Generalized Statistical Mechanics
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| Author | : Constantino Tsallis |
| Publisher | : Springer Nature |
| Total Pages | : 575 |
| Release | : 2023-01-30 |
| Genre | : Science |
| ISBN | : 3030795691 |
This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics. Conceived nearly 150 years ago by Maxwell, Boltzmann and Gibbs, the BG theory, one of the greatest monuments of contemporary physics, exhibits many impressive successes in physics, chemistry, mathematics, and computational sciences. Presently, several thousands of publications by scientists around the world have been dedicated to its nonextensive generalization. A variety of applications have emerged in complex systems and its mathematical grounding is by now well advanced. Since the first edition release thirteen years ago, there has been a vast amount of new results in the field, all of which have been incorporated in this comprehensive second edition. Heavily revised and updated with new sections and figures, the second edition remains the go-to text on the subject. A pedagogical introduction to the BG theory concepts and their generalizations – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT’s, complex networks, among others – is presented in this book, as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions. Introduction to Nonextensive Statistical Mechanics is suitable for students and researchers with an interest in complex systems and statistical physics.
| Author | : Jan Naudts |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 209 |
| Release | : 2011-02-07 |
| Genre | : Mathematics |
| ISBN | : 0857293559 |
The domain of non-extensive thermostatistics has been subject to intensive research over the past twenty years and has matured significantly. Generalised Thermostatistics cuts through the traditionalism of many statistical physics texts by offering a fresh perspective and seeking to remove elements of doubt and confusion surrounding the area. The book is divided into two parts - the first covering topics from conventional statistical physics, whilst adopting the perspective that statistical physics is statistics applied to physics. The second developing the formalism of non-extensive thermostatistics, of which the central role is played by the notion of a deformed exponential family of probability distributions. Presented in a clear, consistent, and deductive manner, the book focuses on theory, part of which is developed by the author himself, but also provides a number of references towards application-based texts. Written by a leading contributor in the field, this book will provide a useful tool for learning about recent developments in generalized versions of statistical mechanics and thermodynamics, especially with respect to self-study. Written for researchers in theoretical physics, mathematics and statistical mechanics, as well as graduates of physics, mathematics or engineering. A prerequisite knowledge of elementary notions of statistical physics and a substantial mathematical background are required.
| Author | : Evaldo M. F. Curado |
| Publisher | : |
| Total Pages | : 8 |
| Release | : 1990 |
| Genre | : |
| ISBN | : |
| Author | : Themis Matsoukas |
| Publisher | : Springer |
| Total Pages | : 363 |
| Release | : 2019-05-08 |
| Genre | : Science |
| ISBN | : 3030041492 |
This book gives the definitive mathematical answer to what thermodynamics really is: a variational calculus applied to probability distributions. Extending Gibbs's notion of ensemble, the Author imagines the ensemble of all possible probability distributions and assigns probabilities to them by selection rules that are fairly general. The calculus of the most probable distribution in the ensemble produces the entire network of mathematical relationships we recognize as thermodynamics. The first part of the book develops the theory for discrete and continuous distributions while the second part applies this thermodynamic calculus to problems in population balance theory and shows how the emergence of a giant component in aggregation, and the shattering transition in fragmentation may be treated as formal phase transitions. While the book is intended as a research monograph, the material is self-contained and the style sufficiently tutorial to be accessible for self-paced study by an advanced graduate student in such fields as physics, chemistry, and engineering.
| Author | : R.K. Pathria |
| Publisher | : Elsevier |
| Total Pages | : 542 |
| Release | : 2017-02-21 |
| Genre | : Science |
| ISBN | : 1483186881 |
Statistical Mechanics discusses the fundamental concepts involved in understanding the physical properties of matter in bulk on the basis of the dynamical behavior of its microscopic constituents. The book emphasizes the equilibrium states of physical systems. The text first details the statistical basis of thermodynamics, and then proceeds to discussing the elements of ensemble theory. The next two chapters cover the canonical and grand canonical ensemble. Chapter 5 deals with the formulation of quantum statistics, while Chapter 6 talks about the theory of simple gases. Chapters 7 and 8 examine the ideal Bose and Fermi systems. In the next three chapters, the book covers the statistical mechanics of interacting systems, which includes the method of cluster expansions, pseudopotentials, and quantized fields. Chapter 12 discusses the theory of phase transitions, while Chapter 13 discusses fluctuations. The book will be of great use to researchers and practitioners from wide array of disciplines, such as physics, chemistry, and engineering.
| Author | : Daniel Charles Mattis |
| Publisher | : World Scientific |
| Total Pages | : 274 |
| Release | : 2003 |
| Genre | : Science |
| ISBN | : 9789812381668 |
Elementary concepts in statistics and probability - The ising model and the lattice gas - Elements of thermodynamics - Statistical mechanics - The world of bosons - All about fermions : theories of metals, superconductors, semiconductors - Kinetic theory - The transfer matrix - Some uses of quantum field theory in statistical physics.
| Author | : Rodney J. Baxter |
| Publisher | : Elsevier |
| Total Pages | : 499 |
| Release | : 2016-06-12 |
| Genre | : Science |
| ISBN | : 1483265943 |
Exactly Solved Models in Statistical Mechanics
| Author | : Sacha Friedli |
| Publisher | : Cambridge University Press |
| Total Pages | : 643 |
| Release | : 2017-11-23 |
| Genre | : Mathematics |
| ISBN | : 1107184827 |
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
| Author | : William D. Henline |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1970 |
| Genre | : Carnegie-Mellon University |
| ISBN | : |
| Author | : Brian Cowan |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 337 |
| Release | : 2005-09-14 |
| Genre | : Science |
| ISBN | : 1911298364 |
Building on the material learned by students in their first few years of study, this book presents an advanced level course on statistical and thermal physics. It begins with a review of the formal structure of statistical mechanics and thermodynamics considered from a unified viewpoint. After a brief revision of non-interacting systems, emphasis is laid on interacting systems. First, weakly interacting systems are considered, where the interest is in seeing how such interactions cause small deviations from the non-interacting case. Second, systems are examined where interactions lead to drastic changes, namely phase transitions. A number of specific examples are given, and these are unified within the Landau theory of phase transitions. The final chapter of the book looks at non-equilibrium systems and the way these evolve towards equilibrium. Here, fluctuations play a vital role, as is formalized in the Fluctuation–Dissipation theorem. Contents:The Methodology of Statistical MechanicsPractical Calculations with Ideal SystemsNon-Ideal GasesPhase TransitionsFluctuations and Dynamics Readership: Upper undergraduate and postgraduate students of statistical mechanics.
