How can one construct dynamical systems obeying the first and second laws of thermodynamics: mean energy is conserved and entropy increases with time? This book answers the question for classical probability (Part I) and quantum probability (Part II). A novel feature is the introduction of heat particles which supply thermal noise and represent the kinetic energy of the molecules. When applied to chemical reactions, the theory leads to the usual nonlinear reaction-diffusion equations as well as modifications of them. These can exhibit oscillations, or can converge to equilibrium. In this second edition, the text is simplified in parts and the bibliography has been expanded. The main difference is the addition of two new chapters; in the first, classical fluid dynamics is introduced. A lattice model is developed, which in the continuum limit gives us the Euler equations. The five Navier???Stokes equations are also presented, modified by a diffusion term in the continuity equation. The second addition is in the last chapter, which now includes estimation theory, both classical and quantum, using information geometry.

How can one construct dynamical systems obeying the first and second laws of thermodynamics: mean energy is conserved and entropy increases with time? This book answers the question for classical probability (Part I) and quantum probability (Part II). A novel feature is the introduction of heat particles which supply thermal noise and represent the kinetic energy of the molecules. When applied to chemical reactions, the theory leads to the usual nonlinear reaction-diffusion equations as well as modifications of them. These can exhibit oscillations, or can converge to equilibrium. In this second edition, the text is simplified in parts and the bibliography has been expanded. The main difference is the addition of two new chapters; in the first, classical fluid dynamics is introduced. A lattice model is developed, which in the continuum limit gives us the Euler equations. The five Navier???Stokes equations are also presented, modified by a diffusion term in the continuity equation. The second addition is in the last chapter, which now includes estimation theory, both classical and quantum, using information geometry.

Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Coleman's Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory. This title, first published in 2017, has been reissued as an Open Access publication on Cambridge Core.

Thermal and statistical physics has established the principles and procedures needed to understand and explain the properties of systems consisting of macroscopically large numbers of particles. By developing microscopic statistical physics and macroscopic classical thermodynamic descriptions in tandem, Statistical and Thermal Physics: An Introduction provides insight into basic concepts and relationships at an advanced undergraduate level. This second edition is updated throughout, providing a highly detailed, profoundly thorough, and comprehensive introduction to the subject and features exercises within the text as well as end-of-chapter problems. Part I of this book consists of nine chapters, the first three of which deal with the basics of equilibrium thermodynamics, including the fundamental relation. The following three chapters introduce microstates and lead to the Boltzmann definition of the entropy using the microcanonical ensemble approach. In developing the subject, the ideal gas and the ideal spin system are introduced as models for discussion. The laws of thermodynamics are compactly stated. The final three chapters in Part I introduce the thermodynamic potentials and the Maxwell relations. Applications of thermodynamics to gases, condensed matter, and phase transitions and critical phenomena are dealt with in detail. Initial chapters in Part II present the elements of probability theory and establish the thermodynamic equivalence of the three statistical ensembles that are used in determining probabilities. The canonical and the grand canonical distributions are obtained and discussed. Chapters 12-15 are concerned with quantum distributions. By making use of the grand canonical distribution, the Fermi-Dirac and Bose-Einstein quantum distribution functions are derived and then used to explain the properties of ideal Fermi and Bose gases. The Planck distribution is introduced and applied to photons in radiation and to phonons on solids. The last five chapters cover a variety of topics: the ideal gas revisited, nonideal systems, the density matrix, reactions, and irreversible thermodynamics. A flowchart is provided to assist instructors on planning a course. Key Features: Fully updated throughout, with new content on exciting topics, including black hole thermodynamics, Heisenberg antiferromagnetic chains, entropy and information theory, renewable and nonrenewable energy sources, and the mean field theory of antiferromagnetic systems Additional problem exercises with solutions provide further learning opportunities Suitable for advanced undergraduate students in physics or applied physics. Michael J.R. Hoch spent many years as a visiting scientist at the National High Magnetic Field Laboratory at Florida State University, USA. Prior to this, he was a professor of physics and the director of the Condensed Matter Physics Research Unit at the University of the Witwatersrand, Johannesburg, where he is currently professor emeritus in the School of Physics.

Statistical Mechanics: Fundamentals and Model Solutions, Second Edition Fully updated throughout and with new chapters on the Mayer expansion for classical gases and on cluster expansion for lattice models, this new edition of Statistical Mechanics: Fundamentals and Model Solutions provides a comprehensive introduction to equilibrium statistical mechanics for advanced undergraduate and graduate students of mathematics and physics. The author presents a fresh approach to the subject, setting out the basic assumptions clearly and emphasizing the importance of the thermodynamic limit and the role of convexity. With problems and solutions, the book clearly explains the role of models for physical systems, and discusses and solves various models. An understanding of these models is of increasing importance as they have proved to have applications in many areas of mathematics and physics. Features Updated throughout with new content from the field An established and well-loved textbook Contains new problems and solutions for further learning opportunity Author Professor Teunis C. Dorlas is at the Dublin Institute for Advanced Studies, Ireland.

The principal message of this book is that thermodynamics and statistical mechanics will benefit from replacing the unfortunate, misleading and mysterious term "entropy" with a more familiar, meaningful and appropriate term such as information, missing information or uncertainty. This replacement would facilitate the interpretation of the "driving force" of many processes in terms of informational changes and dispel the mystery that has always enshrouded entropy.It has been 140 years since Clausius coined the term "entropy"; almost 50 years since Shannon developed the mathematical theory of "information" - subsequently renamed "entropy". In this book, the author advocates replacing "entropy" by "information", a term that has become widely used in many branches of science.The author also takes a new and bold approach to thermodynamics and statistical mechanics. Information is used not only as a tool for predicting distributions but as the fundamental cornerstone concept of thermodynamics, held until now by the term "entropy".The topics covered include the fundamentals of probability and information theory; the general concept of information as well as the particular concept of information as applied in thermodynamics; the re-derivation of the Sackur-Tetrode equation for the entropy of an ideal gas from purely informational arguments; the fundamental formalism of statistical mechanics; and many examples of simple processes the "driving force" for which is analyzed in terms of information.

The principal message of this book is that thermodynamics and statistical mechanics will benefit from replacing the unfortunate, misleading and mysterious term "entropy" with a more familiar, meaningful and appropriate term such as information, missing information or uncertainty. This replacement would facilitate the interpretation of the "driving force" of many processes in terms of informational changes and dispel the mystery that has always enshrouded entropy.It has been 140 years since Clausius coined the term "entropy"; almost 50 years since Shannon developed the mathematical theory of "information" - subsequently renamed "entropy". In this book, the author advocates replacing "entropy" by "information", a term that has become widely used in many branches of science.The author also takes a new and bold approach to thermodynamics and statistical mechanics. Information is used not only as a tool for predicting distributions but as the fundamental cornerstone concept of thermodynamics, held until now by the term "entropy".The topics covered include the fundamentals of probability and information theory; the general concept of information as well as the particular concept of information as applied in thermodynamics; the re-derivation of the Sackur-Tetrode equation for the entropy of an ideal gas from purely informational arguments; the fundamental formalism of statistical mechanics; and many examples of simple processes the "driving force" for which is analyzed in terms of information.

This third edition of one of the most important and best selling textbooks in statistical physics, is a graduate level text suitable for students in physics, chemistry, and materials science.The discussion of strongly interacting condensed matter systems has been expanded. A chapter on stochastic processes has also been added with emphasis on applications of the Fokker-Planck equation.The modern theory of phase transitions occupies a central place. The chapter devoted to the renormalization group approach is largely rewritten and includes a detailed discussion of the basic concepts and examples of both exact and approximate calculations. The development of the basic tools includes a chapter on computer simulations in which both Monte Carlo method and molecular dynamics are introduced, and a section on Brownian dynamics added.The theories are applied to a number of important systems such as liquids, liquid crystals, polymers, membranes, Bose condensation, superfluidity and superconductivity. There is also an extensive treatment of interacting Fermi and Bose systems, percolation theory and disordered systems in general.

This third edition of one of the most important and best selling textbooks in statistical physics, is a graduate level text suitable for students in physics, chemistry, and materials science.The discussion of strongly interacting condensed matter systems has been expanded. A chapter on stochastic processes has also been added with emphasis on applications of the Fokker-Planck equation.The modern theory of phase transitions occupies a central place. The chapter devoted to the renormalization group approach is largely rewritten and includes a detailed discussion of the basic concepts and examples of both exact and approximate calculations. The development of the basic tools includes a chapter on computer simulations in which both Monte Carlo method and molecular dynamics are introduced, and a section on Brownian dynamics added.The theories are applied to a number of important systems such as liquids, liquid crystals, polymers, membranes, Bose condensation, superfluidity and superconductivity. There is also an extensive treatment of interacting Fermi and Bose systems, percolation theory and disordered systems in general.

This thesis explores several interdisciplinary topics at the border of theoretical physics and biology, presenting results that demonstrate the power of methods from statistical physics when applied to neighbouring disciplines. From birth-death processes in switching environments to discussions on the meaning of quasi-potential landscapes in high-dimensional spaces, this thesis is a shining example of the efficacy of interdisciplinary research. The fields advanced in this work include game theory, the dynamics of cancer, and invasion of mutants in resident populations, as well as general contributions to the theory of stochastic processes. The background material provides an intuitive introduction to the theory and applications of stochastic population dynamics, and the use of techniques from statistical physics in their analysis. The thesis then builds on these foundations to address problems motivated by biological phenomena.

Despite more than half a century of theoretical work, the Casimir effect is still not as fully understood as some suppose. In this treatise, the author uncovers new puzzles and paradoxes concerning this mysterious phenomenon. In particular, he clearly demonstrates that the most sophisticated theories fail when confronted with dielectrics in which the refractive index is not uniform but gradually changes.

This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described. Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas.

Geostationary or equatorial synchronous satellites are a daily reminder of our space efforts during the past two decades. The nightly television satellite weather picture, the intercontinental telecommunications of television transmissions and telephone conversations, and the establishrnent of educational programs in remote regions on Earth are constant reminders of the presence of these satellites. As used here, the term 'geo stationary' must be taken loosely because, in the long run, the satellites will not remain 'stationary' with respect to an Earth-fixed reference frame. This results from the fact that these satellites, as is true for all satellites, are incessantly subject to perturbations other than the central-body attraction of the Earth. Among the more predominant pertur bations are: the ellipticity of the Earth's equator, the Sun and Moon, and solar radiation pressure. Higher harmonics of the Earth's potential and tidal effects also influence satellite motion, but they are of second order when compared to the predominant perturbations. This volume deals with the theory of geostationary satellites. It consists of seven chapters. Chapter 1 provides a general discussion including a brief history of geostationary satellites and their practical applications. Chapter 2 describes the Earth's gravitational potential field and the methodology of solving the geostationary satellite problem. Chapter 3 treats the effect of Earth's equatorial ellipticity (triaxiality) on a geostationary satellite. Chapter 4 deals with the effects of the Sun and Moon on the satellite's motion while Chapter 5 presents the combined influences of the Sun, Moon and solar radiation pressure. Chapter 6 describes various station-keeping techniques which may be used to make geostationary satellites practically stationary. Finally, Chapter 7 describes the verification of the theory developed in Chapters 3, 4 and 5 by utilizing the Early Bird synchronous satellite observed data as well as its numerically integrated results.

Thermodynamics is used increasingly in ecology to understand the system properties of ecosystems because it is a basic science that describes energy transformation from a holistic view. In the last decade, many contributions to ecosystem theory based on thermodynamics have been published, therefore an important step toward integrating these theories and encouraging a more wide spread use of them is to present them in one volume.
An ecosystem consists of interdependent living organisms that are also interdependent with their environment, all of which are involved in a constant transfer of energy and mass within a general state of equilibrium or dis-equilibrium. Thermodynamics can quantify exactly how "organized" or "disorganized" a system is - an extremely useful to know when trying to understand how a dynamic ecosystem is behaving.
A part of the Environmental and Ecological (Math) Modeling series, Thermodynamics and Ecology is a book-length study - the first of its kind - of the current thinking on how an ecosystem can be explained and predicted in terms of its thermodynamical behavior. After the introductory chapters on the fundamentals of thermodynamics, the book explains how thermodynamic theory can be specifically applied to the "measurement" of an ecosystem, including the assessment of its state of entropy and enthalpy. Additionally, it will show economists how to put these theories to use when trying to quantify the movement of goods and services through another type of complex living system - a human society.

Multilayer networks is a rising topic in Network Science which characterizes the structure and the function of complex systems formed by several interacting networks. Multilayer networks research has been propelled forward by the wide realm of applications in social, biological and infrastructure networks and the large availability of network data, as well as by the significance of recent results, which have produced important advances in this rapidly growing field. This book presents a comprehensive account of this emerging field. It provides a theoretical introduction to the main results of multilayer network science.

This classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work. The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century.

Emergence and complexity refer to the appearance of higher-level properties and behaviours of a system that obviously comes from the collective dynamics of that system's components. These properties are not directly deducible from the lower-level motion of that system. Emergent properties are properties of the "whole'' that are not possessed by any of the individual parts making up that whole. Such phenomena exist in various domains and can be described, using complexity concepts and thematic knowledges. This book highlights complexity modelling through dynamical or behavioral systems. The pluridisciplinary purposes, developed along the chapters, are able to design links between a wide-range of fundamental and applicative Sciences. Developing such links - instead of focusing on specific and narrow researches - is characteristic of the Science of Complexity that we try to promote by this contribution.

This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane-Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics. This manifests itself through topological choices for the fractional momentum spacings. The general model is derived by mapping exact models of quantized Hall states onto spin chains. The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.

A thorough understanding of statistical mechanics depends strongly on the insights and manipulative skills that are acquired through the solving of problems. Problems on Statistical Mechanics provides over 120 problems with model solutions, illustrating both basic principles and applications that range from solid-state physics to cosmology. An introductory chapter provides a summary of the basic concepts and results that are needed to tackle the problems, and also serves to establish the notation that is used throughout the book. The problems themselves occupy five chapters, progressing from the simpler aspects of thermodynamics and equilibrium statistical ensembles to the more challenging ideas associated with strongly interacting systems and nonequilibrium processes. Comprehensive solutions to all of the problems are designed to illustrate efficient and elegant problem-solving techniques. Where appropriate, the authors incorporate extended discussions of the points of principle that arise in the course of the solutions. The appendix provides useful mathematical formulae.

The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters - written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks - offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.

This book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. Applications of the formalisms are worked out in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The question of gauge dependence of the effective potential and the Nielsen identities are explained. The nonrestoration of some symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are also described thoroughly. Other topics include (1+1)- and (2+1)-dimensional field theories at finite temperature and phase transitions, derivative expansion, linear response theory and the question of infrared divergences at finite temperature. In addition, examples of nonequilibrium phenomena are discussed with the disoriented chiral condensates as an illustration.This book is a very useful tool for graduate students, teachers and researchers in theoretical physics.

This book collects contributions to the XXIII international conference "Nonlinear dynamics of electronic systems". Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.

This book presents a selection of advanced lectures from leading researchers, providing recent theoretical results on strongly coupled quantum field theories. It also analyzes their use for describing new quantum states, which are physically realizable in condensed matter, cold-atomic systems, as well as artificial materials. It particularly focuses on the engineering of these states in quantum devices and novel materials useful for quantum information processing. The book offers graduate students and young researchers in the field of modern condensed matter theory an updated review of the most relevant theoretical methods used in strongly coupled field theory and string theory. It also provides the tools for understanding their relevance in describing the emergence of new quantum states in a variety of physical settings. Specifically, this proceedings book summarizes new and previously unrelated developments in modern condensed matter physics, in particular: the interface of condensed matter theory and quantum information theory; the interface of condensed matter physics and the mathematics emerging from the classification of the topological phases of matter, such as topological insulators and topological superconductors; and the simulation of condensed matter systems with cold atoms in optical lattices.

This book is designed as a practical and intuitive introduction to probability, statistics and random quantities for physicists. The book aims at getting to the main points by a clear, hands-on exposition supported by well-illustrated and worked-out examples. A strong focus on applications in physics and other natural sciences is maintained throughout. In addition to basic concepts of random variables, distributions, expected values and statistics, the book discusses the notions of entropy, Markov processes, and fundamentals of random number generation and Monte-Carlo methods.

Over 130 years ago, James Clerk Maxwell introduced his hypothetical "demon" as a challenge to the scope of the second law of thermodynamics. Fascination with the demon persisted throughout the development of statistical and quantum physics, information theory, and computer science, and links have been established between Maxwell's demon and each of these disciplines. The demon's seductive quality makes it appealing to physical scientists, engineers, computer scientists, biologists, psychologists, and historians and philosophers of science. Since the publication of Maxwell's Demon: Entropy, Information, Computing in 1990, Maxwell's demon has been the subject of renewed and increased interest by numerous researchers in the fields mentioned above. Updated and expanded, Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing retains many of the seminal papers that appeared in the first edition, including the original thoughts of James Clerk Maxwell and William Thomson; a historical review by Martin Klein; and key articles by Leo Szilard, Leon Brillouin, Rolf Landauer, and Charles Bennett that led to new branches of research on the demon. This second edition contains newer articles by Landauer, Bennett, and others, related to Landauer's principle; connections with quantum mechanics; algorithmic information; and the thermodynamics and limits of computation. The book also includes two separate bibliographies: an alphabetical listing by author and a chronological bibliography that is annotated by the editors and contains selected quotes from the books and articles listed. The bibliography has more than doubled in size since publication of the first edition and now contains over 570 entries.