Statistical physics Books

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book presents a modern, interdisciplinary perspective on cities and urban systems that combines new data with tools from statistical physics and urban economics. Analysis of mobility patterns and infrastructure networks, as well as spatial and social organization, provide a quantitative description of cities for scientists interested in modeling these complex systems.Trade Review'Every so often along comes a book that attempts a grand synthesis. Marc Barthelemy has put together many ideas from statistical physics with theory in urban economics, fashioning an approach that demonstrates its essential logic and empirical relevance. A book that must be absorbed by urbanists of every persuasion and used to advance our science of cities.' Michael Batty, University College London'Collective effects are often counterintuitive and defeat our imagination. We need specific models to anticipate financial crashes, traffic jams, mass panics. The spontaneous organization of cities falls in the same category of phenomena created by ourselves, humans, but that -- paradoxically – we struggle to understand. This wonderful book summarizes a large number of data and ideas about how cities grow and self-organize, sometimes not in the most efficient way. In his plea for a new science for cities, Marc Barthelemy musters methods from statistical physics for a problem that concerns an ever-growing fraction of humanity.' Jean-Philippe Bouchaud, Capital Fund Management, Paris'… a multi-disciplinary effort to describe and understand the numerous structural aspects of cities and their evolution … This book makes an effort to bring these different points of view together, to find a common scientific language, and to look at cities as systems that show typical features such as complexity, self-organisation and emergence which can be described in the language of statistical physics. …The whole text is a well-written scientific essay and fully referenced to scientific publications from a broad range of disciplines. The data and models are presented with mathematical rigour and illustrated by numerous black-and-white figures. The book is highly interesting for its multi-disciplinary approach as well as for the data presented, and can be recommended to a wide interested readership with a general understanding of mathematics and statistical physics.' Manuel Vogel, Contemporary Physics'Marc Barthelemy refreshes ideas and opens new avenues for further research in urban/economic quantitative geography. Without ignoring 'Founding Fathers' in geography, he suggests inspiring ideas anchored in physics for modelling urban realities. A path toward multidisciplinary analysis, which has still a long way to go before success.' Isabelle Thomas, Université catholique de LouvainTable of ContentsPreface; Acknowledgements; 1. Urban systems; 2. Models and methods; 3. The spatial organization of cities; 4. Infrastructure networks; 5. Mobility patterns; 6. Multimodality in cities; 7. Socio-economical aspects; 8. Systems of cities; 9. Towards a new science of cities; References; Index.

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Book SynopsisDownscaling is a widely used technique for translating information from large-scale climate models to the spatial and temporal scales needed to assess local and regional climate impacts, vulnerability, risk and resilience. This book is a comprehensive guide to the downscaling techniques used for climate data. A general introduction of the science of climate modeling is followed by a discussion of techniques, models and methodologies used for producing downscaled projections, and the advantages, disadvantages and uncertainties of each. The book provides detailed information on dynamic and statistical downscaling techniques in non-technical language, as well as recommendations for selecting suitable downscaled datasets for different applications. The use of downscaled climate data in national and international assessments is also discussed using global examples. This is a practical guide for graduate students and researchers working on climate impacts and adaptation, as well as for policTable of Contents1. Impacts, adaptation, vulnerability and decision making; 2. Global climate models; 3. Assessing climate change impacts at the regional scale; 4. Dynamical downscaling; 5. Empirical-statistical downscaling; 6. Added value of downscaling; 7. Uncertainty in future projections, and approaches for representing uncertainty; 8. Guidance and recommendations for use of (downscaled) climate information; 9. The future of regional downscaling; Index.

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Book SynopsisProceedings of the Workshop on Surface Disordering.

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Book SynopsisThis is a Nova Science Publication.

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Book SynopsisMain terms in the thermodynamics; Spontaneous and non-spontaneous processes; The first law of thermodynamics for open systems; The second law of thermodynamics and main mathematical equations; Thermodynamics of spontaneous and non- spontaneous processes; Correlation of processes for interacting phase-open systems and the surrounding; Kinetics of entropy variation; The Helmholtz energy for spontaneous and non-spontaneous processes; The Gibbs energy in thermodynamically irreversible processes; Practical examples of influence of relation of spontaneous and non-spontaneous processes on technological and natural phenomena; Equations of equilibrium thermodynamics and the method of determination of the process type basing on thermodynamics of spontaneous and non-spontaneous processes; References; Subject Index.

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Book SynopsisStatistical & Condensed Matter Physics - Over the Horizon

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Book SynopsisThis important book focuses on statistical mechanics which is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level. In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules. This ability to make macroscopic predictions based on microscopic properties is the main asset of statistical mechanics over thermodynamics. Both theories are governed by the second law of thermodynamics through the medium of entropy.

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Book SynopsisThis book presents significant research on antioxidants for chemistry and biology, kinetics and mechanisms of molecular, radical and ion reactions in chemistry and biochemistry, chemistry of ozone (reactions of ozone with organic and inorganic compounds, action of antiozonants), application of electron magnetic resonance and nuclear magnetic resonance in chemistry and biology, investigations of the structure and properties of nanocomposites (nanotubes, particularly), investigations on the structure and properties of nanocomposites (nanotubes, particularly), investigations of heterogeneous-heterophases mechanisms of reaction in polymer matrix, preparation and using of organic papanagnets for investigation of radical reactions in chemistry and biology, investigation of kinetic parameters in biochemical reactions, new designs for processing, mechanisms of oxidation and stabilisation of organic compounds (including polymers), polymer blends, composites and filled polymers (preparation, properties and application), and information about genetic construction, reactions with participants of enzymes.

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Book SynopsisBuilding on the material learned by students in their first few years of study, Topics in Statistical Mechanics (Second Edition) 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. There is a brief revision of non-interacting systems, including quantum gases and a discussion of negative temperatures. Following this, emphasis is on interacting systems. First, weakly interacting systems are considered, where the interest is in seeing how small 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 is given, and these are unified within the Landau theory of phase transitions. The final chapter of the book looks at non-equilibrium systems, in particular the way they evolve towards equilibrium. This is framed within the context of linear response theory. Here fluctuations play a vital role, as is formalised in the fluctuation-dissipation theorem.The second edition has been revised particularly to help students use this book for self-study. In addition, the section on non-ideal gases has been expanded, with a treatment of the hard-sphere gas, and an accessible discussion of interacting quantum gases. In many cases there are details of Mathematica calculations, including Mathematica Notebooks, and expression of some results in terms of Special Functions.

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Book SynopsisCalabi-Yau spaces are complex spaces with a vanishing first Chern class, or, equivalently, with a trivial canonical bundle (sheaf), so they admit a Ricci-flat Kähler metric that satisfies the vacuum Einstein equations. Used to construct possibly realistic (super)string models, they are being studied vigorously by physicists and mathematicians alike. Calabi-Yau spaces have also turned up in computations of probability amplitudes in quantum field theory. This book collects and reviews relevant results on several major techniques of (1) constructing such spaces and (2) computing physically relevant quantities such as spectra of massless fields and their Yukawa interactions. These are amended by (3) stringy corrections and (4) results about the moduli space and its geometry, including a preliminary discussion of the still conjectural universal deformation space. It also contains a lexicon of assorted terms and important results and theorems, which can be used independently.The first edition of Calabi-Yau Manifolds: A Bestiary for Physicists was the first systematic book covering Calabi-Yau spaces, related mathematics, and their application in physics. Thirty years on, this new edition explores the intense development in the field since 1992, providing an additional 400 references. It also addresses advances in machine learning and other computer-aided methods that have recently made physically relevant computations feasible, opened new avenues in the field, and begun to deliver concretely on the now 40-year-old promise of string theory. The presentation of ideas, results, and computational methods is complemented by detailed models and sample computations throughout. This second edition also contains a new closing section, outlining the staggering advances of the past three decades and providing suggestions for future reading.

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Book SynopsisHow 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.Table of ContentsClassical Statistical Dynamics: Introduction, Probability Theory; Linear Dynamics; Isolated Dynamics; Isothermal Dynamics; Driven Systems; Fluid Dynamics; Quantum Statistical Dynamics: Introduction, Quantum Probability; Linear Quantum Dynamics; Isolated Quantum Dynamics; Isothermal and Driven Systems; Infinite Systems; Information Geometry.

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Book SynopsisHow 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.Table of ContentsClassical Statistical Dynamics: Introduction, Probability Theory; Linear Dynamics; Isolated Dynamics; Isothermal Dynamics; Driven Systems; Fluid Dynamics; Quantum Statistical Dynamics: Introduction, Quantum Probability; Linear Quantum Dynamics; Isolated Quantum Dynamics; Isothermal and Driven Systems; Infinite Systems; Information Geometry.

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Book SynopsisIn the first part of this book, classical nonequilibrium statistical mechanics is developed. Starting from the Hamiltonian dynamics of the molecules, it leads through the irreversible kinetic equations to the level of fluid mechanics. For simple systems, all the transport coefficients are determined by the molecular properties.The second part of the book treats complex systems that require a more extensive use of statistical concepts. Such problems, which are at the forefront of research, include: continuous time random walks, non-Markovian diffusion processes, percolation and related critical phenomena, transport on fractal structures, transport and deterministic chaos. These “strange transport processes” differ significantly from the usual (diffusive) transport. Their inclusion in a general treatise on statistical mechanics is a special feature of this invaluable book.Table of ContentsStates, dynamical functions, evolution; general formalism of statistical mechanics; reduced distribution functions and correlation functions; the mean field approximation; weak coupling kinetic equation; kinetic equation for dilute gases; kinetic equation for plasmas; properties of kinetic equations; hydrodynamics and tranport; transport and autocorrelation functions; random walks and transport; critical phenomena; transport on percolation structures; maps and transport.

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Book SynopsisStatistical Mechanics is a renowned and accessible introduction to the subject, containing a large number of chapter-ending problems for students.

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Book SynopsisCosmology describes the evolution of the Universe and is based on a description of its beginning from quantum fluctuations. String theory is the only known consistent theory of quantum gravity that can deal with the highest energy scales near the Planck energy, relevant for cosmology's beginning. As a result, only string theory can give a fully consistent picture of cosmological origins. This book describes the best current avenues for obtaining cosmology from string theory. It is aimed at graduate students, and also researchers, with some familiarity with cosmology and string theory, however no detailed knowledge is required. Table of Contents

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Book SynopsisThe birth of a completely new branch of observational astronomy is a rare and exciting occurrence. For a long time, our theories about gravitational waves—proposed by Albert Einstein and others more than a hundred years ago—could never be fully proven, since we lacked the proper technology to do it. That all changed when, on September 14, 2015, instruments at the LIGO Observatory detected gravitational waves for the first time. This book explores the nature of gravitational waves—what they are, where they come from, why they are so significant and why nobody could prove they existed before now. Written in plain language and interspersed with additional explanatory tutorials, it will appeal to lay readers, science enthusiasts, physical science students, amateur astronomers and to professional scientists and astronomers.Trade Review“The material covered and the manner of presentation are at a level somewhat higher than those of the typical popular-science book aimed at the ‘interested lay reader’. … The book also describes all the major GW detectors currently active, as well as many projects planned or under-development. The writing is fluid, the physical book is nicely typeset and very readable … . I think many readers would enjoy and learn much from this book.” (Jonathan Thornburg, The Observatory, Vol. 142 (1291), December, 2022)Table of ContentsChapter 1. 14th September 2015.- Chapter 2. Gravity – From 850,000,000 BCE to 1915 CE.- Chapter 3. Gravity - From 1915 - through Today - and on towards Tomorrow.- Chapter 4. Gravitational Waves – The Long, Long Journey from Half-Seen Chimeras to Highly Studied Certainties.- Chapter 5. Gravitational Waves – Origins and Sources.- Chapter 6. Gravitational Wave Events – Calling the Roll.- Chapter 7. Into the Unknown - the First Years of the Quest for Gravitational Waves.- Chapter 8. Eureka! – A Beginner’s Guide to Making Successful Gravitational Wave Detectors.- Chapter 9. Gravitational Waves and their Detectors - Into the Future - and Beyond.

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Book SynopsisThis introductory textbook/reference addresses the fundamental and mostly applied kinds of models. The focus is on models of dynamic systems that move and change over time. However, the work also proposes new methods of uncertainty treatment, offering supporting examples.Topics and features: Chapters suitable for textbook use in teaching modeling and simulation Includes sections of questions and answers, helpful in didactic work Proposes new methodology in addition to examining conventional approaches Offers some cognitive, more abstract models to give a wider insight on model building The book’s readership may consist of researchers working on multidisciplinary problems, as well educators and students. It may be used while teaching computer simulation, applied mathematics, system analysis and system dynamics.Table of Contents1. Concept of Model.- 2. Continuous System Models.- 3. Differential inclusions, uncertainty and functional sensitivity.- 4. Functional sensitivity applications.- 5. Attainable sets in flight control.- 6. Discrete event models.- 7. Self-organization, dynamics and agent-based model .- 8. The space of models, semi-discrete events with fuzzy logic.- 9. Models and categories.- 10. Fuzzy time instants and time model.- 11. Reversibility and the 5th dimension.- 12. Modeling, simulation and optimization.

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Book SynopsisThis third edition expands on the original material. Large portions of the text have been reviewed and clarified. More emphasis is devoted to machine learning including more modern concepts and examples. This book provides the reader with the main concepts and tools needed to perform statistical analyses of experimental data, in particular in the field of high-energy physics (HEP).It starts with an introduction to probability theory and basic statistics, mainly intended as a refresher from readers’ advanced undergraduate studies, but also to help them clearly distinguish between the Frequentist and Bayesian approaches and interpretations in subsequent applications. Following, the author discusses Monte Carlo methods with emphasis on techniques like Markov Chain Monte Carlo, and the combination of measurements, introducing the best linear unbiased estimator. More advanced concepts and applications are gradually presented, including unfolding and regularization procedures, culminating in the chapter devoted to discoveries and upper limits.The reader learns through many applications in HEP where the hypothesis testing plays a major role and calculations of look-elsewhere effect are also presented. Many worked-out examples help newcomers to the field and graduate students alike understand the pitfalls involved in applying theoretical concepts to actual data.Trade Review“The book is important because, as AI and data science continue to shape the future, much interdisciplinary work is being done in many different domains. It is a very good example of interdisciplinary physics research using AI and data science. ... Graduate students are often expected to apply theoretical knowledge. This book will be an invaluable resource for them, to jumpstart their research by getting equipped with the right statistical and data analysis toolsets.” (Gulustan Dogan, Computing Reviews, August 8, 2023)Table of ContentsPreface to the third edition Preface to previous edition/s 1 Probability Theory 1.1 Why Probability Matters to a Physicist 1.2 The Concept of Probability 1.3 Repeatable and Non-Repeatable Cases 1.4 Different Approaches to Probability 1.5 Classical Probability 1.6 Generalization to the Continuum 1.7 Axiomatic Probability Definition 1.8 Probability Distributions 1.9 Conditional Probability 1.10 Independent Events 1.11 Law of Total Probability 1.12 Statistical Indicators: Average, Variance and Covariance 1.13 Statistical Indicators for a Finite Sample 1.14 Transformations of Variables 1.15 The Law of Large Numbers 1.16 Frequentist Definition of Probability References 2 Discrete Probability Distributions 2.1 The Bernoulli Distribution 2.2 The Binomial Distribution 2.3 The Multinomial Distribution 2.4 The Poisson Distribution References 3 Probability Distribution Functions 3.1 Introduction 3.2 Definition of Probability Distribution Function 3.3 Average and Variance in the Continuous Case 3.4 Mode, Median, Quantiles 3.5 Cumulative Distribution 3.6 Continuous Transformations of Variables 3.7 Uniform Distribution 3.8 Gaussian Distribution 3.9 X^2 Distribution 3.10 Log Normal Distribution 3.11 Exponential Distribution3.12 Other Distributions Useful in Physics 3.13 Central Limit Theorem 3.14 Probability Distribution Functions in More than One Dimension 3.15 Gaussian Distributions in Two or More Dimensions References 4 Bayesian Approach to Probability 4.1 Introduction 4.2 Bayes’ Theorem 4.3 Bayesian Probability Definition 4.4 Bayesian Probability and Likelihood Functions 4.5 Bayesian Inference 4.6 Bayes Factors 4.7 Subjectiveness and Prior Choice 4.8 Jeffreys’ Prior 4.9 Reference priors 4.10 Improper Priors 4.11 Transformations of Variables and Error Propagation References 5 Random Numbers and Monte Carlo Methods 5.1 Pseudorandom Numbers 5.2 Pseudorandom Generators Properties 5.3 Uniform Random Number Generators 5.4 Discrete Random Number Generators 5.5 Nonuniform Random Number Generators 5.6 Monte Carlo Sampling 5.7 Numerical Integration with Monte Carlo Methods 5.8 Markov Chain Monte Carlo References 6 Parameter Estimate 6.1 Introduction 6.2 Inference 6.3 Parameters of Interest 6.4 Nuisance Parameters 6.5 Measurements and Their Uncertainties 6.6 Frequentist vs Bayesian Inference 6.7 Estimators 6.8 Properties of Estimators 6.9 Binomial Distribution for Efficiency Estimate 6.10 Maximum Likelihood Method 6.11 Errors with the Maximum Likelihood Method 6.12 Minimum X^2 and Least-Squares Methods 6.13 Binned Data Samples 6.14 Error Propagation 6.15 Treatment of Asymmetric Errors References7 Combining Measurements7.1 Introduction7.2 Simultaneous Fits and Control Regions7.3 Weighted Average7.4 X^2 in n Dimensions7.5 The Best Linear Unbiased EstimatorReferences 8 Confidence Intervals8.1 Introduction8.2 Neyman Confidence Intervals8.3 Binomial Intervals8.4 The Flip-Flopping Problem8.5 The Unified Feldman–Cousins ApproachReferences 9 Convolution and Unfolding9.1 Introduction9.2 Convolution9.3 Unfolding by Inversion of the Response Matrix9.4 Bin-by-Bin Correction Factors9.5 Regularized Unfolding9.6 Iterative Unfolding9.7 Other Unfolding Methods9.8 Software Implementations9.9 Unfolding in More DimensionsReferences10 Hypothesis Tests10.1 Introduction10.2 Test Statistic10.3 Type I and Type II Errors10.4 Fisher’s Linear Discriminant10.5 The Neyman–Pearson Lemma10.6 Projective Likelihood Ratio Discriminant10.7 Kolmogorov–Smirnov Test10.8 Wilks’ Theorem10.9 Likelihood Ratio in the Search for a New SignalReferences 11 Machine Learning11.1 Supervised and Unsupervised Learning11.2 Terminology11.3 Machine Learning Classification from a Statistical Point of View11.4 Bias-Variance tradeo11.5 Overtraining11.6 Artificial Neural Networks 11.7 Deep Learning11.8 Convolutional Neural Networks11.9 Boosted Decision Trees11.10 Multivariate Analysis ImplementationsReferences 12 Discoveries and Upper Limits12.1 Searches for New Phenomena: Discovery and Upper Limits12.2 Claiming a Discovery12.3 Excluding a Signal Hypothesis12.4 Combined Measurements and Likelihood Ratio12.5 Definitions of Upper Limit12.6 Bayesian Approach12.7 Frequentist Upper Limits12.8 Modified Frequentist Approach: the CLs Method12.9 Presenting Upper Limits: the Brazil Plot12.10 Nuisance Parameters and Systematic Uncertainties12.11 Upper Limits Using the Profile Likelihood12.12 Variations of the Profile-Likelihood Test Statistic12.13 The Look Elsewhere EffectReferences Index

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Book SynopsisThis book is a brief and accessible popular science text intended for a broad audience and of particular interest also to science students and specialists. Using a minimum of mathematics, a number of qualitative and quantitative examples, and clear illustrations, the author explains the science of thermodynamics in its full historical context, focusing on the concepts of energy and its availability and transformation in thermodynamic processes. His ultimate aim is to gain a deep understanding of the second law—the increase of entropy—and its rather disheartening message of a universe descending inexorably into chaos and disorder. It also examines the connection between the second law and why things go wrong in our daily lives. Readers will enhance their science literacy and feel more at home on the science side of author C. P. Snow's celebrated two-culture, science-humanities divide, and hopefully will feel more at home in the universe knowing that the disorder we deal with in our daily lives is not anyone's fault but Nature's. Table of ContentsChapter 1. Introduction.- Chapter 2. The Nature of Heat.- Chapter 3. The Laws of Thermodynamics- Chapter 4. Statistical Interpretation of the Second Law of Thermodynamics- Chapter 5. Implications of the Second Law of Thermodynamics: Why Things Go Wrong.- Chapter 6. So, What's To Do?

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Book SynopsisThis textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams.After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential. Trade Review“Lynch has successfully captured this: I find this book to be uniquely successful in teaching a branch of mathematics together with computing while inspiring students to look at references and explorations beyond the text.” (Patrick Shipman, SIAM Review, Vol. 62 (2), 2020)“This book is meant as an upper level undergraduate or graduate text in dynamical systems. … this is an attractive text, one that I wish I had access to when I was learning dynamical systems, and one that I would be glad to teach from.” (John Starrett, MAA Reviews, July 28, 2019)Table of ContentsPreface.- A Tutorial Introduction to Python.- Differential Equations.- Planar Systems.- Interacting Species.- Limit Cycles.- Hamiltonian Systems, Lyapunov Functions, and Stability.- Bifurcation Theory.- Three-Dimensional Autonomous Systems and Chaos.- Poincaré Maps and Nonautonomous Systems in the Plane.- Local and Global Bifurcations.- The Second Part of Hilbert's Sixteenth Problem.- Delay Differential Equations.- Linear Discrete Dynamical Systems.- Nonlinear Discrete Dynamical Systems.- Complex Iterative Maps.- Electromagnectic Waves and Optical Resonators.- Fractals and Multifractals.- Image Processing with Python.- Chaos Control and Synchronization.- Neural Networks.- Binary Oscillator Computing.- Coursework and Examination-Type Questions.- Solutions to Exercises.- Index of Python Programs.- Index.

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Book SynopsisGoing beyond traditional textbook topics, 'A Modern Course in Statistical Physics' incorporates contemporary research in a basic course on statistical mechanics. From the universal nature of matter to the latest results in the spectral properties of decay processes, this book emphasizes the theoretical foundations derived from thermodynamics and probability theory underlying all concepts in statistical physics. This completely revised and updated third edition continues the comprehensive coverage of numerous core topics and special applications, allowing professors flexibility in designing individualized courses. The inclusion of advanced topics and extensive references makes this an invaluable resource for researchers as well as students -- a textbook that will be kept on the shelf long after the course is completed.Trade Review"In summary, I enthusiastically recommend Reichl's third edition of A Modern Course in Statistical Physics for the advanced student and active researcher . . . I will most definitely keep Reichl's Modern Course in close reach, and expect to be frequently consulting this volume, not only when preparing graduate-level courses, but occasionally also for the sake of my group's research activities." (J Stat Phys, 2010) Table of ContentsPreface to the Third Edition xiii Preface to the First Edition xv 1 Introduction 1 2 Complexity and Entropy 5 2.1 Introduction 5 2.2 Counting Microscopic States 5 2.3 Multiplicity and Entropy of Macroscopic Physical States 9 2.4 Multiplicity and Entropy of a Spin System 10 2.4.1 Multiplicity of a Spin System 10 2.4.2 Entropy of Spin System 11 2.4.2.1 Entropy and Fluctuations About Equilibrium 12 2.4.2.2 Entropy and Temperature 12 2.5 Multiplicity and Entropy of an Einstein Solid 14 2.5.1 Multiplicity of an Einstein Solid 15 2.5.2 Entropy of the Einstein Solid 15 2.6 Multiplicity and Entropy of an Ideal Gas 16 2.6.1 Multiplicity of an Ideal Gas 17 2.6.2 Entropy of an Ideal Gas 18 2.7 Problems 19 3 Thermodynamics 21 3.1 Introduction 21 3.2 Energy Conservation 23 3.3 Entropy 24 3.3.1 Carnot Engine 24 3.3.2 The Third Law 28 3.4 Fundamental Equation of Thermodynamics 29 3.5 Thermodynamic Potentials 32 3.5.1 Internal Energy 33 3.5.2 Enthalpy 34 3.5.3 Helmholtz Free Energy 35 3.5.4 Gibbs Free Energy 37 3.5.5 Grand Potential 38 3.6 Response Functions 40 3.6.1 Thermal Response Functions (Heat Capacity) 40 3.6.2 Mechanical Response Functions 42 3.7 Stability of the Equilibrium State 45 3.7.1 Conditions for Local Equilibrium in a PVT System 45 3.7.2 Conditions for Local Stability in a PVT System 46 3.7.3 Implications of the Stability Requirements for the Free Energies 50 3.7.4 Correlations Between Fluctuations 52 3.8 Cooling and Liquefaction of Gases 55 3.9 Osmotic Pressure in Dilute Solutions 58 3.10 The Thermodynamics of Chemical Reactions 61 3.10.1 The Affinity 62 3.11 Problems 67 4 The Thermodynamics of Phase Transitions 75 4.1 Introduction 75 4.2 Coexistence of Phases: Gibbs Phase Rule 76 4.3 Classification of Phase Transitions 77 4.4 Classical Pure PVT Systems 79 4.4.1 Phase Diagrams 79 4.4.2 Coexistence Curves: Clausius–Clapeyron Equation 80 4.4.3 Liquid–Vapor Coexistence Region 83 4.4.3.1 Lever Rule 84 4.4.3.2 Law of Corresponding States 84 4.4.3.3 Response Functions in the Coexistence Region 85 4.4.4 The van der Waals Equation 87 4.4.5 Steam Engines – The Rankine Cycle 90 4.5 Binary Mixtures 93 4.5.1 Equilibrium Conditions 94 4.6 The Helium Liquids 96 4.6.1 Liquid He 4 97 4.6.1.1 Thermomechanical Effect 97 4.6.2 Liquid He 3 99 4.6.3 Liquid He 3 –He 4 Mixtures 100 4.7 Superconductors 101 4.8 Ginzburg–Landau Theory 104 4.8.1 Theoretical Background 105 4.8.2 Applications of Ginzburg–Landau Theory 108 4.8.2.1 Superfluids 108 4.8.2.2 The Curie Point 108 4.8.2.3 Superconductors 109 4.9 Critical Exponents 110 4.9.1 Definition of Critical Exponents 110 4.9.2 The Critical Exponents for Pure PVT Systems 111 4.9.3 The Critical Exponents for the Curie Point 113 4.9.4 The Critical Exponents for Mean Field Theories 114 4.10 Problems 116 5 Equilibrium Statistical Mechanics I – Canonical Ensemble 121 5.1 Introduction 121 5.2 Probability Density Operator-Canonical Ensemble 123 5.2.1 Energy Fluctuations 124 5.3 Semiclassical Ideal Gas of Indistinguishable Particles 125 5.3.1 Approximations to the Partition Function for Semiclassical Ideal Gases 126 5.3.2 Maxwell–Boltzmann Distribution 129 5.4 Interacting Classical Fluids 131 5.4.1 Density Correlations and the Radial Distribution Function 132 5.4.2 Magnetization Density Correlations 134 5.5 Heat Capacity of a Debye Solid 135 5.6 Order–Disorder Transitions on Spin Lattices 139 5.6.1 Exact Solution for a One-Dimensional Lattice 140 5.6.2 Mean Field Theory for a d-Dimensional Lattice 142 5.6.3 Mean Field Theory of Spatial Correlation Functions 145 5.6.4 Exact Solution to Ising Lattice for d = 2 146 5.7 Scaling 148 5.7.1 Homogeneous Functions 148 5.7.2 Widom Scaling 149 5.7.3 Kadanoff Scaling 152 5.8 Microscopic Calculation of Critical Exponents 155 5.8.1 General Theory 156 5.8.2 Application to Triangular Lattice 158 5.8.3 The S 4 Model 161 5.9 Problems 163 6 Equilibrium Statistical Mechanics II – Grand Canonical Ensemble 167 6.1 Introduction 167 6.2 The Grand Canonical Ensemble 168 6.2.1 Particle Number Fluctuations 169 6.2.2 Ideal Classical Gas 170 6.3 Virial Expansion for Interacting Classical Fluids 172 6.3.1 Virial Expansion and Cluster Functions 172 6.3.2 The Second Virial Coefficient, B 2 (T) 174 6.3.2.1 Square-Well Potential 175 6.3.2.2 Lennard-Jones 6–12 Potential 176 6.4 Black Body Radiation 178 6.5 Ideal Quantum Gases 181 6.6 Ideal Bose–Einstein Gas 183 6.6.1 Bose–Einstein Condensation 187 6.6.2 Experimental Observation of Bose–Einstein Condensation 189 6.7 Ideal Fermi–Dirac Gas 191 6.8 Momentum Condensation in an Interacting Fermi Fluid 197 6.9 Problems 204 7 Brownian Motion and Fluctuation–Dissipation 207 7.1 Introduction 207 7.2 Brownian Motion 208 7.2.1 Langevin Equation 209 7.2.2 Correlation Function and Spectral Density 210 7.3 The Fokker–Planck Equation 212 7.3.1 Probability Flow in Phase Space 214 7.3.2 Probability Flow for Brownian Particle 214 7.3.3 The Strong Friction Limit 217 7.3.3.1 Spectral Decomposition of the Fokker–Planck Equation 218 7.4 Dynamic Equilibrium Fluctuations 221 7.4.1 Regression of Fluctuations 223 7.4.2 Wiener–Khintchine Theorem 225 7.5 Linear Response Theory and the Fluctuation – Dissipation Theorem 226 7.5.1 Linear Response Theory and the Fluctuation – Dissipation Theorem 227 7.5.2 Causality 228 7.5.2.1 Piece-Wise Constant Force 230 7.5.3 The Fluctuation–Dissipation Theorem 231 7.5.4 Power Absorption 233 7.5.4.1 Delta Function Force 234 7.5.4.2 Oscillating Force 234 7.6 Microscopic Linear Response Theory 235 7.6.1 The Perturbed Density Operator 235 7.6.2 The Electric Conductance 236 7.6.3 Power Absorption 241 7.6.4 Thermal Noise 242 7.7 Problems 243 8 Hydrodynamics 247 8.1 Introduction 247 8.2 Navier–Stokes Hydrodynamic Equations 248 8.2.1 Balance Equations 248 8.2.1.1 Mass Density Equations 250 8.2.1.2 Momentum Balance Equation 250 8.2.1.3 Energy and Entropy Balance Equations 252 8.2.2 Entropy Source and Entropy Current 253 8.2.3 Transport Coefficients 257 8.3 Linearized Hydrodynamic Equations 260 8.3.1 Linearization of the Hydrodynamic Equations 260 8.3.2 Transverse Hydrodynamic Modes 264 8.3.3 Longitudinal Hydrodynamic Modes 265 8.3.4 Dynamic Correlation Function and Spectral Density 267 8.4 Light Scattering 268 8.4.1 Scattered Electric Field 270 8.4.2 Intensity of Scattered Light 272 8.5 Hydrodynamics of Mixtures 274 8.5.1 Entropy Production in Multicomponent Systems 275 8.5.2 Fick’s Law for Diffusion 277 8.5.3 Thermal Diffusion 279 8.6 Thermoelectricity 280 8.6.1 The Peltier Effect 280 8.6.2 The Seebeck Effect 282 8.6.3 Thomson Heat 284 8.7 Superfluid Hydrodynamics 284 8.7.1 Superfluid Hydrodynamic Equations 284 8.7.2 Sound Modes 288 8.8 Problems 291 9 Transport Coefficients 295 9.1 Introduction 295 9.2 Elementary Transport Theory 295 9.2.1 The Mean Free Path 296 9.2.2 The Collision Frequency 296 9.2.3 Tracer Particle Current 298 9.2.4 Transport of Molecular Properties 300 9.2.5 The Rate of Reaction 301 9.3 The Boltzmann Equation 303 9.3.1 Derivation of the Boltzmann Equation 304 9.4 Linearized Boltzmann Equation 304 9.4.1 Kinetic Equations for a Two-Component Gas 305 9.4.2 Collision Operators 306 9.5 Coefficient of Self-Diffusion 308 9.5.1 Derivation of the Diffusion Equation 308 9.5.2 Eigenfrequencies of the Lorentz–Boltzmann Equation 309 9.6 Coefficients of Viscosity and Thermal Conductivity 311 9.6.1 Derivation of the Hydrodynamic Equations 311 9.6.2 Eigenfrequencies of the Boltzmann Equation 315 9.6.3 Shear Viscosity and Thermal Conductivity 317 9.7 Computation of Transport Coefficients 318 9.7.1 Sonine Polynomials 319 9.7.2 Diffusion Coefficient 319 9.7.3 Thermal Conductivity 321 9.7.4 Shear Viscosity 323 9.8 Problems 324 10 Nonequilibrium Phase Transitions 327 10.1 Introduction 327 10.2 Near Equilibrium Stability Criteria 328 10.3 The Chemically Reacting Systems 330 10.3.1 The Brusselator – A Nonlinear Chemical Model 330 10.3.2 Boundary Conditions 332 10.3.2.1 Case I Boundary Conditions 332 10.3.2.2 Case II Boundary Conditions 332 10.3.3 Stability Analysis 333 10.3.3.1 Real Frequency ω(k) 334 10.3.3.2 Complex Frequency ω(k) 334 10.3.4 Chemical Crystals 335 10.4 The Rayleigh–Bénard Instability 337 10.4.1 Hydrodynamic Equations and Boundary Conditions 337 10.4.1.1 Rigid Surface Boundary Conditions 339 10.4.1.2 Smooth Surface Boundary Conditions 339 10.4.2 Linear Stability Analysis 340 10.5 Problems 343 Appendix A Probability 345 A.1 Definition of Probability 345 A.2 Probability Distribution Functions 347 A.2.1 Discrete Stochastic Variables 348 A.2.2 Continuous Stochastic Variables 348 A.2.3 Characteristic Function 349 A.2.4 Jointly Distributed Stochastic Variables 350 A.3 Binomial Distributions 351 A.3.1 The Binomial Distribution 351 A.3.2 The Gaussian (or Normal) Distribution 353 A.3.3 The Poisson Distribution 356 A.4 Markov Chains 358 A.5 Probability Density for Classical Phase Space 359 A.6 Quantum Probability Density Operator 363 A.7 Problems 366 Appendix B Exact Differentials 369 Appendix C Ergodicity 373 Appendix D Number Representation 377 D. 1 The Number Representation 383 D. 1. 1 The Number Representation for Bosons 383 D.1. 2 The Number Representation for Fermions 385 D.1. 3 Thermodynamic Averages of Quantum Operators 387 Appendix E Scattering Theory 389 Appendix F Useful Mathematics and Information 395 F. 1 Series Expansions 395 F. 2 Reversion of Series 395 F. 3 Derivatives 395 F. 4 Integrals 395 References 397 Index 403

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Book SynopsisA look at Statistical Physics by renowned Russia-Soviet physicist Yuri Klimontovich of the Moscow State University, MSU Faculty of Physics.

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Book SynopsisThis book aims to cover a broad range of topics in statistical physics, including statistical mechanics (equilibrium and non-equilibrium), soft matter and fluid physics, for applications to biological phenomena at both cellular and macromolecular levels. It is intended to be a graduate level textbook, but can also be addressed to the interested senior level undergraduate. The book is written also for those involved in research on biological systems or soft matter based on physics, particularly on statistical physics.Typical statistical physics courses cover ideal gases (classical and quantum) and interacting units of simple structures. In contrast, even simple biological fluids are solutions of macromolecules, the structures of which are very complex. The goal of this book to fill this wide gap by providing appropriate content as well as by explaining the theoretical method that typifies good modeling, namely, the method of coarse-grained descriptions that extract the most salient features emerging at mesoscopic scales. The major topics covered in this book include thermodynamics, equilibrium statistical mechanics, soft matter physics of polymers and membranes, non-equilibrium statistical physics covering stochastic processes, transport phenomena and hydrodynamics. Generic methods and theories are described with detailed derivations, followed by applications and examples in biology. The book aims to help the readers build, systematically and coherently through basic principles, their own understanding of nonspecific concepts and theoretical methods, which they may be able to apply to a broader class of biological problems.Table of Contents1. Introduction : Biological Systems, and Physical ApproachesBring Physics to Life, Bring Life to Physics. Part A: Equilibrium Structures and Properties. 2. Basic Concepts of Relevant Thermodynamics. 2.1 The First Law and Thermodynamic Potentials. 2.2 The Second Law and Thermodynamic Variational Principles. 3. Basic Methods of Equilibrium Statistical Physics. 3.1 Boltzmann’s Entropy and Probability, Microcanonical Ensemble Theory. 3.2 Canonical Ensemble Theory. 3.3 The Gibbs Canonical Ensemble. 3.4 Grand Canonical Ensemble Theory. 4. Statistical Mechanics of Fluids and Solutions. 4.1 Phase-space Description of Fluids. 4.2 Fluids of Non-interacting Particles. 4.3 Fluids of Interacting Particles. 4.4 Extension to Solutions: Coarse-grained Descriptions. 5. The Coarse-grained Descriptions for Biological Complexes. 6. Water and Weak Electrostatic Interactions. 6.1 Thermodynamic Properties of Water. 6.2 The Interactions in Water. 6.3 Screened Coulomb Interaction. 7. Law of Chemical Forces: Transitions, Reactions and Self-assembly. 7.1 Law of Mass Action (LMA). 7.2 Self-Assembly. 8. Lattice and Ising Models. 8.1 Adsorption and Aggregation of Molecules. 8.2 Binary Mixtures. 8.3 1-D Ising Model and Applications. 9. Response, Fluctuations, Correlations, and Scatterings. 9.1 Linear Responses and Fluctuations: Fluctuation-Response Theorem. 9.2 Scatterings, Fluctuations, and Structures of Matter. 10. Mesoscopic model for Polymers: Flexible Chains. 10.1 Random Walk Model for a Flexible Chain. 10.2 A Flexible Chain under External Fields and Confinements. 10.3 Effects of Segmental Interactions. 10.4 Scaling Theory. 11. Mesoscopic model for Polymers: Semi-flexible Chain Model and Polyelectrolytes. 11.1 Worm-like chain model. 11.2 Fluctuations in nearly straight semi-flexible chains and the force-extension relation. 11.3 Polyelecrolytes. 12. Membranes and Elastic Surfaces. 12.1 Membrane Self-assembly and Transition. 12.2 Mesoscopic Model for Elastic Energies and Shapes. 12.3 Effects of Thermal Undulations. Part B: Non-equilibrium Phenomena. 13.Brownian Motions. 13.1 Brownian Motion/Diffusion Equation Theory. 13.2 Diffusive Transport in Cells. 13.3 Brownian Motion/Langevin Equation Theory. 14. Stochastic Processes, Markov Chains and Master Equations. 14.1 Markov Processes. 14.2 Master Equation. 15. Theory of Markov Processes & The Fokker-Planck Equations. 15.1 Fokker-Planck Equation (FPE). 15.2 The Langevin and Fokker-Planck Equations from Phenomenology and Effective Hamiltonian. 15.3 Solutions of Fokker-Planck Equations, Transition Probabilities and Correlation Functions. 16. The Mean-First Passage Times and Barrier Crossing Rates. 16.1 First Passage Time and Applications. 16.2 Rate Theory: Flux-over Population Method. 17. Dynamic Linear Responses and Time Correlation Functions. 17.1 Time-dependent Linear Response Theory. 17.2 Applications of the Fluctuation–dissipation Theorem. 18. Noise-induced Resonances: Stochastic Resonance and Resonant Activation, and Stochastic Ratchet. 18.1 Stochastic Resonance. 18.2 Resonant Activation (RA) and Stochastic Ratchet. 18.3 Stochastic ratchet. 19. Transport Phenomena and Fluid Dynamics. 19.1 Hydrodynamic Transport Equations. 19.2 Dynamics of Viscous Flow. 20. Dynamics of Polymers and Membranes in Fluids. 20.1 Dynamics of Flexible Polymers. 20.2 Dynamics of a Semiflexible Chain. 20.3 Dynamics of Membrane Undulation. 20.4 A Unified View. 21. Epilogue.

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Book SynopsisThe occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, the fractional quantum statistics of quasiparticles in the fractional quantized Hall effect (FQHE) contributes to the understanding of states found there. Very recent work has indicated that similar possibilities arise for two-dimensional films in certain states of liquid 3He. Perhaps most exciting, although quite speculative at this moment, are recent attempts to apply fractional statistics to spin systems, and specifically to the behaviour of the 2-dimensional copper oxide layers that seem to be critical to the phenomenon of high-temperature superconductivity. It has recently been shown that fractional statistics automatically implies superconductivity of a qualitatively new kind. This collection of reprints with comprehensive commentary will serve as a valuable reference for those interested in the subject but have found it difficult to acquire basic knowledge, or a coherent view of the whole, due to the scattered literature available at present.Trade Review"This is the first book to appear on the topic of anyons in condensed matter physics, a topic now very fashionable because of its possible relevance to high-temperature superconductivity." Science (USA) "I recommend the book for students and specialists in condensed matter physics or theoretical physics, who might want to experience the freshness and novelty of the fractional statistics concepts." Physics World, 1991 "This timely volume offers a clear introduction to the rudiments of fractional statistics ... provides a thought-provoking refresher course in superfluidity and the quantum mechanics of indistinguishable particles." Physics Today, 1992

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Book SynopsisThe material for these volumes has been selected from the past twenty years' examination questions for graduate students at University of California at Berkeley, Columbia University, the University of Chicago, MIT, State University of New York at Buffalo, Princeton University and University of Wisconsin.Trade Review"This collection will present students with the opportunity to test their comprehension and lecturers with ideas for problems." Contemporary Physics

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Book SynopsisThe material for these volumes has been selected from the past twenty years' examination questions for graduate students at University of California at Berkeley, Columbia University, the University of Chicago, MIT, State University of New York at Buffalo, Princeton University and University of Wisconsin.Trade Review"This collection will present students with the opportunity to test their comprehension and lecturers with ideas for problems." Contemporary Physics

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Book SynopsisPotts Models and Related Problems in Statistical MechanicsTrade Review"This is an excellent survey of the Potts model and related matters in statistical mechanics. The first chapter constitutes a good introduction to statistical mechanics with a discussion of modelling principles, partition functions and Hamiltonians, lattices, statistical mechanics functions such as free energy. There are good general discussions of phase transitions, order parameters and critical exponents. Then the Potts models are defined and related to dichromatic polynomials and to the special case of the Ising model. The chapter ends with a discussion of block spin renormalization ... This book is a fine source of basic results about the Potts model and its mathematical physics environment." Mathematical Reviews

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Book SynopsisAt present, existing literature on this subject matter can only be said to relate in minor areas to this work. Important concepts in statistical mechanics, such as frustration, localization, Lifshitz and Griffiths singularities, multicritical points, modulated phases, superselection sectors, spontaneous symmetry breaking and the Haldane phase, strange attractors and the Hausdorff dimension, and many others, are illustrated by exactly soluble lattice models. There are examples of simple lattice models which are shown to give rise to spectacular phase diagrams, with multicritical points and sequences of modulated phases. The models are chosen to enable a concise exposition as well as a connection with real physical systems (as dilute antiferromagnets, spin glasses and modulated magnets). A brief introduction to the properties of dynamical systems, an overview of conformal invariance and the Bethe Ansatz and a discussion of some general methods of statistical mechanics related to spontaneous symmetry breaking, are included in the appendices. A number of exercises are included in the text to help the comprehension of the most representative issues.Table of ContentsDilute systems; lattice models with competing interactions; spin glasses; quantum lattice systems with competing interactions; a brief introduction to dynamical system; the theorems of Aubry; Bethe Ansatz and conformal invariance; unicity of phases, unicity in a sector, and spontaneous symmetry breaking.

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Book SynopsisThe purpose of this textbook is to bring together, in a self-contained introductory form, the scattered material in the field of stochastic processes and statistical physics. It offers the opportunity of being acquainted with stochastic, kinetic and nonequilibrium processes. Although the research techniques in these areas have become standard procedures, they are not usually taught in the normal courses on statistical physics. For students of physics in their last year and graduate students who wish to gain an invaluable introduction on the above subjects, this book is a necessary tool.Table of ContentsPart 1 Stochastic processes and the master equation: stochastic processes; Markovian processes; master equations; Kramers Moyal expansion; Brownian motion, Langevian and Fokker-Planck equations. Part 2 Distribution, BBGKY hierarchy, density operator: probability density as a fluid; BBGKY hierarchy; microscopic balance equations; density operator. Part 3 Linear nonequilibrium thermodynamics and onsager relations: onsager regretion to equilibrium hipotesis; onsager relations; minimum production of entropy. Part 4 Linear response theory, fluctuation-disipation theorem: correlation functions - definitions and properties; linear response theory; fluctuation-disipation theorem. Part 5 Instabilities and far from equilibrium phase-transitions: instabilities, bifurcations, limit circles; noise induced transitions; pattern formation - reaction-diffusion; pattern propagation.

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Book SynopsisNewer Edition Available: Equilibrium Statistical Physics (3rd Edition)This revised and expanded edition of one of the important textbook in statistical physics, is a graduate level text suitable for students in physics, chemistry, and materials science.After a short review of basic concepts, the authors begin the discussion on strongly interacting condensed matter systems with a thorough treatment of mean field and Landau theories of phase transitions. Many examples are worked out in considerable detail. Classical liquids are treated next. Along with traditional approaches to the subject such as the virial expansion and integral equations, newer theories such as perturbation theory and density functional theories are introduced.The modern theory of phase transitions occupies a central place in this book. The development is along historical lines, beginning with the Onsager solution of the two-dimensional Ising model, series expansions, scaling theory, finite-size scaling, and the universality hypothesis. A separate chapter is devoted to the renormalization group approach to critical phenomena. The development of the basic tools is completed in a new chapter on computer simulations in which both Monte Carlo and molecular dynamics techniques are introduced.The remainder of the book is concerned with a discussion of some of the more important modern problems in condensed matter theory. A chapter on quantum fluids deals with Bose condensation, superfluidity, and the BCS and Landau-Ginzburg theories of superconductivity. A new chapter on polymers and membranes contains a discussion of the Gaussian and Flory models of dilute polymer mixtures, the connection of polymer theory to critical phenomena, a discussion of dense polymer mixtures and an introduction to the physical properties of solid and fluid membranes. A chapter on linear response includes the Kubo formalism, the fluctuation-dissipation theorem, Onsager relations and the Boltzmann equation. The last chapter is devoted to disordered materials.Each chapter contains a substantial number of exercises. A manual with a complete set of solutions to these problems is available under separate cover.Table of ContentsReview of Thermodynamics; Statistical Ensembles; Mean Field and Landau Thoery; Dense Gases and Liquids; Critical Phenomena, Part 1; Critical Phenomena II: The Renormalization Group, Quantum Fluids; Linear Response Throey; Disordered Systems.

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Book SynopsisThis book aims to describe in simple terms the new area of statistical mechanics known as spin-glasses, encompassing systems in which quenched disorder is the dominant factor. The book begins with a non-mathematical explanation of the problem, and the modern understanding of the physics of the spin-glass state is formulated in general terms. Next, the 'magic' of the replica symmetry breaking scheme is demonstrated and the physics behind it discussed. Recent experiments on real spin-glass materials are briefly described to demonstrate how this somewhat abstract physics can be studied in the laboratory. The final chapters of the book are devoted to statistical models of neural networks.The material here is self-contained and should be accessible to students with a basic knowledge of theoretical physics and statistical mechanics. It has been used for a one-term graduate lecture course at the Landau Institute for Theoretical Physics.Table of ContentsThe Ising magnetic systems; physics of the spin glass state; replica method; replica symmetry breaking; physics of the replica symmetry breaking; replica symmetry breaking solution near Tc; ultrametricity; scaling in the space of spin glass states; experiments; partial annealing; statistical models of neural networks; the Hopfield model; partial annealing in neural networks; other kinds of neural networks. Appendix: stability of the replica-symmetric solutions.

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Book SynopsisThis 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.

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Book SynopsisThis invaluable textbook is an introduction to statistical physics that has been written primarily for self-study. It provides a comprehensive approach to the main ideas of statistical physics at the level of an introductory course, starting from the kinetic theory of gases and proceeding all the way to Bose-Einstein and Fermi-Dirac statistics. Each idea is brought out with ample motivation and clear, step-by-step, deductive exposition. The key points and methods are presented and discussed on the basis of concrete representative systems, such as the paramagnet, Einstein's solid, the diatomic gas, black body radiation, electric conductivity in metals and superfluidity.The book is written in a stimulating style and is accompanied by a large number of exercises appropriately placed within the text and by self-assessment problems at the end of each chapter. Detailed solutions of all the exercises are provided.Table of ContentsThe kinetic theory of gases - velocity and position distributions of molecules in a gas; Brownian motion; transport coefficients; statistical physics of a paramagnets - essential background in thermodynamics; thermodynamics with magnetic variables; microscopic states and averages; isolated paramagnet - microcanonical ensemble, subsystems and temperature; paramagnet at a given temperature; order, disorder and entropy; comparison with experiment; statistical physics and thermodynamics - the canonical ensemble and thermodynamics; harmonic oscillator and Einstein solid; statistical mechanics of classical systems; statistical mechanics of an ideal gas; the Gibbs paradox and the Third Law; fluctuations and thermodynamic quantities; from ideal gas to photon gas - an ideal gas of molecules with internal degrees of freedom; gases in chemical reactions; phonon gas and the Debye model; thermodynamics of electromagnetic radiation; of fermions and bosons - grand canonical ensemble; statistical mechanics of identical quantum particles; electrical conductivity in metals; boson gas.

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Book SynopsisThis 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.Table of ContentsThermodynamic behaviour - ensembles; the thermodynamic limit for thermodynamic functions - lattice systems; the thermodynamic limit for thermodynamic functions - continuous systems; low density expansions and correlation functions; the problem of phase transitions; group invariance of physical states; the states of statistical mechanics. Appendix: some mathematical tools.

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Book SynopsisThis book covers the foundations of classical thermodynamics, with emphasis on the use of differential forms of classical and quantum statistical mechanics, and also on the foundational aspects. In both contexts, a number of applications are considered in detail, such as the general theory of response, correlations and fluctuations, and classical and quantum spin systems. In the quantum case, a self-contained introduction to path integral methods is given. In addition, the book discusses phase transitions and critical phenomena, with applications to the Landau theory and to the Ginzburg-Landau theory of superconductivity, and also to the phenomenon of Bose condensation and of superfluidity. Finally, there is a careful discussion on the use of the renormalization group in the study of critical phenomena.Table of ContentsThermodynamics; equilibrium classical statistical mechanics; spin Hamiltonians 1 - classical; equilibrium quantum statistical mechanics; identical particles in quantum statistical mechanics; spin Hamiltonians 2 - quantum; phase transitions and critical phenomena; model systems, scaling laws and mean field theories; superconductivity and superfluidity; the renormalization group and critical phenomena.

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Book SynopsisThe book explores several open questions in the philosophy and the foundations of statistical mechanics. Each chapter is written by a leading expert in philosophy of physics and/or mathematical physics. Here is a list of questions that are addressed in the book:

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Book SynopsisThis book is the sixth volume of reviews on advanced problems of phase transitions and critical phenomena, with the first five volumes appearing in 2004, 2007, 2012, 2015, and 2018. It aims to provide an overview of those aspects of criticality and related topics that have attracted much attention due to the recent contributions. The six 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 for the previous 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 topic.The level of presentation makes the book readable both for professionals and the students in the field. On a larger scale, the book may contribute to promoting and deepening studies of phase transitions and critical phenomena.

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Book SynopsisThe aim of this book is to present Classical Thermodynamics in a unified way, from the most fundamental principles to non-uniform systems, thereby requiring the introduction of coarse graining methods, leading for instance to phase field methods. Solutions thermodynamics and temperature-concentration phase diagrams are covered, plus also a brief introduction to statistical thermodynamics and topological disorder. The Landau theory is included along with a general treatment of multicomponent instabilities in various types of thermodynamic applications, including phase separation and order-disorder transitions. Nucleation theory and spinodal decomposition are presented as extreme cases of a single approach involving the all-important role of fluctuations.In this way, it is hoped that this coverage will reconcile in a unified manner techniques generally presented separately in physics and materials texts.

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Book SynopsisThese lecture notes cover Statistical Mechanics at the level of advanced undergraduates or postgraduates. After a review of thermodynamics, statistical ensembles are introduced, then applied to ideal gases, including degenerate gases of bosons and fermions, followed by a treatment of systems with interaction, of real gases, and of stochastic processes.The book offers a comprehensive and detailed, as well as self-contained, account of material that can and has been covered in a one-semester course for students with a basic understanding of thermodynamics and a solid background in classical mechanics.

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Book SynopsisThese lecture notes cover Statistical Mechanics at the level of advanced undergraduates or postgraduates. After a review of thermodynamics, statistical ensembles are introduced, then applied to ideal gases, including degenerate gases of bosons and fermions, followed by a treatment of systems with interaction, of real gases, and of stochastic processes.The book offers a comprehensive and detailed, as well as self-contained, account of material that can and has been covered in a one-semester course for students with a basic understanding of thermodynamics and a solid background in classical mechanics.

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Book SynopsisThis book formulates a unified approach to the description of many-particle systems combining the methods of statistical physics and quantum field theory. The benefits of such an approach are in the description of phase transitions during the formation of new spatially inhomogeneous phases, as well in describing quasi-equilibrium systems with spatially inhomogeneous particle distributions (for example, self-gravitating systems) and metastable states. The validity of the methods used in the statistical description of many-particle systems and models (theory of phase transitions included) is discussed and compared. The idea of using the quantum field theory approach and related topics (path integration, saddle-point and stationary-phase methods, Hubbard-Stratonovich transformation, mean-field theory, and functional integrals) is described in detail to facilitate further understanding and explore more applications. To some extent, the book could be treated as a brief encyclopedia of methods applicable to the statistical description of spatially inhomogeneous equilibrium and metastable particle distributions. Additionally, the general approach is not only formulated, but also applied to solve various practically important problems (gravitating gas, Coulomb-like systems, dusty plasmas, thermodynamics of cellular structures, non-uniform dynamics of gravitating systems, etc.).Table of ContentsForeword; Introduction; Statistical Physics of Interacting Particle Systems; Statistical Description of Phase Transitions; Path Integration and the Field Theory; Peculiarity of Calculation of Some Models; Statistical Description of the Condensed Matter; Inhomogeneous Distribution in Systems of Interacting Particles; Cellular Structures in the Condensed Matter; Statistical Description of Nonequilibrium Interacting Systems; Conclusions; Bibliography;

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