This modern and self-contained book offers a clear and accessible introduction to the important topic of machine learning with neural networks. In addition to describing the mathematical principles of the topic, and its historical evolution, strong connections are drawn with underlying methods from statistical physics and current applications within science and engineering. Closely based around a well-established undergraduate course, this pedagogical text provides a solid understanding of the key aspects of modern machine learning with artificial neural networks, for students in physics, mathematics, and engineering. Numerous exercises expand and reinforce key concepts within the book and allow students to hone their programming skills. Frequent references to current research develop a detailed perspective on the state-of-the-art in machine learning research.

This book describes the theory of how processes on the unobservable molecular scale give rise to observable effects such as diffusion and electrical noise on the macroscopic or laboratory scale. It puts the modern theory into historical context, and features new applications, statistical mechanics derivations, and the mathematical background of the topic.

This book is designed for use in an introductory course in thermodynamics. It is aimed at students of Physics, Chemistry, Materials Science, and Engineering. As an undergraduate text, it gives a clear description of the theoretical framework of thermodynamics, while providing specific examples of its use in a wide variety of problems. These examples include topics that are atypical of undergraduate texts, such as biological systems, atmospheric phenomena, and polymers.

The narrative is infused with historical notes on the characters who make up the story of thermodynamics, enlivening the material while keeping the reader engaged.

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.

* Materials are presented to guide the reader with ease through a difficult subject by providing extra help whenever needed to overcome the more demanding technical and conceptual aspects * Active reading strategies (conceptual problems, discussion questions, worked examples with comments, end of chapter problems, further reading etc.) to stimulate engagement with the text through active, critical thought * Well-balanced textbook design (including introductions, illustrations, keywords defined, highlights, notes in margins, summary of key ideas and concepts, boxes with additional topics that complement the materials presented in the main text)

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.

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.

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.

Potts Models and Related Problems in Statistical Mechanics

In this unique book, Arieh Ben-Naim invites the reader to experience the joy of appreciating something which has eluded understanding for many years -- entropy and the Second Law of Thermodynamics. The book has a two-pronged message: first, that the Second Law is not "infinitely incomprehensible" as commonly stated in textbooks of thermodynamics but can, in fact, be comprehended through sheer common sense; and second, that entropy is not a mysterious quantity that has "resisted understanding" but a simple, familiar and easily comprehensible concept. Written in an accessible style, the book guides the reader through an abundance of dice games and examples from everyday life. The author paves the way for readers to discover for themselves what entropy is, how it changes, and most importantly, why it always changes in one direction in a spontaneous process.

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.

This second part of Continuum Thermodynamics is designed to match almost one-to-one the chapters of Part I. This is done so that the reader studying thermodynamics will have a deepened understanding of the subjects covered in Part I. The aims of the book are in particular: the illustration of basic features of some simple thermodynamical models such as ideal and viscous fluids, non-Newtonian fluids, nonlinear solids, interactions with electromagnetic fields, and diffusive porous materials. A further aim is the illustration of the above subjects by examples and simple solutions of initial and boundary problems as well as simple exercises to develop skills in the construction of interdisciplinary macroscopic models.

The wide application of technologies in new mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties (e.g materials with 'memory'). Of equal importance is the understanding of the physical behaviour of these materials and consequently developing mathematical modelling techniques for prediction.

This self contained text discusses the mathematical modelling used with these types of electromagnetic materials. It provides a carefully structured, coherent, and comprehensive treatment of electromagnetism of continuous media. The authors provide a systematic review of known subjects along with original results about thermodynamics of electromagnetic materials, well-posedness of initial boundary-value problems, variational settings, and wave propagation. Models of non-linear materials, non-local materials (superconductors), and hysteretic (magnetic) materials are also developed in detail.

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.

This book explores the challenges our society faces in making the transition to renewable resource use in a way that is truly sustainable - environmentally, economically and socially. After exploring the physical limits the laws of thermodynamics impose on resource exploitation, the book outlines options for managing resources within these limits. It then moves on to look at the resources themselves (from fossil fuels, through minerals to renewable resources such as timber) and the salient question of how the relentless increase in consumption is putting untenable strain on resource use. Case studies investigate what is being done across a range of sectors - and what is and isn't working. The second half of the book turns to solutions, from the promise of industrial ecology to a new economy based on renewable resources such as biobased materials from agricultural crops and forests. Suitable for under- and postgraduate courses on environmental limits and resource use, and continuing professional development - particularly resource management, materials, industrial ecology, energy, resource economics and engineering.

This book explores the challenges our society faces in making the transition to renewable resource use in a way that is truly sustainable - environmentally, economically and socially. After exploring the physical limits the laws of thermodynamics impose on resource exploitation, the book outlines options for managing resources within these limits. It then moves on to look at the resources themselves (from fossil fuels, through minerals to renewable resources such as timber) and the salient question of how the relentless increase in consumption is putting untenable strain on resource use. Case studies investigate what is being done across a range of sectors - and what is and isn't working. The second half of the book turns to solutions, from the promise of industrial ecology to a new economy based on renewable resources such as biobased materials from agricultural crops and forests. Suitable for under- and postgraduate courses on environmental limits and resource use, and continuing professional development - particularly resource management, materials, industrial ecology, energy, resource economics and engineering.

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.

The thermodynamic limit is a mathematical technique for modeling crystals or other macroscopic objects by considering them as infinite periodic arrays of molecules. The technique allows models in solid state physics to be derived directly from models in quantum chemistry. This book presents new results, many previously unpublished, for a large class of models and provides a survey of the mathematics of thermodynamic limit problems. The authors both work closely with Fields Medal-winner Pierre-Louis Lion, and the book will be a valuable tool for applied mathematicians and mathematical physicists studying nonlinear partial differential equations.

The fifth edition of "Thermodynamic and Transport Properties of Fluids" incorporates two new tables: other material is being retained essentially as in the fourth edition, although tables beyond p.11 will be on different pages.

The new tables are as follows: Data of Refrigerant 134a (tetrafluoroethane - CH2F-CF3) are being added because this refrigerant is environmentally more acceptable than Refrigerant 12 which it replaces. The table of R12 is being retained, however, because R12 will survive in much equipment for a long time. At present it is still uncertain whether R134a is a medium-term substitute, or will be used for much longer than a decade.

Figure 15.11 from "Engineering Thermodynamics, Work and Heat Transfer" (Rogers & Mayhew, Longman 1992) is being included. The table contains, for selected substances, molar enthalpies and molar Gibbs functions of formation, and Equilibrium constants of formation, as well as molar heat capacities and absolute entropies.

This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statistical mechanics. This will interest specialists of various fields, especially the (classical and quantum) plasma physics. However, quantum physics - to which a major part is devoted - will be of more interest since, not only it applies to quantum plasma physics, but also to nuclear matter and to strong magnetic field, cosmology, etc. Although the domain of gauge theory is not covered in this book, the topic is not completely forgotten, in particular in the domain of plasma physics. This book is particularly readable for graduate students and a fortiori to young researchers for whom it offers methods and also appropriate schemes to deal with the current problems encountered in astrophysics, in strong magnetic, in nuclear or even in high energy physics.

This book is an introductory text on fundamental aspects of combustion including thermodynamics, heat and mass transfer and chemical kinetics which are used to systematically derive the basic concepts of combustion. Apart from the fundamental aspects, many of the emerging topics in the field like microscale combustion, combustion dynamics, oxy-fuel combustion and combustion diagnostics are also covered in the book. This would help the beginners in the subject to get initiated to the state of the art topics. Key Features: Coverage of the essential aspects of combustion engineering suitable for both beginners and practicing professionals Topics like entropy generation, microscale combustion, combustion diagnostics, second law-based analysis exclusive to the title Balanced treatment of thermodynamics, transport phenomena and chemical kinetics Discussion on state of the art techniques in combustion diagnostics Illustrates combustion of gaseous, liquid and solid fuels along with emission of pollutants and greenhouse gases

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.

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 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.