This book covers the broad subject of equilibrium statistical mechanics along with many advanced and modern topics such as nucleation, spinodal decomposition, inherent structures of liquids and liquid crystals. Unlike other books on the market, this comprehensive text not only deals with the primary fundamental ideas of statistical mechanics but also covers contemporary topics in this broad and rapidly developing area of chemistry and materials science.

This invaluable book provides a broad introduction to a rapidly growing area of nonequilibrium statistical physics. The first part of the book complements the classical book on the Langevin and Fokker-Planck equations (H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer, 1996)). Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book, such as the method of similarity solution, the method of characteristics, transformation of diffusion processes into the Wiener process in different prescriptions, harmonic noise and relativistic Brownian motion. Connection between the Langevin equation and Tsallis distribution is also discussed.Due to the growing interest in the research on the generalized Langevin equations, several of them are presented. They are described with some details.Recent research on the integro-differential Fokker-Planck equation derived from the continuous time random walk model shows that the topic has several aspects to be explored. This equation is worked analytically for the linear force and the generic waiting time probability distribution function. Moreover, generalized Klein-Kramers equations are also presented and discussed. They have the potential to be applied to natural systems, such as biological systems.

Thermodynamics and information touch theory every facet of chemistry. However, the physical chemistry curriculum digested by students worldwide is still heavily skewed toward heat/work principles established more than a century ago. Rectifying this situation, Chemical Thermodynamics and Information Theory with Applications explores applications drawn from the intersection of thermodynamics and information theory-two mature and far-reaching fields. In an approach that intertwines information science and chemistry, this book covers: The informational aspects of thermodynamic state equations The algorithmic aspects of transformations-compression, expansion, cyclic, and more The principles of best-practice programming How molecules transmit and modify information via collisions and chemical reactions Using examples from physical and organic chemistry, this book demonstrates how the disciplines of thermodynamics and information theory are intertwined. Accessible to curiosity-driven chemists with knowledge of basic calculus, probability, and statistics, the book provides a fresh perspective on time-honored subjects such as state transformations, heat and work exchanges, and chemical reactions.

Weighted Residual Methods: Principles, Modifications and Applications introduces a range of WRMs, providing examples that show how they can be used to solve complex engineering problems with greater accuracy and computational efficiency. Examples focus on non-linear problems, including the motion of a spherical particle, nanofluid flow and heat transfer, magnetohydrodynamic flow and heat transfer, and micropolar fluid flow and heat transfer. These are important factors in understanding processes, such as filtration, combustion, air and water pollution and micro contamination. In addition to the applications, the reader is provided with full derivations of equations and summaries of important field research.

This book is the fifth volume of papers on advanced problems of phase transitions and critical phenomena, the first four volumes appeared in 2004, 2007, 2012, and 2015. It aims to compile reviews in those aspects of criticality and related subjects that are of current interest. The seven chapters discuss criticality of complex systems, where the new, emergent properties appear via collective behaviour of simple elements. Since all complex systems involve cooperative behaviour between many interconnected components, the field of phase transitions and critical phenomena provides a very natural conceptual and methodological framework for their study.As the first four volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the 'Ising lectures' - a traditional annual workshop on phase transitions and critical phenomena which aims to bring together scientists working in the field of phase transitions with university students and those who are interested in the subject.

Der Grundkurs Theoretische Physik deckt in 7 Banden alle fur das Diplom und fur Bachelor/Master-Studiengange massgeblichen Gebiete ab. Jeder Band vermittelt das im jeweiligen Semester notwendige theoretisch-physikalische Rustzeug. UEbungsaufgaben mit ausfuhrlichen Loesungen dienen der Vertiefung des Stoffs. Der 6. Band zur Statistischen Physik wurde fur die Neuauflage grundlegend uberarbeitet und um aktuelle Entwicklungen erganzt. Durch die zweifarbige Gestaltung ist der Stoff jetzt noch ubersichtlicher gegliedert.

Ecosystems, the human brain, ant colonies, and economic networks are all complex systems displaying collective behaviour, or emergence, beyond the sum of their parts. Complexity science is the systematic investigation of these emergent phenomena, and stretches across disciplines, from physics and mathematics, to biological and social sciences. This introductory textbook provides detailed coverage of this rapidly growing field, accommodating readers from a variety of backgrounds, and with varying levels of mathematical skill. Part I presents the underlying principles of complexity science, to ensure students have a solid understanding of the conceptual framework. The second part introduces the key mathematical tools central to complexity science, gradually developing the mathematical formalism, with more advanced material provided in boxes. A broad range of end of chapter problems and extended projects offer opportunities for homework assignments and student research projects, with solutions available to instructors online. Key terms are highlighted in bold and listed in a glossary for easy reference, while annotated reading lists offer the option for extended reading and research.

The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides fundamental theory, concepts, modelling and analysis of the physical, mathematical, thermodynamical and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems involving phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics and functional analysis, and is thoroughly enriched with many appropriate references for an in-depth background reading on theorems. This new edition includes more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems. The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems.

This book highlights latest advancement in Mathematics, Physics and Chemistry. With the theme of "Innovative Science towards Sustainability and Industrial Revolution 4.0", ICFAS 2020 brings together leading experts, scientific communities and industrialists working in the field of applied sciences and mathematics from all over the world to share the most recent developments and cutting-edge discoveries addressing sustainability and industrial revolution 4.0 in the field. The conference topics include green materials, molecular modelling, catalysis, nanodevices and nanosystems, smart materials applications, solar cells technology, computational mathematics, data analysis and visualization, and numerical analysis. The contents of this book are useful for researchers, students, and industrial practitioners in the areas of Mathematics, Physics and Chemistry as most of the topics are in line with IR 4.0.

Flocks of birds, schools of fish and swarms of locusts display amazing forms of collective motion, while huge numbers of glow worms can emit light signals with almost unbelievable synchronization. These and many other collective phenomena in animal societies take place according to laws very similar to those governing the collective behavior in the inanimate nature, such as the magnetization of iron and the light radiation of lasers. During recent years, this has led to the study of swarm behavior as a challenging new field of science, in which ideas from the physical world are applied in order to understand the formation and structure of animal swarms. From these studies, it has become clear that such collective behavior of animals emerges in a self-organized way, without any need of overall coordination. In this book, we present different swarm phenomena of the animal world and compare them to their counterparts in physics, in a conceptual and non-technical way, addressed to a general readership.

Application of New Cybernetics in Physics describes the application of new cybernetics to physical problems and the resolution of basic physical paradoxes by considering external observer influence. This aids the reader in solving problems that were solved incorrectly or have not been solved. Three groups of problems of the new cybernetics are considered in the book: (a) Systems that can be calculated based on known physics of subsystems. This includes the external observer influence calculated from basic physical laws (ideal dynamics) and dynamics of a physical system influenced even by low noise (observable dynamics). (b) Emergent systems. This includes external noise from the observer by using the black box model (complex dynamics), external noise from the observer by using the observer's intuition (unpredictable dynamics), defining boundaries of application of scientific methods for system behavior prediction, and the role of the observer's intuition for unpredictable systems. (c) Methods for solution of basic physical paradoxes by using methods of the new cybernetics: the entropy increase paradox, Schroedinger's cat paradox (wave package reduction in quantum mechanics), the black holes information paradox, and the time wormholes grandfather paradox. All of the above paradoxes have the same resolution based on the principles of new cybernetics. Indeed, even a small interaction of an observer with an observed system results in their time arrows' alignment (synchronization) and results in the paradox resolution and appearance of the universal time arrow.

This book focuses on Creep in Ceramics. The book consists of two parts. In part A general knowledge of creep in ceramics is considered, while part B specifies creep in technologically important ceramics, namely creep in oxide ceramics, carnides and nitrides. While covering all relevant information regarding raw materials and characterization of creep in ceramics, the book also summarizes most recent innovations and developments in this field as a result of extensive literature search.

This book explores water geothermometry, a highly relevant topic in the exploration and exploitation of geothermal energy. Presenting theoretical geothermometers and indicators of CO2 fugacity, it describes a rigorous new approach entirely based on thermodynamics. The book will appeal to geothermal geoscientists, especially those working in research institutions and companies around the globe. It is also of interest to students on advanced courses in applied geochemistry, water-rock interaction and other related areas.

'The four laws that do not drive the universe: elements of thermodynamics for the curious and intelligent. The second purpose of Ben-NaimaEURO (TM)s book is to explain thermodynamics and show its relationship to information theory. This explanation makes the present book worth reading in its own right. Ben-NaimaEURO (TM)s discussion of the information basis of the second law is lucid and well worth reading.'CHOICEThis book provides a clear and mystery-free presentation of the central concepts in thermodynamics - probability, entropy, Helmholtz energy and Gibbs energy. It presents the concepts of entropy, free energy and various formulations of the Second Law in a friendly, simple language. It is devoid of all kinds of fancy and pompous statements made by authors of popular science books who write on this subject.The book focuses on the Four Laws of Thermodynamics. As it is said in the dedication page, this book is addressed to readers who might have already been exposed to Atkins' book having a similar title. It challenges both the title, and the contents of Atkins' book, Four Laws That Drive The Universe. One can glean from the title of this new book that the author's views are diametrically opposed to the views of Atkins.The book is addressed to any curious and intelligent reader. It aims to tickle, and hopefully to satisfy your curiosity. It also aims to challenge your gray matter, and to enrich your knowledge by telling you some facts and ideas regarding the Four Laws of Thermodynamics.

This book is the distilled essence of the author teaching statistical mechanics to juniors, seniors and graduate students for over 50 years in various course settings. It uses a unique approach that leads naturally into the development of all possible ensembles. Much of the later chapters on polymers has previously been available only in the literature. Throughout the book, the assumption is made that the reader is still relatively raw, and mathematical detail is provided that other books leave to the abilities of the reader. While this produces a plethora of equations that mature scientists would regard as unnecessary, it is intended to help those just coming into the field and who want to get the idea without suffering hours of agony wondering, 'where did that come from?'.

This book is the distilled essence of the author teaching statistical mechanics to juniors, seniors and graduate students for over 50 years in various course settings. It uses a unique approach that leads naturally into the development of all possible ensembles. Much of the later chapters on polymers has previously been available only in the literature. Throughout the book, the assumption is made that the reader is still relatively raw, and mathematical detail is provided that other books leave to the abilities of the reader. While this produces a plethora of equations that mature scientists would regard as unnecessary, it is intended to help those just coming into the field and who want to get the idea without suffering hours of agony wondering, 'where did that come from?'.

In this new textbook, a number of unusual applications are discussed in addition to the usual topics covered in a course on Statistical Physics. Examples are: statistical mechanics of powders, Peierls instability, graphene, Bose-Einstein condensates in a trap, Casimir effect and the quantum Hall effect. Superfluidity and super-conductivity (including the physics of high-temperature superconductors) have also been discussed extensively.The emphasis on the treatment of these topics is pedagogic, introducing the basic tenets of statistical mechanics, with extensive and thorough discussion of the postulates, ensembles, and the relevant statistics. Many standard examples illustrate the microcanonical, canonical and grand canonical ensembles, as well as the Bose-Einstein and Fermi-Dirac statistics.A special feature of this text is the detailed presentation of the theory of second-order phase transitions and the renormalization group, emphasizing the role of disorder. Non-equilibrium statistical physics is introduced via the Boltzmann transport equation. Additional topics covered here include metastability, glassy systems, the Langevin equation, Brownian motion, and the Fokker-Planck equation.Graduate students will find the presentation readily accessible, since the topics have been treated with great deal of care and attention to detail.

Temperature and heat, entropy and order or disorder are key classical concepts of physics. These are challenged by searching matter under extreme conditions, such as high (relativistic) energy, strong acceleration or gravitation, or unusual complexity due to long range correlations. In our quest for quark matter all these conditions might occur simultaneously. This book, strongly motivated by the authors' everyday research experiences in the field of high-energy heavy-ion collisions, aims to bundle these challenges to modern physics.

The main topic is at the heart of thermodynamics --the very concept of temperature, its use and extensions. New developments on this issue are both applications and foundations of non-extensive statistics, as well as concepts borrowed from gravity and string theory to describe the surprisingly statistical behavior of elementary matter at the highest accelerator energies of the world.

The reader will benefit from bringing these new developments in one book together, by having the view of classical and modern concepts at the heart of physics across the problems related to high-energy, high acceleration and high complexity.

After reviewing the classical approaches, the author discusses the dual-gravity and non-extensive statistical aspects of heavy-ion collisions, describing these experimental findings with the use of the concept of temperature."

This textbook establishes a theoretical framework for understanding deep learning models of practical relevance. With an approach that borrows from theoretical physics, Roberts and Yaida provide clear and pedagogical explanations of how realistic deep neural networks actually work. To make results from the theoretical forefront accessible, the authors eschew the subject's traditional emphasis on intimidating formality without sacrificing accuracy. Straightforward and approachable, this volume balances detailed first-principle derivations of novel results with insight and intuition for theorists and practitioners alike. This self-contained textbook is ideal for students and researchers interested in artificial intelligence with minimal prerequisites of linear algebra, calculus, and informal probability theory, and it can easily fill a semester-long course on deep learning theory. For the first time, the exciting practical advances in modern artificial intelligence capabilities can be matched with a set of effective principles, providing a timeless blueprint for theoretical research in deep learning.

This textbook introduces thermodynamics with a modern approach, starting from four fundamental physical facts (the atomic nature of matter, the indistinguishability of atoms and molecules of the same species, the uncertainty principle, and the existence of equilibrium states) and analyzing the behavior of complex systems with the tools of information theory, in particular with Shannon's measure of information (or SMI), which can be defined on any probability distribution. SMI is defined and its properties and time evolution are illustrated, and it is shown that the entropy is a particular type of SMI, i.e. the SMI related to the phase-space distribution for a macroscopic system at equilibrium. The connection to SMI allows the reader to understand what entropy is and why isolated systems follow the Second Law of Thermodynamics. The Second Llaw is also formulated for other systems, not thermally isolated and even open with respect to the transfer of particles. All the fundamental aspects of thermodynamics are derived and illustrated with several examples in the first part of the book. The second part addresses important applications of thermodynamics, covering phase transitions, mixtures and solutions (including the Kirkwood-Buff approach and solvation thermodynamics), chemical equilibrium, and the outstanding properties of water.This textbook is unique in two aspects. First, thermodynamics is introduced with a novel approach, based on information theory applied to macroscopic systems at equilibrium. It is shown that entropy is a particular case of Shannon's measure of information (SMI), and the properties and time evolution of the SMI are used to explain the Second Law of Thermodynamics. This represents a real breakthrough, as classical thermodynamics cannot explain entropy, nor clarify why systems should obey the Second Law. Second, this textbook offers the reader the possibility to get in touch with important and advanced applications of thermodynamics, to address the topics discussed in the second part of the book. Although they may go beyond the content of a typical introductory course on thermodynamics, some of them can be important in the curriculum chosen by the student. At the same time, they are of appealing interest to more advanced scholars.

'Ben-Naim convincingly argues that SMI not only gives a simpler and more broadly applicable definition of entropy, but also clears up much of the historical and modern confusion surrounding the second law. This book will interest any individual who wants to understand how SMI gives a clear definition of entroy.'CHOICE ConnectThis book discusses the proper definitions of entropy, the valid interpretation of entropy and some useful applications of the concept of entropy. Unlike many books which apply the concept of entropy to systems for which it is not even defined (such as living systems, black holes and the entire universe), these applications will help the reader to understand the meaning of entropy. It also emphasizes the limitations of the applicability of the concept of entropy and the Second Law of Thermodynamics. As with the previous books by the author, this book aims at a clear and mystery-free presentation of the central concept in thermodynamics - the entropy.In this book, the concepts of entropy and the Second Law are presented in a friendly, simple language. It is devoid of all kinds of fancy and pompous statements made by authors of popular science books who write on this subject.

'Ben-Naim convincingly argues that SMI not only gives a simpler and more broadly applicable definition of entropy, but also clears up much of the historical and modern confusion surrounding the second law. This book will interest any individual who wants to understand how SMI gives a clear definition of entroy.'CHOICE ConnectThis book discusses the proper definitions of entropy, the valid interpretation of entropy and some useful applications of the concept of entropy. Unlike many books which apply the concept of entropy to systems for which it is not even defined (such as living systems, black holes and the entire universe), these applications will help the reader to understand the meaning of entropy. It also emphasizes the limitations of the applicability of the concept of entropy and the Second Law of Thermodynamics. As with the previous books by the author, this book aims at a clear and mystery-free presentation of the central concept in thermodynamics - the entropy.In this book, the concepts of entropy and the Second Law are presented in a friendly, simple language. It is devoid of all kinds of fancy and pompous statements made by authors of popular science books who write on this subject.

This book is a compilation of selected reviews by Professor Michael E Fisher. Fisher's major contributions to physics have been in equilibrium statistical mechanics, and have spanned the entire range of that subject. He has been credited with bringing together, and teaching a common language to chemists and physicists working on diverse problems of phase transitions.About the Book by the AuthorTalking informally in a clear way came naturally once intrigued by a field of science; that helped me accept the invitation to publish a collection of review articles. And working actively in an area has led me to express what is new in basic terms, with lots of figures framed, typically, via two- or three-dimensional images. Also encouraging was that my reviews - with crucial references - were recognized in 1983 by the U.S. National Academy of Sciences through their James Murray Luck Award for 'excellence in scientific reviewing.'However, the first article in this collection is by my postdoctoral mentor, Cyril Domb, whose inaugural lecture at King's College London was entitled: 'Statistical Physics and its Problems.' This provides readers with a context for some of the topics later reviewed in greater depth. Among the aspects then explained, are the various critical exponents: , , , and - the special exponents and for the correlation functions, and the scaling relations. Phase diagrams are examined thoroughly along with tricritical and bicritical points, Kosterlitz-Thouless points, protocriticality, etc. Random walks along with vicious walkers and their reunions are introduced. Biophysics is touched upon. The final article: 'Statistical Physics in the Oeuvre of Chen Ning Yang,' stems from the 2015 Conference on 60 Years of Yang-Mills Gauge Field Theories.In conclusion, it is hoped that a wide range of readers (and some experts also!) will enjoy dipping into the variety of reviews collected here.