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Constantino Tsallis

Bio: Constantino Tsallis is an academic researcher from National Institute of Standards and Technology. The author has contributed to research in topics: Statistical mechanics & Entropy (statistical thermodynamics). The author has an hindex of 61, co-authored 337 publications receiving 24535 citations. Previous affiliations of Constantino Tsallis include Massachusetts Institute of Technology & National Council for Scientific and Technological Development.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a generalized form of entropy was proposed for the Boltzmann-Gibbs statistics with the q→1 limit, and the main properties associated with this entropy were established, particularly those corresponding to the microcanonical and canonical ensembles.
Abstract: With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS q ≡k [1 – ∑ i=1 W p i q ]/(q-1), whereq∈ℝ characterizes the generalization andp i are the probabilities associated withW (microscopic) configurations (W∈ℕ). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq→1 limit.

8,239 citations

Book
14 Oct 2009
TL;DR: In this article, the Boltzmann-Gibbs Statistical Mechanics (BSM) theory is generalized to nonextensive statistical mechanics and applied in thermodynamic and non-thermodynamic applications.
Abstract: Basics or How the Theory Works.- Historical Background and Physical Motivations.- Learning with Boltzmann-Gibbs Statistical Mechanics.- Generalizing What We Learnt: Nonextensive Statistical Mechanics.- Foundations or Why the Theory Works.- Stochastic Dynamical Foundations of~Nonextensive Statistical Mechanics.- Deterministic Dynamical Foundations of Nonextensive Statistical Mechanics.- Generalizing Nonextensive Statistical Mechanics.- Applications or What for the Theory Works.- Thermodynamical and Nonthermodynamical Applications.- Last (But Not Least).- Final Comments and Perspectives.

1,793 citations

Journal ArticleDOI
TL;DR: In this paper, the Gibbs-Jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form S and of physically appropriate constraints, and the consequences of some special choices for (iii) and their formal and practical implications for the various physical systems that have been studied in the literature are analyzed.
Abstract: The Gibbs–Jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form S and of physically appropriate constraints. For instance, for the usual canonical ensemble, one adopts (i) S 1 =−k∑ i p i ln p i , (ii) ∑ipi=1, and (iii) ∑ i p i e i =U 1 ({ei}≡ eigenvalues of the Hamiltonian; U1≡ internal energy). Equilibrium consists in optimizing S1 with regard to {pi} in the presence of constraints (ii) and (iii). Within the recently introduced nonextensive statistics, (i) is generalized into Sq=k[1−∑ipiq]/[q−1] (q→1 reproduces S1), (ii) is maintained, and (iii) is generalized in a manner which might involve piq. In the present effort, we analyze the consequences of some special choices for (iii), and their formal and practical implications for the various physical systems that have been studied in the literature. To illustrate some mathematically relevant points, we calculate the specific heat respectively associated with a nondegenerate two-level system as well as with the classical and quantum harmonic oscillators.

1,278 citations

Book ChapterDOI

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01 Jan 2022
TL;DR: The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas as discussed by the authors , and it was originally introduced by Clausius in 1865 along abstract lines focusing on thermodynamical irreversibility of macroscopic physical processes.
Abstract: The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas. It was originally introduced by Clausius in 1865 along abstract lines focusing on thermodynamical irreversibility of macroscopic physical processes. In the next decade, Boltzmann made the genius connection—further developed by Gibbs—of the entropy with the microscopic world, which led to the formulation of a new and impressively successful physical theory, thereafter named statistical mechanics. The extension to quantum mechanical systems was formalized by von Neumann in 1927, and the connections with the theory of communications and, more widely, with the theory of information were respectively introduced by Shannon in 1948 and Jaynes in 1957. Since then, over fifty new entropic functionals emerged in the scientific and technological literature. The most popular among them are the additive Renyi one introduced in 1961, and the nonadditive one introduced in 1988 as a basis for the generalization of the Boltzmann–Gibbs and related equilibrium and nonequilibrium theories, focusing on natural, artificial and social complex systems. Along such lines, theoretical, experimental, observational and computational efforts, and their connections to nonlinear dynamical systems and the theory of probabilities, are currently under progress. Illustrative applications, in physics and elsewhere, of these recent developments are briefly described in the present synopsis.

877 citations

Book
15 Apr 2004
TL;DR: A great variety of complex phenomena in many scientific fields exhibit power-law behavior, reflecting a hierarchical or fractal structure as mentioned in this paper, and these phenomena seem to be susceptible to description using approaches drawn from thermodynamics or statistical mechanics, particularly approaches involving the maximization of entropy and of Boltzmann-Gibbs statistical mechanics.
Abstract: A great variety of complex phenomena in many scientific fields exhibit power-law behavior, reflecting a hierarchical or fractal structure. Many of these phenomena seem to be susceptible to description using approaches drawn from thermodynamics or statistical mechanics, particularly approaches involving the maximization of entropy and of Boltzmann-Gibbs statistical mechanics and standard laws in a natural way. The book addresses the interdisciplinary applications of these ideas, and also on various phenomena that could possibly be quantitatively describable in terms of these ideas.

843 citations


Cited by
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Journal ArticleDOI
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.

9,441 citations

Journal ArticleDOI
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.

7,412 citations

Proceedings ArticleDOI
22 Jan 2006
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

7,116 citations

Journal ArticleDOI
TL;DR: An overview of the CHARMM program as it exists today is provided with an emphasis on developments since the publication of the original CHARMM article in 1983.
Abstract: CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecu- lar simulation program. It has been developed over the last three decades with a primary focus on molecules of bio- logical interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estima- tors, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numer- ous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

7,035 citations

Journal ArticleDOI
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations