The science of statistical mechanics is concerned with defining the thermodynamic properties of a macroscopic sample in terms of the properties of the microscopic systems of which it is composed. The aim of this book is to provide a clear, logical, and self-contained treatment of equilibrium statistical mechanics starting from Boltzmann's two statistical assumptions, and to present a wide variety of applications to diverse physical assemblies. The coverage is enhanced and extended through an extensive set of accessible problems. An appendix provides an introduction to non-equilibrium statistical mechanics through the Boltzmann equation and its extensions. The book assumes introductory courses in classical and quantum mechanics, as well as familiarity with multi-variable calculus and the essentials of complex analysis. Some knowledge of thermodynamics is assumed, although the book starts with an appropriate review of that topic. The targeted audience is first-year graduate students, and advanced undergraduates, in physics, chemistry, and the related physical sciences. The goal of this text is to help the reader obtain a clear working knowledge of the very useful and powerful methods of equilibrium statistical mechanics and to enhance the understanding and appreciation of the more advanced texts.

This book looks at global atmospheric processes from a physical standpoint using available current and past observational data taken from measurements of relevant atmospheric parameters. It describes various aspects of the current atmospheric state and its future evolution, focusing primarily on the energetic balance of the Earth and atmosphere, and taking into consideration the multi-faceted global equilibrium between these two systems, carbon, and water. The analysis presented in this book restricts itself to those objects and processes that allow us to obtain reliable conclusions and numerical estimations, in contrast to current climate models with much larger numbers of parameters for describing the same problems. As a result, in spite of the roughness of numerical parameters, the book unveils a reliable and transparent physical picture of energetic phenomena in the global atmosphere. In particular, it shows that approximately only one-fourth of atmospheric water returns from the atmosphere to the Earth in the form of free molecules. It was shown that the contemporary warming of our planet has an anthropogenic character, and that the average global temperature increases due to an increase of the concentration of atmospheric CO2 molecules, via an increase in atmospheric moisture, as well as an increase in the amount of aerosols in the atmosphere. Accumulation of atmospheric carbon dioxide plays a subsidiary role in this process and gives approximately one-third in a change of the global temperature, while an increase in the amount of atmospheric water by as little as only 0.3% per year explains the observed warming of the Earth. The book shows how the greenhouse instability of the atmosphere evidently has its origins in the Eocene epoch, presenting an analysis of the influence of various types of global energetic processes on the climate that differs from the official stance on these problems.

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.

The book aims to explain the basic ideas of thermal physics intuitively and in the simplest possible way. It is aimed at making the reader feel comfortable with the ideas of entropy and free energy. Thermal physics is prone to misunderstanding, confusion and is often being overlooked. However, a good foundation is necessary to prepare the reader for advanced level studies.

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.

The use of thermodynamics in biological research can be equated to an energy book-keeping system. While the structure and function of a molecule is important, it is equally important to know what drives the energy force. This volume presents sophisticated methods for estimating the thermodynamic parameters of specific protein-protein, protein-DNA and small molecule interactions.

* Elucidates the relationships between structure and energetics and their applications to molecular design, aiding researchers in the design of medically important molecules * Provides a "must-have" methods volume that keeps MIE buyers and online subscribers up-to-date with the latest research * Offers step-by-step lab instructions, including necessary equipment, from a global research community

This book covers in great detail the Rouse-segment-based molecular theories in polymer viscoelasticity -- the Rouse theory and the extended reptation theory (based on the framework of the Doi-Edwards theory) -- that have been shown to explain experimental results in a consistently quantitative way. The explanation for the 3.4 power law of viscosity, quantitative line-shape analyses of viscoelastic responses and agreements between different sorts of viscoelastic responses, the consistency between the viscoelasticity and diffusion results, the clarification of the onset of entangelement, the discovery of the number of entanglement strands per cubed entanglement distance being a universal constant and the basic mechanism of the glass transition-related thermorheological complexity are discussed or shown in great detail. The mystery behind the success of the Rouse-segment-based molecular theories over the entropic region of a viscoelastic response is revealed by the Monte Carlo simulations on the Fraenkel chains. Specifically, the simulation studies give a natural explanation for the coexistence of the energy-driven and entropy-driven modes in a viscoelastic response and provide a theoretical basis resolving the paradox that the experimentally determined sizes of Rouse and Kuhn segments are nearly the same. This book starts from a very fundamental level; each chapter is built upon the contents of the previous chapters. Thus, the readers may use the book as a textbook and eventually reach an advanced research level. This book is also a useful source of reference for physicists, chemists and material scientists.

Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. A wide group of researchers, along with students and teachers will, thus, benefit from this definitive book on nonlinear dynamics.

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 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.

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.

This textbook is for undergraduate students on a basic course in Statistical Mechanics. The prerequisite is thermodynamics. It begins with a study of three situations -- the closed system and the systems in thermal contact with a reservoir -- in order to formulate the important fundamentals: entropy from Boltzmann formula, partition function and grand partition function. Through the presentation of quantum statistics, Bose statistics and Fermi-Dirac statistics are established, including as a special case the classical situation of Maxell-Boltzmann statistics. A series of examples ensue it: the harmonic oscillator, the polymer chain, the two level system, bosons (photons, phonons, and the Bose-Einstein condensation) and fermions (electrons in metals and in semiconductors). A compact historical note on influential scientists forms the concluding chapter. The unique presentation starts off with the principles, elucidating the well-developed theory, and only thereafter the application of theory. Calculations on the main steps are detailed, leaving behind minimal gap. The author emphasizes with theory the link between the macroscopic world (thermodynamics) and the microscopic world.

* Explores the exciting and new topic of econophysics * Multidisciplinary approach, that will be of interest to students and researchers from physics, engineering, mathematics, statistics, and other physical sciences * Useful to both students and researchers

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 volume presents a collection of original and peer-reviewed articles related with the applications of Statistical Physics dedicated to Professor Dr Leopoldo Garcia-Colin, in commemoration of his 80th birthday in 2010. Professor Garcia-Colin has worked in many different fields of statistical physics, and has applied it to biological physics, solid state physics, relativity and cosmology. These are pioneering works of Prof Garcia-Colin involved in all various fields which have their roots in Mexico. His influence is found in each of these works that cover a wide range of topics including thermodynamics, statistical mechanics and kinetic theory applied to biological systems, cosmology and condensed matter, among others.Papers contributed by important experts in the field, such as J Lebowitz, as well as the latest classical applications of statistical physics can be found in this volume.

This book is devoted to analysis of Monte Carlo methods developed in rarefied gas dynamics. Presented is the short history of the development of such methods, described are their main properties, their advantages and deficiencies. It is shown that the contemporary stage in the progress of computational methods cannot be regarded without a complex approach to the preparation of algorithms taking into account all the peculiarities of the problem under consideration, that is, of the physical nature of a process, the mathematical model and the theoretical aspects of computational mathematics and stochastic processes. Thoroughly investigated is the possibility of application of Monte Carlo methods in some kindred areas of science which are non-traditional for the use of statistical modeling (continuous media, turbulence). Considered are the possible directions of development of statistical modeling.

This textbook is for undergraduate students on a basic course in Statistical Mechanics. The prerequisite is thermodynamics. It begins with a study of three situations -- the closed system and the systems in thermal contact with a reservoir -- in order to formulate the important fundamentals: entropy from Boltzmann formula, partition function and grand partition function. Through the presentation of quantum statistics, Bose statistics and Fermi-Dirac statistics are established, including as a special case the classical situation of Maxell-Boltzmann statistics. A series of examples ensue it: the harmonic oscillator, the polymer chain, the two level system, bosons (photons, phonons, and the Bose-Einstein condensation) and fermions (electrons in metals and in semiconductors). A compact historical note on influential scientists forms the concluding chapter. The unique presentation starts off with the principles, elucidating the well-developed theory, and only thereafter the application of theory. Calculations on the main steps are detailed, leaving behind minimal gap. The author emphasizes with theory the link between the macroscopic world (thermodynamics) and the microscopic world.

This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.

This is a masters/graduate level textbook on statistical physics. The basics of the discipline and its application in the current topics of interest like BoseEinstein condensate, statistical astrophysics and phase transitions have been discussed with thoroughness.

This is a systematic introduction and development of a course material tried successful over a number of years. Feedback from the students tells that it has immensely helped them in their later research.

This is the first comprehensive monograph on a new thermodynamic theory that goes beyond the classical theory of irreversible processes. In contrast to the classical approach, the local equilibrium hypothesis is abandoned, and the basic variables are complemented by non-equilibrium quantities. The claims made for extended thermodynamics are confirmed by the kinetic theory of gases and statistical mechanics. The book covers a wide spectrum of applications, and also contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The present edition reflects new developments in the theory of applications, adds new problems and provides a more detailed comparison with other fields of active research. It contains 130 proposed problems, whose detailed solutions, as well as wide bibliography on extended irreversible thermodynamics and related topices, may be unloaded from the www.uab.es/dep-fisica/eit website.

This practical introduction to the analysis of data collected from reliability studies offers clear, detailed explanations of the best and most up-to-date techniques available. Topics include survival analysis with covariates, the assessment of systems performance, reliability growth models, dependency (which encompasses both engineering and statistical approaches), and practical aspects of analysis. A wealth of interesting case studies appear throughout the text, lending "real-world" examples to the more theoretical discussions. Throughout, the authors stress the need for investigators to understand the background and nature of their data if they are to select the most appropriate analysis method. They also provide in-depth treatments of the mathematical and statistical bases underlying each technique. Accessible and comprehensive, the book will be welcomed by students, professionals, and statisticians who are interested in the practical aspects of reliability data analysis.

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

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

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