudolf Hanel

Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…

Statistical Mechanics · Physics 2009-11-10 Constantino Tsallis , Celia Anteneodo , Lisa Borland , Roberto Osorio

We have studied finite $N$-body $D$-dimensional nonextensive ideal gases and harmonic oscillators, by using the maximum-entropy methods with the $q$- and normal averages ($q$: the entropic index). The validity range, specific heat and…

Statistical Mechanics · Physics 2015-05-18 Hideo Hasegawa

The features of the fundamental thermodynamical relation (expressing entropy as function of state variables) that arise from the self-gravitating character of a system are analyzed. The models studied include not only a spherically…

General Relativity and Quantum Cosmology · Physics 2009-10-28 Erik A. Martinez

Tsallis has proposed a generalization of Boltzmann-Gibbs thermostatistics by introducing a family of generalized nonextensive entropy functionals with a single parameter $q$. These reduce to the extensive Boltzmann-Gibbs form for $q=1$, but…

Statistical Mechanics · Physics 2007-05-23 Bruce M. Boghosian

The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…

Statistical Mechanics · Physics 2008-11-26 Jörn Dunkel , Peter Talkner , Peter Hänggi

Complex systems that are characterized by strong correlations and fat-tailed distribution functions have been argued to be incompatible within the framework of Boltzmann-Gibbs entropy. As an alternative, so-called generalized entropies were…

Statistical Mechanics · Physics 2022-08-15 Rudolf Hanel , Stefan Thurner

Our previous works have shown the statistical mechanics of self-gravitating system. In this paper, we will show its thermodynamics and compare our results with observations and simulations. We propose that our statistical mechanics can be…

Cosmology and Nongalactic Astrophysics · Physics 2011-12-30 Dong-Biao Kang

We demonstrate that the Gibbs-Shannon entropy is applicable to non-equilibrium systems of any size and boundary conditions. The change in microscopic entropy can be attributed to the stochastic nature of dynamic processes and to the…

Statistical Mechanics · Physics 2020-10-13 Jianzhong Wu

There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this…

Information Theory · Computer Science 2009-06-30 Oded Kafri

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…

Probability · Mathematics 2007-05-23 Christof Kuelske , Arnaud Le Ny , Frank Redig

We are interested in the study of Gibbs and equilbrium probabilities on the lattice $\mathbb{R}^{\mathbb{N}}$. Consider the unilateral full-shift defined on the non-compact set $\mathbb{R}^{\mathbb{N}}$ and an $\alpha$-H\"older continuous…

Dynamical Systems · Mathematics 2021-11-09 Artur O. Lopes , Victor Vargas

We consider Pimsner algebras that arise from C*-correspondences of finite rank, as dynamical systems with their rotational action. We revisit the Laca-Neshveyev classification of their equilibrium states at positive inverse temperature…

Operator Algebras · Mathematics 2019-02-26 Evgenios T. A. Kakariadis