Predictive Statistical Mechanics
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Predictive Statistical Mechanics
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Author : Roberto Luzzi
language : en
Publisher:
Release Date : 2014-01-15
Predictive Statistical Mechanics written by Roberto Luzzi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Predictive Statistical Mechanics
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Author : Roberto Luzzi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Predictive Statistical Mechanics written by Roberto Luzzi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
Chapters 1 to 5 include a description of the philosophy, foundations, and construction (methodology) of the formalism, including the derivation of a nonequilibrium grand-canonical ensemble for far-from-equilibrium systems as well as the derivation of a quantum nonlinear kinetic theory and a response function theory together with a theory of scattering. In chapter 6 applications of the theory are cataloged, making comparisons with experimental data (a basic step for the validation of any theory). Chapter 7 is devoted to the description of irreversible thermodynamics, providing a far-reaching generalization of Informational-Statistical Thermodynamics. The last chapter gives an overall picture of the formalism, and questions and criticisms related to it are discussed.
E T Jaynes
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Author : Edwin T. Jaynes
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-04-30
E T Jaynes written by Edwin T. Jaynes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-04-30 with Mathematics categories.
The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance.
E T Jaynes Papers On Probability Statistics And Statistical Physics
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Author : R.D. Rosenkrantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
E T Jaynes Papers On Probability Statistics And Statistical Physics written by R.D. Rosenkrantz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance.
Statistical Foundations Of Irreversible Thermodynamics
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Author : Roberto Luzzi
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 2000-10-11
Statistical Foundations Of Irreversible Thermodynamics written by Roberto Luzzi and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-11 with Science categories.
Some aspects of the physics of many-body systems arbitrarily away from equilibrium, mainly the characterization and irreversible evolution of their macroscopic state, are considered. The present status of phenomenological irreversible thermodynamics is described. An approach for building a statistical thermodynamics - dubbed Informational-Statistical-Thermodynamics - based on a non-equilibrium statistical ensemble formalism is presented. The formalism can be considered as encompassed within the scope of the so-called Predictive Statistical Mechanics, in which the predictability of future states in terms of the knowledge of present and past states, and the question of historicity in the case of systems with complex behaviour, is its main characteristic. The book is recommended for researchers in the area of non-equilibrium statistical mechanics and thermodynamics, as well as a textbook for advanced courses for graduate students in the area of condensed matter physics.
Scaling Limits In Statistical Mechanics And Microstructures In Continuum Mechanics
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Author : Errico Presutti
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-01
Scaling Limits In Statistical Mechanics And Microstructures In Continuum Mechanics written by Errico Presutti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.
Making Sense Of Statistical Mechanics
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Author : Jean Bricmont
language : en
Publisher: Springer Nature
Release Date : 2022-02-11
Making Sense Of Statistical Mechanics written by Jean Bricmont and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-11 with Science categories.
Many people, including physicists, are confused about what the Second Law of thermodynamics really means, about how it relates to the arrow of time, and about whether it can be derived from classical mechanics. They also wonder what entropy really is: Is it all about information? But, if so, then, what is its relation to fluxes of heat? One might ask similar questions about probabilities: Do they express subjective judgments by us, humans, or do they reflect facts about the world, i.e. frequencies. And what notion of probability is used in the natural sciences, in particular statistical mechanics? This book addresses all of these questions in the clear and pedagogical style for which the author is known. Although valuable as accompaniment to an undergraduate course on statistical mechanics or thermodynamics, it is not a standard course book. Instead it addresses both the essentials and the many subtle questions that are usually brushed under the carpet in such courses. As one of the most lucid accounts of the above questions, it provides enlightening reading for all those seeking answers, including students, lecturers, researchers and philosophers of science.
Uncertainty Quantification And Predictive Computational Science
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Author : Ryan G. McClarren
language : en
Publisher: Springer
Release Date : 2018-11-23
Uncertainty Quantification And Predictive Computational Science written by Ryan G. McClarren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-23 with Science categories.
This textbook teaches the essential background and skills for understanding and quantifying uncertainties in a computational simulation, and for predicting the behavior of a system under those uncertainties. It addresses a critical knowledge gap in the widespread adoption of simulation in high-consequence decision-making throughout the engineering and physical sciences. Constructing sophisticated techniques for prediction from basic building blocks, the book first reviews the fundamentals that underpin later topics of the book including probability, sampling, and Bayesian statistics. Part II focuses on applying Local Sensitivity Analysis to apportion uncertainty in the model outputs to sources of uncertainty in its inputs. Part III demonstrates techniques for quantifying the impact of parametric uncertainties on a problem, specifically how input uncertainties affect outputs. The final section covers techniques for applying uncertainty quantification to make predictions under uncertainty, including treatment of epistemic uncertainties. It presents the theory and practice of predicting the behavior of a system based on the aggregation of data from simulation, theory, and experiment. The text focuses on simulations based on the solution of systems of partial differential equations and includes in-depth coverage of Monte Carlo methods, basic design of computer experiments, as well as regularized statistical techniques. Code references, in python, appear throughout the text and online as executable code, enabling readers to perform the analysis under discussion. Worked examples from realistic, model problems help readers understand the mechanics of applying the methods. Each chapter ends with several assignable problems. Uncertainty Quantification and Predictive Computational Science fills the growing need for a classroom text for senior undergraduate and early-career graduate students in the engineering and physical sciences and supports independent study by researchers and professionals who must include uncertainty quantification and predictive science in the simulations they develop and/or perform.
Frontiers Of Nonequilibrium Statistical Physics
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Author : Gerald T. Moore
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Frontiers Of Nonequilibrium Statistical Physics written by Gerald T. Moore and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The four-week period fran May 20 to June 16, 1984 was an intensive period of advanced study on the foundations and frontiers of nonequili brium statistical physics (NSP). During the first two weeks of this period, an advanced-study course on the "Foundations of NSP" was con ducted in Albuquerque under the sponsorship of the University of New Mexico Center for High-Technology Materials. This was followed by a two-week NATO Advanced Study Insti tute on the "Frontiers of NSP" in Santa Fe under the same directorship. Many Students attended both meetings. This book comprises proceedings based on those lectures and covering a broad spectrum of topics in NSP ranging fran basic problems in quantum measurement theory to analogies between lasers and Darwinian evolution. The various types of quantum distribution functions and their uses are treated by several authors. other tools of NSP, such as Langevin equations, Fokker-Planck equations, and master equations, are developed and applied to areas such as laser physics, plasma physics, Brownian motion, and hydrodynamic instabilities. The properties and experimental detection of squeezed states and antibunching are described, as well as experimental tests of the violation of Bell's inequality. Information theory, mean-field theory, reservoir theory, entropy maximization, and even a novel nonlinear generalization of quantum mechanics are used to discuss nonequilibrium phenanena and the approach toward thermodynamic equilibrium.
Statistical Mechanics And The Physics Of Many Particle Model Systems
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Author : Kuzemsky Alexander Leonidovich
language : en
Publisher: World Scientific
Release Date : 2017-02-24
Statistical Mechanics And The Physics Of Many Particle Model Systems written by Kuzemsky Alexander Leonidovich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-24 with Science categories.
The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models. This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography. The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.